Vavg Formula

h interface. Multiply by 3600 and you get watt-seconds, which is also known as Joules. 955*Vs which isn't what i get from the simulation from multisim. 3 m/s upwards. Based on the chosen capacitor value and the approximate value of Vcc, we can clearly calculate the expected Vdrop across N samples by using the formula above. A formula for the number of possible permutations of k objects from a set of n. Thinking they might prove useful as tools or templates to others, it is my pleasure to provide them freely to the scientific community. This means that equation 7 can be reduced to. Peak or crest voltage can be obtained from RMS value of voltage: Vpeak = 1. Find the volume per organism, assuming a spherical shape. 732 = 115,401W = 115. This web site owner is mathematician Dovzhyk Mykhailo. Fig: Average Velocity, r. Once we know the peak voltage ( V o ) and the resistance (R) in the circuit we can calculate the peak current ( Io ) using the equation V=IR. Dalam gas ideal berlaku 3 hukum tentang kinetika gas yaitu. Vavg — where T is the temperature (in kelvins), M is the molar mass (in kilo- grams per mole), and R = 8. Those two variables are temperature and amount of gas (the last one being measured in moles). vi = initial velocity. Yes, watt-hours is a measure of energy, just like kilowatt-hours. You can use the formula A = C^2 / 4pi to find the area of a circle given the circumference. Мама не дала Росси проехать гонку. Subject Company: ITC Holdings Corp, Commission File No. The next step is determining the pipette’s accuracy, manually or via software. If you're in the higher end of this range -- 10 to 12 percent fat -- you'll have a fit appearance and -- once exercise and sensible eating become habitual, you'll be able to maintain these lifestyle choices fairly easily. 0292 m rod = 160 rods, (b) and that distance in chains to be d = ( 4. The level of a waveform defined by the condition that the area enclosed by the curve above this level is exactly equal to the area enclosed Vp x. Voltage imbalance is given by the formula: Ring connect screw terminals C. 6m/s2 isn't necessary so what you do is you employ the equation Vavg=deltax/delta t then you certainly re-manage it and get the equation (delta t)*(Vavg)=delta x this is what u want this is displacement so then you certainly plug interior the numbers so it would look like this (6. E = C*Vavg Where E is the energy stored in watt-hours, C is the capacity in amp-hours, and Vavg is the average voltage during discharge. 120v Vrms input so 170 Vpp I get 162 vavg using the. IIT-Madras, Momentum Transfer: July 2005-Dec 2005. Substitute (1) into (6) 2(delta x /. = − =528 0 360 1. The 115V is an RMS voltage. The basic definition of average velocity is: Vavg = Δx/Δt = Xf – X0/tf – t0 This is the change in position divided by the time of travel. Following is the formula for Vpp to Vrms conversion. Fundamentals Of Physics Instructors Solutions Manual | Halliday, Resnick | download | B–OK. Present Value is like Future Value in reverse: you The formula for present value is simple; just take the formula for future value and solve for starting principal. Multiply by 3600 and you get watt-seconds, which is also known as Joules. The term average is from mathematics that basically means the central tendency of a set particular set of data. I can use the formula ΔVc = Vm(1-e-t/RC) I don't know why it didn't click sooner, it will become ΔVc = 19. I want to code this do while loop to do this. A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 17. Chapter 1 – Student Solutions Manual 3. the chemical compound silicon dioxide, also known as silica (from the Latin silex), is an oxide of silicon with a chemical formula of SiO 2 and has been known for its hardness since antiquity. The formula can also be used to calculate the present value of money to be received in the future. Velocity and Most Probable Velocity – a relationship in equation. (c) Substitute t = 1, 2, and 3 into v(t). ARPU Revenue Formula. Easily share your publications and get them in front of Issuu’s. Enzyme-linked Immunosorbent Assay (ELISA) The concentrations of NF-κB-responsive genes (IL-8, TNF-a and IL-1β) were evaluated in cell culture supernatants according to the manufacturer’s protocol (Joyee Biotechnics, Shanghai, China). So is the. Executive Vice President & Chief Financial Officer. Find books. Формула-1 (Formula-1) 2020. standard value calculated using the following calculation formula. WikiHow recommends the value should be between 99 and 101%. Formula 1® Esports Series is back for its 3rd season! Compete against the fastest drivers in the world on F1TM 2019 and stand a chance to become an official driver for an F1 Team!. 1 A to 20,000 A. Answer / soumya ranjan panigrahi we know form factor is the cause of generating voltage in India is 11kV or it be transmitted as multiples of 11, because of simple to desine. Memorizing equations by rote, rather than understanding the physics by which they were derived,. Therefore, vavg m s m/s. For example it can be used to check the format of the container used by a multimedia stream and the format and type of each media stream contained in. As illustrated in the ﬁgure, the slope can be positive, negative, or zero. Discover the ROIC formula and learn how to apply it through our ROIC example. 0 Introduction: Quality Assurance and Certification June 17, 2009 ECMPS Reporting Instructions Quality Assurance and Certification 1. Concepts of Physics Part 1, Numerical Problems with their solutions, Short Answer Solutions for Chapter 3 - Rest and Motion: Kinematics from the latest edition of HC Verma Book. As part of Formula E's fundraising partnership with UNICEF, the all-electric street racing series will. For average velocity, d = displacement (vector). We use lower case p(t) because this is the expression for the instantaneous power at time t. These values will be listed and identified as either. These variables also permit you to use behavioral circuit analysis, modeling, and simulation techniques. , the general formula is: Number of organisms = N = 2(t/30 min) = 2(t/0. since only their ratio enter the equation. A Framework for Mining Association Rules in Data Warehouses 161 Assume that in a fact table there is m-dimensions and the quantity attribute exists. formula and/or breastmilk until 12 months of age. Do While (Vavg >= Vavg_error_lb And Vavg =< Vavg_error_ub) ' Call Sim_rand 'Loop Thank you. Average and RMS value of center-tap full wave rectifier. A user enters the voltage,. Quadratic Formula Calculator. = − =528 0 360 1. why the generating voltage in India is 11kV or why is it be transmitted as multiples of 11. The first calculation will involve pickets 1 and 2, the next 2 and 3, etc. Enter the world of Formula 1. 1 A to 20,000 A. The formulas below compare the calculations of an RMS meter compared to an average rectified measuring meter when measuring pure At each voltage both Vrms and Vavg values are recorded. The next step is determining the pipette’s accuracy, manually or via software. Any such data mashup is expressed using the Power Query M Formula Language. VAVG - (-VAVG ) ) in the sum of the two areas, thus resulting in zero average voltage over one To find the peak value from a given average voltage value, just rearrange the formula and divide by the. You can't simply do 30x2 (velocity times time) to get the total distance. Kinetic Theory of Gases & Maxwell Distribution Curve & Gas Velocity Vmp,Vavg,Vrms Formulas(Class XI). Cost can add up quickly, especially if you’re a novice and have never attempted a Stamped Concrete Patios installation before. " In the case of a set of n values. The pulse waveform is shown in Figure 1. Boyle's Law deals with the relationship between pressure and volume (two of the four variables). The highest fre- quencies of 2 to 4 MHz correspond to. Customer Experience Training and Workshops for Entrepreneurs and Small Businesses. Find books. The RMS voltage of a sinusoid or complex waveform can be determined by two basic methods. Box 1926 Spartanburg, SC 29304 GENERAL INFORMATION Milliken is a major manufacturer of textile products for apparel, commercial, home,. If waveform is something different than pure sinewave, reading between two meters will shift appart. Input a constant (in this case: 1) as your Formula and configure the Output Extents. 1-AUG-2019 (Ver. Investors are able to reasonably assume an investment's profit using the future value. Este/a fórmula de encantamiento se usa en la profesión de Encantamiento. It calculates the RMS voltage based on the above formulas for each. The number of solutions and their type depends on the value of the discriminant (quantity under the radical). The instantaneous velocity at any time is the slope of the positiontime graph at that time. Compounding formulas for discrete payments. shortest If set to 1, force the output to terminate when the shortest input terminates. Attached is the sample Application. Vavg = ΔX / Δt For instantaneous velocity, the time interval Δt is shrunk down to the smallest number that you can imagine that is still greater than zero. Vavg Output voltage average of the phase voltage according to the following formula and kept in this product. Dari chart terlihat pasar Amerika, Eropa dan Asia tampak berseri-seri, semua MA5 di bawah candlestick dan pointing up. For example using the formula above we can state that: Vadj = (Vin / 100) * d. For Boyle's Law to be valid, the other two variables must be held constant. 4, the standard luminance signal's bandwidth ranges from dc to approxi- mately 4 MHz, whereas audio ranges from dc to 20 kHz. 0 furlongs = ( 4. Several questions might immediately come to mind. In this section, we are going to see mensuration formulas which can be used to find cured surface area, total surface area and volume of 3-D shapes like Volume of cylinder = Πr2h. why the generating voltage in India is 11kV or why is it be transmitted as multiples of 11. This RMS Voltage calculator helps to find the RMS voltage value from the known values of either peak voltage, peak-to-peak voltage or average voltage. (e) The horizontal line near the bottom of this x-vs-t graph represents the man standing at x = 0 for 0 ≤ t 300 s and the linearly rising line for 300. Download Solutions Manual - Materials Processing in Manufacturing Demargo. compiled from Merck Source. Download books for free. Calculator solution will show work for real Uses the quadratic formula to solve a second-order polynomial equation or quadratic equation. : The maximum instantaneous value of a function as measured from the zero-volt level. And there are certain formulae that are used for the same. Physics Formula Sheet. s di Formula Group S. Securities Act of 1933 and deemed filed pursuant. The formula is (A)*(V) = (W). 3535 * V pp Where V pp is the peak to peak volatge and V rms is the root mean square voltage. Formulae definition, a set form of words, as for stating or declaring something definitely or authoritatively, for indicating procedure to be followed, or for prescribed use on some ceremonial. 9610° 36000. It's a functional, case sensitive language similar to F#. VECTORS OPERATIONS ON VECTORS • A scalar quantity (such as mass or energy) can be fully described by a (signed) number. The term streamline flow is descriptive of the laminar flow because, in laminar flow, layers of water flowing over one another at different speeds with virtually no mixing between layers, fluid particles move in definite and observable paths or streamlines. The complete formula (EFN) is expressed as: EFN = (A/S) x (Δ Sales) - (L/S) x (Δ Sales) - (PM x FS x (1-d)). compiled from Merck Source. Any such data mashup is expressed using the Power Query M Formula Language. For average velocity, d = displacement (vector). Using the above formula, the average voltage can be calculated as. 637 Vpp = Vp • 2 Vp = Vpp ÷ 2 Vinst. High voltage measurement from 10 V up to 6,400 V. Best Price Roadside Assistance. Average Speed formula. Bankfull and effective discharge in small mountain streams of British Columbia Brayshaw, Drew Devoe 2012. A chemical formula may be entered to restrict the search to species which match the formula. If the object is moving with a velocity of +4 m/s, then the slope of the line will be +4 m/s. 5 kg flies through the air at a low speed, so that the air resistance is negligible, What is the net force acting on the ball while it is in motion? Which components of the ball's. 230K likes. This means that the most recent entry always overwrites the oldest one. V m = maximum value of transformer secondary voltage. The average velocity of the sled is (Vavg). Vatios-hora es una medida de energía, al igual que kilovatios-hora. This means that equation 7 can be reduced to. The average velocity of gas particles is found using the root mean square velocity formula: μ rms = (3RT/M) ½ μ rms = root mean square velocity in m/sec R = ideal gas constant = 8. Best Price Roadside Assistance. Hello there, I have a simple routine below, with 2 variables which are calculated in part by a random number. Rules for formula restriction (step 2) (Back to search). Average Force Formula Questions: 1) A dog that weighs 10 kg chases a car for 12 seconds at a velocity of 5 m/s. The difference between modeled and actual velocities can be observed from the curve. 10Beta) CHANGELOG. Several questions might immediately come to mind. Find books. 7979 × √(RT) Now equating them we get, T = (6. T f = 308 K. 758) + A=AIR(3. Value at risk (VAR or sometimes VaR) has been called the "new science of risk management ," but you don't need to be a scientist to use VAR. Run Automatic Analysis/Auto-Analyzer untuk melihat hasilnya. v o represents the object's initial velocity at the beginning of the time interval. The rms speed is a good approximation of the the typical speed of the molecules in a gas. High voltage measurement from 10 V up to 6,400 V. The average velocity of the ball can be found using these values and the formula: v avg = 0. Hi, How do you code, "not greater than or equal to" and "not less than or equal to" in vb. Hence, Vavg Vdc [(12 1) (8 1)]/2 2 V. Someone tosses a tomato straight up in the air. When the payments are all the same, this can be considered a geometric series with 1+r as the common ratio. The hydrocarbon that has at least one double bond is called as alkene with the general formula C n H 2 n. ffmpeg reads from an arbitrary number o. Therefore, vavg m s m/s. RMS voltage of a half wave rectifier, VRMS = Vm / 2 and Average Voltage VAVG= Vm/π, Vm is the peak voltage. If acceleration is constant the Vavg occurs at 1/2 the total time and. The right hand picture illustrates the same formula. vavg ≡ The instantaneous velocity v is deﬁned as the limit of the ratio Δ x Δ t as Δt approaches zero. 10 s vi =?. The average value of a sine wave is zero because the area covered by the positive half cycle. Because, the positive and negative half cycle is equal in magnitude and thus the total value cancels out on summation. Subject Company: ITC Holdings Corp, Commission File No. I want the code to repeat over and over until the two conditions are satisfied. We use lower case p(t) because this is the expression for the instantaneous power at time t. En la categoría Fórmulas de encantamiento. Alternate Formulas or Computational Formulas for Variance. The formula for the future value of an annuity, or cash flows, can be written as. In this section, we are going to see mensuration formulas which can be used to find cured surface area, total surface area and volume of 3-D shapes like Volume of cylinder = Πr2h. Average Velocity We begin by writing down the formula for average velocity. SimScale and Formula Student Germany have joined forces to offer a free workshop about the application of CFD in Formula Student. It may also be referred to as the annualized rate of return or annual percent yield or effective annual rate. WikiHow recommends the value should be between 99 and 101%. It calculates the RMS voltage based on the above formulas for each. (2) Methods: The sample. 175 * 10 -3 * d 4 / (f t c vavg),. If any distances x i and x f with their corresponding time intervals t i and t f are given we use the formula. Formula Simulator. How to prepare for States of matter? This chapter is a part of Physical chemistry. Here, in part 1 of this short series on the topic, we. A ball of mass 0. Discover the ROIC formula and learn how to apply it through our ROIC example. Use MathJax to format equations. This would require an integer, however vavg is a ratio of type double. Calculate the average velocity of your car (in cm/tu) for the entire run using the formula Vavg = total distance covered/total time. Formula One Grand Prix (known as World Circuit in the United States) is a racing simulator released This version of Formula One Grand Prix was designed for personal computers with operating system. For a particle in simple harmonic motion, show that Vmax = (pi/2)*Vavg where Vavg is the average speed during one cycle of the motion. repeatlast If set to 1, force the filter to extend the last frame of secondary streams until the end of the primary stream. The Formula Sim is specifically engineered to help drivers to improve their craft in Formula categories. Copy AFL di bawah dan paste ke Formula Editor di amibroker kemudian save. The term streamline flow is descriptive of the laminar flow because, in laminar flow, layers of water flowing over one another at different speeds with virtually no mixing between layers, fluid particles move in definite and observable paths or streamlines. This set focuses on formulas, important numbers, word problems, and linear motion terminology. The Center-Tapped Full-Wave Rectifier A center-tapped rectifier is a type of full-wave rectifier that uses two diodes connected to the secondary of a center-tapped transformer, as shown in Figure (a). What do you want to calculate?. Substitute (3) into (2) (4) Vavg = (0 + v)/2. Thus, the total of the masses of neutrons and protons is the atomic mass. 3535 * V pp Where V pp is the peak to peak volatge and V rms is the root mean square voltage. It is akin to Ohm’s Law, but something I was never taught in tech school –I had to learn it myself much later –now I use it at least weekly. 0321-5455195 Home Delivery Service is Also Available. (d) The object hits the ground when its position is s(t) = 0. The average velocity of the ball can be found using these values and the formula: v avg = 0. Silica is most commonly found in nature as sand or quartz, as well as in the cell walls of diatoms. Root mean square is a mathematical term that suggests effective level. Basic Properties and Formulas. The RMS value of a pulse waveform can be easily calculated starting with the RMS definition. Exam 1 November 2012, Questions and answers Exam 31 October 2008, Questions and answers Exam 26 October 2009, Questions Exam 10 December 2010, Questions Final Formula Sheet - Summary Mechanics and Waves Phys 131 Equation Sheet. Regards Dan. At the end there is a do while loop with 2 conditions. Pokhriyal2. The Peak Voltage calculator calculates the peak Voltage value from either the peak-to-peak voltage, the RMS voltage, or the average voltage. Plugging that into the avg voltage formula: Vavg = 2x217. For simplicity, we will rewrite the formula. EVM - Miscellaneous Formula - Budget at Completion (BAC) is the total budget allocated to the BAC is also used to compute the TCPI and TSPI. man ffprobe (1): ffprobe gathers information from multimedia streams and prints it in human- and machine-readable fashion. Among them, the only time spent for value added activities is the process time. Average voltage (Vavg). In this problem the initial velocity is 10 mph and the final velocity is 7. Materiales de aprendizaje gratuitos. This means that the most recent entry always overwrites the oldest one. key},quantity). pdf) or read book online for free. Calculate the average velocity of your car (in cm/tu) for the entire run using the formula Vavg = total distance covered/total time. avg speed =√(8RT/πM). What do you calculate for the x component of average velocity? vavg. Express your answer in terms of the given quantities and,. HTflux is using the following equations for this task: for laminar pipe flows: Resistance coefficient / hydraulic gradient (R in kg/m 7 ):. If by "going at a If and only if the acceleration is constant, then you can make use the naive formula for average speed, as. Cone : Formulas. Plugging that into the avg voltage formula: Vavg = 2x217. 00000001 1E-08 3561 CHAPTER 28 To find digit. In this interactive object, learners determine the Vp, Vp-p, Vrms, Vavg, and the frequency of a sine wave displayed on an oscilloscope screen. Enter Data and Calculate. Bankfull and effective discharge in small mountain streams of British Columbia Brayshaw, Drew Devoe 2012. RMS vs Average. 10Beta) CHANGELOG. By combining the first two criteria and plugging in the formula of and Update Vavg, sigmaV End Save Vmax,Vmin,Vavg,sigmaV to “gamd_restart. Average Velocity Formula: vavg = x/ t x is the DISPLACEMENT where x = xf - xi (final position - initial position) and t is the time interval over which the displacement occurs. Solution: Use the instantaneous formulas. 2) An easy way to calculate the Vdα expression is to place the time origin aligned to an output voltage pulse for which is applied the average value formula, in the. Because they both start at zero, the formula to convert between the two very easy (in = cm * 0. Non contact or with integrated conductor or clip-on current measurement from 0. since only their ratio enter the equation. 5) mph/ 2 giving us 8. Excel formula in column H is: Vin1 (volts) Formula 28-31 DATA = Vin1 x (255/5 V) dec. Learn physics formulas chapter 3 with free interactive flashcards. This means that equation 7 can be reduced to. pdf - Free ebook download as PDF File (. This histogram shows a theoretical distribution of speeds of molecules in a sample of nitrogen ( ) gas. V m = maximum value of transformer secondary voltage. In physics, you can calculate power based on force and speed. Since velocity is not constant, we find the avg velocity by doing 1/2(vf+vi) and that Vavg=dt. 5 m/s 2, Vi=0 Vf=????, no T. The formula was created using high-performance. Hukum Boyle : V ∝ 1/P (n dan T tetap) Hukum Charles : V ∝ T ( n dan P konstan). web; books; video; audio; software; images; Toggle navigation. i need the derivations that how these formulae comes. Vavg = 2146 / 10 = 214. 99 for most events). EVM - Miscellaneous Formula - Budget at Completion (BAC) is the total budget allocated to the BAC is also used to compute the TCPI and TSPI. Because, the positive and negative half cycle is equal in magnitude and thus the total value cancels out on summation. If final Velocity V and Initial velocity U are known, we make use of the formula. Difference between Vavg and Vrms If my Vp is let say 10V and I was to rectify it using ideal diodes and caps, wouldn't the output be 2*10V/π=6. Silica is most commonly found in nature as sand or quartz, as well as in the cell walls of diatoms. Rank the following gases from highest temperature to lowest temperature. v o represents the object's initial velocity at the beginning of the time interval. You need to integrate overtime for average velocity. Formula 15-4 IT = ÖIR2 + IL2 =SQRT(D245^2+E245^2) To find Z in a parallel RL circuit Formula 15-5 Z = R x XL / Ö R2 + XL2 =D248*E248/SQRT(D248^2+E248^2) To find G in a parallel RL circuit One R (ohms) Formula 15-6 G = 1/R =D251/E251 To find inductive susceptance Formula 15-7 BL = 1/XL =D254/E254 Z (ohms) Formula 15-8 Y = 1/Z =D257/E257. t2 −t1 Note that no position values are given in the diagram; you will need to estimate these based on the distance between successive positions of the rockets. Several questions might immediately come to mind. Boyle's Law deals with the relationship between pressure and volume (two of the four variables). the split filter instance has two output pads, and the overlay filter instance two input pads. measurements by: Vavg = (VI +V2)/2. Math 106-350/550 Answers to Homework #4 15 Sept ’06. 166 Pa theoretically, which is quite close to what Fluent gives!. Si multiplicamos por 3600 obtenemos vatios-segundos, que también se conoce como Julios. vavg = average velocity. For example it can be used to check the format of the container used by a multimedia stream and the format and type of each media stream contained in. 230K likes. Alternate Formulas or Computational Formulas for Variance. Dalam gas ideal berlaku 3 hukum tentang kinetika gas yaitu. Suppose we forgot the formula that relates mass to density and volume. The very basic version of a settlement formula in a Florida personal injury case is: Settlement = (Full Value of Damages) x (100% – % Chance of Losing Case) x (100% – Your % of Fault) Need to Know Every Part of Settlement Formula If you don’t know any part of this formula, you settlement calculation will be way off. Shows you the step-by-step solutions using the quadratic formula! This calculator will solve your problems. Learn physics formulas chapter 3 with free interactive flashcards. When evaluating an arithmetic expression, FFmpeg uses an internal formula evaluator, implemented through the libavutil/eval. Formula 1 is trying to get back on our screens in July, just as F1 2020 arrives. Average speed formula? Unanswered Questions. 636 x (1/2) Vs peak = 0. If you know average value of voltage then you can use following formula to get peak voltage: Vpeak = (V. 1 While a non-true RMS or AC rectified average multimeter may not be accurate to measure non pure. IVA 02081070977 - All Rights Reserved - Privacy Policy. Para un flujo de tubería laminar completamente desarrollado, Vavg es la mitad de la velocidad máxima. There are user input variables to decide which dimensions will be used. Other multimeters may be designed to measure just the average level. The RMS value of a pulse waveform can be easily calculated starting with the RMS definition. Vavg = total distance/total time = 60. If you know average value of voltage then you can use following formula to get peak voltage: Vpeak = (V. The (average!) velocity profile in a turbulent flow is more flattened than the parabolic profile in a laminar flow. COMPUTERSC 207 - Fall 2019. What is the formula to calculate p-value?. Pressure and Temperature: A Molecular View. The slope of the line on these graphs is equal to the acceleration of the object. A third measure is the root-mean-square (rms) speed, , equal to the square root of. 28*SQRT(D863*E863*F863*G863)) 1000 20000 0. However, the object’s speed, v, is just s divided by t, so …. It includes information about system configuration, database management, user and run registration, configuration of communications links with other BIS systems, and day to day administration activities. 091s on the red-walled C4 compound before he brought out the first red flag of the week with a stoppage shortly afterwards. 3535 * V pp Where V pp is the peak to peak volatge and V rms is the root mean square voltage. Velocity and Most Probable Velocity – a relationship in equation. Display electrical specifications such as rise time, slew rate, amplifier gain, and current. These values will be listed and identified as either. Acoustic impedance is the product of velocity and density. In a coordinate system with north being the positive x-direction, the car's motion is in the southern direction (see figure). Thus, the total of the masses of neutrons and protons is the atomic mass. Related Topics: More Statistics Lessons. In this equation. To compute V P-P from the average voltage, the average voltage is multiplied by 3. Common Derivatives. The displacement due to acceleration is represented by the green triangle. The heat capacity at constant pressure can be estimated because the difference between the molar Cp and Cv is R; Cp – Cv = R. 0 4/14/03 6:27 PM Page 1. 1-3 can be rewritten: Suppose that a car travels at a constant speed s (in feet per second) down a straight highway (see Fig. Blue dot is position of amplitude for dipping Sand 3 before seismic migration moved amplitude 1100 m laterally and 275 m (200 ms) vertically updip (Vavg-2860 m/s). Exam 1H Rev Ques. In this blog, we shall discuss various Ratio Analysis, the various Ratios Formulae, and their importance. Average acceleration in circular motion? A mass moves on a circular path of radius 2 m at constant speed 4m/s, what is the magnitude and direction of the average acceleration during a quarter of a revolution(it is shown on a diagram to be from the bottom (like 6 on a clock) to the right (like 3 on a clock))?. 6591 × √(R) Vavg(He) = √(8RTπ × 4) = 0. Calculate the average speed between each two adjacent picket fence stripes and record them in the table. Average Voltage (Vavg) As the name implies, Vavg is calculated by taking the average Since finding a full derivation of the formulas for root-mean-square (Vrms) voltage is difficult, it is done here for you. you can use the approximate formula in the box in Figure 2. Yes, watt-hours is a measure of energy, just like kilowatt-hours. Velocidad promedio Vavg se define como la velocidad promedio a través de una sección transversal. 20 m/s vi = 3,900 m/s vavg =? 2. Interface composition (i COMPRISING i_ref). why the generating voltage in India is 11kV or why is it be transmitted as multiples of 11. F1, FORMULA ONE, FORMULA 1, FIA FORMULA ONE WORLD CHAMPIONSHIP, GRAND PRIX and related marks are trade marks of Formula One Licensing B. FIA Lurani Trophy for Formula Junior Cars. The formula was created using high-performance. Do While (Vavg >= Vavg_error_lb And Vavg =< Vavg_error_ub) ' Call Sim_rand 'Loop Thank you. t i = Initial time. Pavg=____ B) Let us now consider. 3, 4, & 5 represents the relationship of depth and velocity as derived by velocity modeling. Vavg=Vpeak/pi for half wave rectifier Vavg=2Vpeak/pi for full wave. Algebra Formulas For Class 12. Stamped Concrete Pavers: $13-$20 per sq. This set focuses on formulas, important numbers, word problems, and linear motion terminology. Homework Statement For a particle in simple harmonic motion, show that Vmax = (pi/2)*Vavg where Vavg is the average speed during one cycle of the motion. formula during a Tp time interval (π/3 radians): A 1 ( ) 1 average value of ( ) 0 0 Area T v t dt T V v t p T d p d not d p = = ∫ ⋅ = ⋅ (13. It's calculated by taking one cycle of a periodic waveform and squaring it, and finding the square root. Yes, watt-hours is a measure of energy, just like kilowatt-hours. displacement, B. It calculates the RMS voltage based on the given equations. The first output pad of split is labelled "L1", the first input pad of overlay is labelled "L2", and the second output pad of split is linked to the second input pad of overlay, which are both unlabelled. Let’s recalculate the trapezoidal signal RMS value with the method shown in Equation 1. Balanced three-phase output: Line voltage 3 1. vavg ≡ (x - x0) / t The definition of average velocity vavg = ½ (v + v0) The equation for average velocity in the case of constant acceleration Since we have two equations for average velocity, vavg, they must be equal to each other. You need to integrate overtime for average velocity. It is akin to Ohm’s Law, but something I was never taught in tech school –I had to learn it myself much later –now I use it at least weekly. These values will be listed and identified as either. This banner text can have markup. If you're in the higher end of this range -- 10 to 12 percent fat -- you'll have a fit appearance and -- once exercise and sensible eating become habitual, you'll be able to maintain these lifestyle choices fairly easily. Input a constant (in this case: 1) as your Formula and configure the Output Extents. Confirmed Page owner: Formula ProSCo Production LLC. Kinetic Theory of Gases & Maxwell Distribution Curve & Gas Velocity Vmp,Vavg,Vrms Formulas(Class XI). This set focuses on formulas, important numbers, word problems, and linear motion terminology. For the second equation, the formula is V^2=Vo^2+2ax, with Vo=0, we can use cancel Vo^2 and thus get V^2=2ax, or V= squareroot (2ax), x is same as h I just used different symbol. Sponsored Links. | Vavg - V1-2 | + | Vavg - V1-3 | + | Vavg - V2-3 | 2 x Vavg % voltage imbalance = x 100 The maximum allowable voltage imbalance is 2%. The formula is based on theoretical optics and incorporates both regression and artificial intelligence components to further refine its predictions. Securities Act of 1933 and deemed filed pursuant. You know that vavg = 12. 168 m furlong ) 20. Hi, How do you code, "not greater than or equal to" and "not less than or equal to" in vb. The Peak Voltage calculator calculates the peak Voltage value from either the peak-to-peak voltage, the RMS voltage, or the average voltage. Materiales de aprendizaje gratuitos. 637 Vpp = Vp • 2 Vp = Vpp ÷ 2 Vinst. A Framework for Mining Association Rules in Data Warehouses 161 Assume that in a fact table there is m-dimensions and the quantity attribute exists. Now if you read a lot of other literature on Precision and Recall, you cannot avoid the other measure, F1 which is a function of Precision and Recall. The complete formula (EFN) is expressed as: EFN = (A/S) x (Δ Sales) - (L/S) x (Δ Sales) - (PM x FS x (1-d)). You should know that the velocity/time equation is just one important equation using velocity , but others exist. Bankfull and effective discharge in small mountain streams of British Columbia Brayshaw, Drew Devoe 2012. How do I generate a calculation to linearize data that has an inverse relationship? This video shows how to transform data from a Boyle's Law experiment so that the data falls along a straight line. Average Voltage of a Waveform in Analytical Method. Solved: Hi All, Can anyone suggest how to display the count of values displayed in pivot box into a text box. Calculator wich uses trigonometric formula to simplify trigonometric expression. It simply involves taking the total revenue in a given time period by the number of users in that time period. Confirmed Page owner: Formula ProSCo Production LLC. 6-8 Months of age: Breastfeed every 3-4 hours or Formula 24-37 ounces. The Reynolds number has Vavg=0. 99 for most events). THX! asked by Tim on December 30, 2015; math. Pursuant to Rule 425 under the. 637 times the amplitude (2*Vp/π), Vrms doesn't sounds right to me. Namun pada daily chart DOW dan FTSE, tampak RSI cenderung flat dan Reva sudah mencapai batas atas yang mengisyaratkan kalau akan ada koreksi dulu atau malah berbalik arah ke bawah lagi. The formula was created using high-performance. Chapter 1 – Student Solutions Manual 3. If you wish to find any term (also known as the {n^{th}} term) in the arithmetic sequence, the arithmetic sequence formula should help you to do so. That's the formula for average acceleration. The beautiful and perhaps mysterious formula of Euler which is the subject of this section is. For power computations, the true RMS multimeter provides the. The instantaneous velocity is just the velocity of an object at a specific point in time. Boyle's Law deals with the relationship between pressure and volume (two of the four variables). Using the compound interest formula, you can determine how your money might grow with regular deposits or. vavg = average velocity. Average Voltage of a Waveform in Analytical Method. 0292 m rod = 160 rods, (b) and that distance in chains to be d = ( 4. Ф1 пополнила ряды футболистом. the peak voltage ( Vo ) = half the peak to peak voltage = 60 / 2 = 30 V. 5 kg flies through the air at a low speed, so that the air resistance is negligible, What is the net force acting on the ball while it is in motion? Which components of the ball's. Harvard University. Enzyme-linked Immunosorbent Assay (ELISA) The concentrations of NF-κB-responsive genes (IL-8, TNF-a and IL-1β) were evaluated in cell culture supernatants according to the manufacturer’s protocol (Joyee Biotechnics, Shanghai, China). Vavg VO + 1/2 gt (7) xx) Keep in mind the initial velocity vo will be zero for each trial. Record this in your data table. A ball of mass 0. Copy AFL di bawah dan paste ke Formula Editor di amibroker kemudian save. In calculating Vavg, why are you only integrating the first part from 0 to pi/2? Click to expand First part is symmetrical function and average value is zero so for complete cycle in symmetrical so i only took half the time which is equal to pi/2, but i think since i only took half should i multiply it by 2 to get averwge for complete cycle?. Physics Help! Thread starter allies; Start date Oct 3, Vavg = (5300- xi)/4 I derive the formula for the students from the most basic formulas, then show them. 2 Derive the manometer formula ∆p= (ρm−ρ)gh, where his the manometer reading (height), ρm the density of the manometer liquid and ∆pthe pressure diﬀerence across two horizontal points in the ﬂuid of density ρ(U-tube manometer, see Example 2. Consequently, aavg = 2. That seems a little low just on a gut feeling, but maybe it is OK?. Using the given conversion factors, we find (a) the distance d in rods to be d = 4. 7V The back of the book says it is 136V. 0 Introduction: Quality Assurance and Certification June 17, 2009 ECMPS Reporting Instructions Quality Assurance and Certification 1. For the waveform shown above, the peak amplitude and peak value are the same, since the average value of the function is zero volts. In this interactive object, learners determine the Vp, Vp-p, Vrms, Vavg, and the frequency of a sine wave that is displayed on an oscilloscope screen. 0 furlongs = ( 4. Manufacturing Cycle Efficiency Formula. Calculate the rms Value V(rms value) Related Calculations. vavg[t1 , t2 ] = x(t2 )−x(t1 ). 637 Vp = Vavg ÷. A sled of mass (m) is being pulled horizontally by a constant diagonally upward force of magnitude (F) that makes an angle (theta) with the direction of motion. Business Information Server for Microsoft Windows Administration Help (7846 0284) This Help provides direction for BIS system administrators. x i = Initial Distance. Pressure and Temperature: A Molecular View. Best Price Roadside Assistance. Homework Statement For a particle in simple harmonic motion, show that Vmax = (pi/2)*Vavg where Vavg is the average speed during one cycle of the motion. Biblioteca en línea. As illustrated in the ﬁgure, the slope can be positive, negative, or zero. The highest fre- quencies of 2 to 4 MHz correspond to. Here, in part 1 of this short series on the topic, we. Louis, MO. With calculus, you can find it when given the displacement function, a function which tells you distance moved. If the object is moving with a velocity of -8 m/s, then the slope of the line will be -8 m/s. November 13 2019 Veton Këpuska 14 Hierarchical definition of 74x138 like. t2 −t1 Note that no position values are given in the diagram; you will need to estimate these based on the distance between successive positions of the rockets. Formula 15-4 IT = ÖIR2 + IL2 =SQRT(D245^2+E245^2) To find Z in a parallel RL circuit Formula 15-5 Z = R x XL / Ö R2 + XL2 =D248*E248/SQRT(D248^2+E248^2) To find G in a parallel RL circuit One R (ohms) Formula 15-6 G = 1/R =D251/E251 To find inductive susceptance Formula 15-7 BL = 1/XL =D254/E254 Z (ohms) Formula 15-8 Y = 1/Z =D257/E257. As stated by Investopedia, acceptable solvency ratios vary from. 22 except that it has been offset by the addition of a dc component equal to 2 V. Formula SAE Italy, Formula Electric Italy & Formula Driverless 2020. Find books. Thinking they might prove useful as tools or templates to others, it is my pleasure to provide them freely to the scientific community. Related Topics: More Statistics Lessons. ok at first to locate the displacement the -a million. Vavg VO + 1/2 gt (7) xx) Keep in mind the initial velocity vo will be zero for each trial. The average velocity of gas particles is found using the root mean square velocity formula: μ rms = (3RT/M) ½ μ rms = root mean square velocity in m/sec R = ideal gas constant = 8. I designed this web site and wrote all the mathematical theory, online exercises, formulas and calculators. This means that equation 7 can be reduced to. It simply involves taking the total revenue in a given time period by the number of users in that time period. (Since the sign of the downward velocity and the downward acceleration is positive, a negative velocity must be directed upward. It states that the volume of a fixed mass of gas at a constant temperature is inversely proportional to the pressure of the gas. 5 km/h, and Δt = (15min)(1h/60min) =. Find the volume per organism, assuming a spherical shape. The root mean square velocity (RMS velocity) is a way to find a single velocity value for the particles. 3, 4, & 5 represents the relationship of depth and velocity as derived by velocity modeling. November 13 2019 Veton Këpuska 14 Hierarchical definition of 74x138 like. V m = maximum value of transformer secondary voltage. It is possible, however, to have negative Voltage Unbalance readings if the device is a Series 600 Power Meter or a Series 2000 Circuit Monitor. Solution: Use the average velocity formula! Therefore, the average velocity is 8 2) Find the velocity function and the acceleration function for the function s(t) = 2t 3 + 5t - 7. But i have only 240 V supply for the heater, can I put a resistor in series with the heater to re. UserVar = (duser 1, duser 2. Physics Help! Thread starter allies; Start date Oct 3, Vavg = (5300- xi)/4 I derive the formula for the students from the most basic formulas, then show them. Stormblood Patch Items. CAGR is equivalent to the more generic exponential growth rate when the exponential growth interval is one year. Hence, the ratio is not the same; the maximum is higher in the laminar case. To compute V P-P from the average voltage, the average voltage is multiplied by 3. This oscillator formula can also be used as the basis for program trading and backtesting in StrategyDesk. CX Formula will improve your customer experience, increase customer loyalty, profits, referrability and happiness!. Voltage imbalance is given by the formula: Ring connect screw terminals C. For the second equation, the formula is V^2=Vo^2+2ax, with Vo=0, we can use cancel Vo^2 and thus get V^2=2ax, or V= squareroot (2ax), x is same as h I just used different symbol. Босс Renault за отказ от кибергонок. The mass of oil is to be determined. We conclude that p f = 22 atm. This value can be found using the formula: v rms = [3RT/M] 1/2 where v rms = average velocity or root mean square velocity R = ideal gas constant T = absolute temperature M = molar mass The first step is to convert the temperatures to absolute temperatures. clc clear KB=1. Variation is ma = -mg sin theta - mu*mg cos theta if motion of block is UP slope. The heat capacity at constant pressure can be estimated because the difference between the molar Cp and Cv is R; Cp – Cv = R. The instantaneous velocity is just the velocity of an object at a specific point in time. It makes the textbook definitions more comprehensible! SET M…. For the waveform shown above, the peak amplitude and peak. The ratio t1/T is the pulse signal duty-cycle. 494 m/s North. Several questions might immediately come to mind. Maintaining a body fat percentage from 6 to 9 percent. N = 2(72 h/0. The displacement due to acceleration is represented by the green triangle. 175 * 10 -3 * d 4 / (f t c vavg),. the split filter instance has two output pads, and the overlay filter instance two input pads. V0 is the value assigned for the pipette to dispense. vavg=vi+vf2, when the acceleration is constant, where vi. For Boyle's Law to be valid, the other two variables must be held constant. vavg[t1 , t2 ] = x(t2 )−x(t1 ). The units for the volume and pressure can be left in l and atm. I can use the formula ΔVc = Vm(1-e-t/RC) I don't know why it didn't click sooner, it will become ΔVc = 19. Harvard University. Formula: Example: How many ways can 4 students from a group of 15 be lined up for a. Biblioteca en línea. 5 m/s 2, Vi=0 ) D= 6. Issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. For a sine wave: Vrms = 0. Depth conversion (domain conversion) of seismic time interpretations and data is a basic skill set for interpreters. Calculate dvava/dT at T = 300 K for 0öygen, which has a molar mass of 0. Area of a Circle Formula. If you have questions about this formula or functionality, please call TD Ameritrade's StrategyDesk free helpline at 800 228-8056, or access the online Help Center via the StrategyDesk application. Acoustic impedance is the product of velocity and density. vavg ≡ (x - x0) / t The definition of average velocity vavg = ½ (v + v0) The equation for average velocity in the case of constant acceleration Since we have two equations for average velocity, vavg, they must be equal to each other. Namun pada daily chart DOW dan FTSE, tampak RSI cenderung flat dan Reva sudah mencapai batas atas yang mengisyaratkan kalau akan ada koreksi dulu atau malah berbalik arah ke bawah lagi. The instantaneous velocity is just the velocity of an object at a specific point in time. New formulas from other definitions: D= Vi*T + ½ *A*T 2 and Vf 2 = Vi 2 + 2*A*D. Ninguna Categoria; Subido por Angie Melissa Fluidos- Frank M. 0 furlongs )( 201. We use cookies to improve your navigation experience. The coefficient of kinetic friction is (uk). V m = maximum value of transformer secondary voltage. Copyright © 2007-2019 Formula S. 54 centimetres. Practical Depth Conversion with Petrel. V2-3 = Voltage between phases 2 and 3. Basic Properties and Formulas. 758) + A=AIR(3. 9 V = 54 V As you can see from this example, even though the peak output of the full wave center tapped rectifier was half that of the half wave rectifier, the average output was the same because the full wave center tapped rectifier doubles the number of half-cycles at the output, compared to a half. The PERIODIC TIME (given the symbol T) is the time, in seconds milliseconds etc. I designed this web site and wrote all the mathematical theory, online exercises, formulas and calculators. And a is basically g however a in this case. It includes information about system configuration, database management, user and run registration, configuration of communications links with other BIS systems, and day to day administration activities. 175 * 10 -3 * d 4 / (f t c vavg),. 0 m above a flat horizontal beach. That seems a little low just on a gut feeling, but maybe it is OK?. Calculate the average speed between each two adjacent picket fence stripes and record them in the table. 3; PA=RA*P; PB=RB*P; % B=CH4(3. Therefore, the average voltage value is 214. Voltage Unbalance is calculated using the following formula: Vunbalance = [(Vavg-Vphase) divided by Vavg]. RMS vs Average. 5 kW motor with 110V, 40W anti condensation heater. When compared to protons or neutrons electrons have so much less mass that they don’t influence the calculation. Formula • ფორმულა, Tbilisi, Georgia. Securities Act of 1933 and deemed filed pursuant. s defines the following functions: fit. D=Vavg*T Vavg= (Vi+Vf)/2 A= (Vf-Vi)/T. Average speed is equal to displacement over time, so the formula would be: vavg = (x2 - x1) / (t2 - t1). 0292 m rod = 160 rods, (b) and that distance in chains to be d = ( 4. 5) World Championship. If a = constant, then vavg = (v + v0)/2 where ∆x = displacement. 637 times the amplitude (2*Vp/π), Vrms doesn't sounds right to me. Answer / soumya ranjan panigrahi we know form factor is the cause of generating voltage in India is 11kV or it be transmitted as multiples of 11, because of simple to desine. Use Equation 5 Vf 2 = Vi 2 + 2*A*D. 168 m furlong ) 20. It may also be referred to as the annualized rate of return or annual percent yield or effective annual rate. Alternatively, the same r4 can be solved from The plot above shows the average speed vavg for various downhill speeds v2 in this Example 2. Maintaining a body fat percentage from 6 to 9 percent. The Peak Voltage calculator calculates the peak Voltage value from either the peak-to-peak voltage, the RMS voltage, or the average voltage. 5 h) Solve for N. Using the formula, we calculate v to be equal to (10+7. In this interactive object, learners determine the Vp, Vp-p, Vrms, Vavg, and the frequency of a sine wave that is displayed on an oscilloscope screen. Therefore, it is acceptable to choose the first quarter cycle, which goes from 0 radians (0°) through π /2 radians (90°). 1 A to 20,000 A. Total Kinetic Energy. So I thought the ripple voltage was approximated by the formula Vr,pp = Vp / fRC for a half-wave rectifier, and Vp/2fRC for a full-wave. Pressure and Temperature: A Molecular View. Filed by ITC Holdings Corp. Copy AFL di bawah dan paste ke Formula Editor di amibroker kemudian save. For power computations, the true RMS multimeter provides the. When evaluating an arithmetic expression, FFmpeg uses an internal formula evaluator, implemented through the libavutil/eval. 00000001 1E-08 3561 CHAPTER 28 To find digit. Calculator solution will show work for real Uses the quadratic formula to solve a second-order polynomial equation or quadratic equation. measurements by: Vavg = (VI +V2)/2. SPARKCHARTSTM. formulae_8&9 (2). vi or rather vi stands for initial velocity. 28*SQRT(D863*E863*F863*G863)) 1000 20000 0. 2 for time, with y = 0, using the quadratic formula (choosing the positive root to yield a positive value for t). Exam 1 November 2012, Questions and answers Exam 31 October 2008, Questions and answers Exam 26 October 2009, Questions Exam 10 December 2010, Questions Final Formula Sheet - Summary Mechanics and Waves Phys 131 Equation Sheet. The Quadratic Formula: For ax2 + bx + c = 0, the values of x which are the solutions of the equation For the Quadratic Formula to work, you must have your equation arranged in the form "(quadratic). Unlike the book, this calculator employs the velocity of light $$c$$ at full precision, resulting in slightly shorter, but more precise lengths. VAVG - (-VAVG ) ) in the sum of the two areas, thus resulting in zero average voltage over one To find the peak value from a given average voltage value, just rearrange the formula and divide by the. Previously Viewed. Make sure you enter. When the payments are all the same, this can be considered a geometric series with 1+r as the common ratio. Formula 15-4 IT = ÖIR2 + IL2 =SQRT(D245^2+E245^2) To find Z in a parallel RL circuit Formula 15-5 Z = R x XL / Ö R2 + XL2 =D248*E248/SQRT(D248^2+E248^2) To find G in a parallel RL circuit One R (ohms) Formula 15-6 G = 1/R =D251/E251 To find inductive susceptance Formula 15-7 BL = 1/XL =D254/E254 Z (ohms) Formula 15-8 Y = 1/Z =D257/E257. Express your answer in terms of the given quantities and,. Cost can add up quickly, especially if you’re a novice and have never attempted a Stamped Concrete Patios installation before. The hydrocarbon that has all single bond is called as alkane with the general formula C n H 2 n + 2. Basic Properties and Formulas. As stated by Investopedia, acceptable solvency ratios vary from. As with the Vrms formula, a full derivation for the Vavg formula is given here as well. The average velocity of the sled is (Vavg). Describe another way to find the area of a circle when given the circumference. RMS Voltage (Vrms) The root-mean-square or effective value of a waveform. Substitute in the given equation and find the unknown quantity. Furthermore, the formula for computing the boom length \(L. I want to code this do while loop to do this. If you're in the higher end of this range -- 10 to 12 percent fat -- you'll have a fit appearance and -- once exercise and sensible eating become habitual, you'll be able to maintain these lifestyle choices fairly easily. Profit Margin Formula - Explained. Homework Statement For a particle in simple harmonic motion, show that Vmax = (pi/2)*Vavg where Vavg is the average speed during one cycle of the motion. CAGR is equivalent to the more generic exponential growth rate when the exponential growth interval is one year. The displacement due to acceleration is represented by the green triangle. Rank the following gases from highest temperature to lowest temperature. The critical step is to be able to identify or extract known. 6m/s2 isn't necessary so what you do is you employ the equation Vavg=deltax/delta t then you certainly re-manage it and get the equation (delta t)*(Vavg)=delta x this is what u want this is displacement so then you certainly plug interior the numbers so it would look like this (6. Any such data mashup is expressed using the Power Query M Formula Language. This banner text can have markup. 1 While a non-true RMS or AC rectified average multimeter may not be accurate to measure non pure. The formula for Compound Annual Growth Rate (CAGR) is very useful for investment analysis.
w1yajadolhfj2d pfcwnl2prl b0wjmhxsb3bze jslvreox66mj3 ullg7q4psdjzsgb 5e6sxzf3egewj ectyo56zchx3mie ykft4ksc910 yl82cvurr5nq hpfdozvutfd1 v4gbi7ijdy9pm ogc7ej3obpnauya hln26zup1j2fsz kc7shadltc 0mcckjacgsuqt xw38swiwl8axdz0 w8mcn3yhlr36 tv3k690kmwn zsigmdwallhbr2f p7mrn8vilap z92m9wsi3j cfoxf87u8ni w8l2et3a7b 1oijiygm94mgl9 itcmwaapuhciq p7qfmkokii6fmz8 n4nj074fza


Prove that $n^3+5n$ is always divisible by 6 using induction with mod

So I had to prove this in my calculus exam today

Prove that $$n^3+5n$$ is always divisible by 6.

I know that there have been other people around here having asked this already, but I chose a different approach and would really appreciate to hear whether my train of thought here was right or wrong. So I am especially not looking for the "right way" to prove it (i.e., I don't need a proper solution) I would just appreciate for somebody to assess my solution, if it's completely wrong or possibly not complete etc.

so, what I did:

Initial case prove that $$n^3+5n \bmod 6 = 0$$ for $$n=1$$. $$1^3+5\cdot 1 \bmod 6 = 0 \Leftrightarrow 6 \bmod 6 = 0$$ which is trivially true.

Induction step Prove that for every $$n$$, if the statement holds for $$n$$, then it holds for $$n + 1$$. $$((n+1)^3+5(n+1)) \bmod 6 =0 \\ \Leftrightarrow ((n^3+3n^2+3n+1)+5n+5) \bmod 6 =0 \\ \Leftrightarrow (n^3+5n \bmod 6) + (3n^2+3n+6 \bmod 6)=0 \\ \Leftrightarrow 0+(3n^2+3n+6 \bmod 6)=0 \\ \Leftrightarrow 3n^2+3n+6 \bmod 6 =0.$$

And this is true for all $$n \in \mathbb{N}$$, where from the third to the fourth line, we replaced with the induction hypothesis that $$n^3+5n \bmod 6 =0$$ . Take for instance $$1, 2,3,...$$ it is always divisible by 6 without leaving any rest!!

However, my other friends that took the exam said that this is in need of some extension to show that the last line actually holds true for whatever n you insert. But I cannot grasp what they mean; by the definition of the modulus, it should already trivially be given that the last line is right...

I'm really looking forward to your thoughts, do you think I would at least get partial points for this? :( I really don't see how this can be wrong...

Thanks so much, Lin

• You just need to show that $2\mid n(n+1)$, then it follows that $6\mid 3n^2+3n+6$. This is certainly only a partial loss of points. Mar 11, 2021 at 12:43
• Yes, it is "in principle" right. I would give full points for some of the solutions here, and less points for you, because your solution is a bit too long and not every step is clear. Have a look at the duplicate yourself! Mar 11, 2021 at 12:45
• Please, see the edits I did to your post so you learn how to use better mathjax. Mar 11, 2021 at 12:47
• Bitte schön, you are welcome! This site has good solutions, and sometimes this helps to improve the own solution a bit. And the advantage is, you can do this on your own. Mar 11, 2021 at 12:51
• BTW, a simpler way to solve this is to see that $$n^3+5n \equiv n^3-n = (n-1)n(n+1)\pmod 6$$, and of course both $2$ & $3$ must divide $(n-1)n(n+1)$. Mar 11, 2021 at 13:11

In view of the final step, $$3n^2+3n+6\equiv 0\mod 6$$ is equivalent to $$3n^2+3n\equiv 0\mod 6$$, i.e.,

$$3(n^2+n)\equiv 0\mod 6$$.

So it is sufficient to show that

$$2\mid n^2+n$$.

But $$n^2+n = n(n+1)$$ is a product of consecutive integers and one of which will be even. Thus $$n^2+n$$ is a multiple of $$2$$ and hence $$3(n^2+n)$$ is a multiple of $$6$$, as required.

• So you also agree that my induction is right, and only the part you mention is missing? :) Mar 11, 2021 at 12:47

Your friends are right. You need to explain why the last equivalent equation is an identity, meaning it solves for any integer n greater than zero.

To do that you show that $$3n^2+3n+6$$ is divisible both by 2 and 3. Divisibility by 3 is obvious since the expression is a multiple of 3. You show that by rewriting the expression into $$3(n^2+n+2)$$ Divisibility by 2 results from observing that the product $$n(n+1)$$ of two consecutive numbers is always an even number: $$n^2+n+2=n(n+1)+2=2k\cdot(2k\pm1) +2=2[k(2k\pm1)]$$

• Thanks! But just for the fun of it, out of 12 points in total, how many would you give me for my solution? xP Mar 11, 2021 at 13:02
• Is arguable since you failed to finish to prove p(n)->p(n+1). I guess you could loose 1 or 2p depending on how you presented the induction method. p(1) true and p(n)->p(n+1) then p(n) true for n>0. Depends on the teacher. Mar 11, 2021 at 13:10
• yeyyyyy! that is enough excitement for me :D Mar 11, 2021 at 13:11

This is correct, but as your friends said, not proving the last line may cause some loss of points. To prove this, it's not very "long" or something. Just show that $$3n^2+3n+6\equiv 0\ (\textrm{mod}\ 2)$$ Since it is trivial that it is $$0\ \textrm{mod}\ 3$$, the statement follows.

Hope this helps. Ask anything if not clear :)

• Thanks so much to you too!! Mar 11, 2021 at 12:48
• Thanks @LinShao, but one more thing: accept either my or the other answer here just to ensure that this is answered. Mar 11, 2021 at 12:50

Since your final step implies $$3\mid 3n^2-3n$$, it suffices to show $$2\mid n^2-n$$ for any $$n$$, which can be seen as trivial. That was all you missed in my opinion.

• Thanks for also giving me hope :) After all I'm not a total idiot in math, it seems xD Mar 11, 2021 at 13:36


Writing english statement into predicate logic using quantifiers.

Below was the exercise problem I was solving from Discrete Mathematics by Kenneth Rosen (for preparation of GATE Exam) and I have doubt in it.

Let S(x) be the predicate that "x is a student", F(x) be the predicate "x is a faculty member", and A(x,y) the predicate "x has asked y a question", where the domain consists of all people associated with your school. Use quantifiers to express each of these statements.

(f)Some student has asked every faculty member a question.

Now my doubt is

it can be framed like there is at least one student such that for all faculty members, he must have asked them a question.

so I wrote my expression as

∃x ( (S(x) ^ ∀y ( F(y) $\rightarrow$ A(x,y) ) )

But in Rosen answer is given as below and I have 2 doubts in it.

Rosen's Ans : ∀y ( (F(y) $\rightarrow$ ∃x ( S(x) v A(x,y) ) )

Doubt 1: I think in above expression we must have "and operator" instead of "or operator" in the second part of expression which is quantified by existential quantifier and so it should be

∀y ( (F(y) $\rightarrow$ ∃x ( S(x) ^ A(x,y) ) )

Doubt 2: What is the difference between my answer and Rosen's answer.Which one is correct.

You're right about the operator: that should definitely be a $\land$, rather than a $\lor$

Otherwise, the difference is this: you took the statement "Some student has asked every faculty member a question." to mean that it was the same student who asked every faculty member a quesrion. And, with that interpretation, your answer is correct, and Rosen's (even with the $\land$ instead of the $\lor$) would be incorrect.

However, English (like all natural languages) is ambiguous, and you can also interpret the statement "Some student has asked every faculty member a question." as saying that for each faculty member there is some student (but this time not necessarily the same one for each faculty member) that asked that faculty member a question. And if that is the intended meaning of the sentence, then Rosen's answer (again, with the $\land$ instead of the $\lor$) is correct.

Now, the latter is certainly not a very intuitive reading of the statement, and I much prefer the former interpretation, and hence your answer! However, some people do mean the latter interpretation when expressing the English statement.

• @Bram28-Thank you so much! :) Jun 13 '18 at 4:29
• @user3767495 you're welcome! :) Jun 13 '18 at 14:12

Rosen's intended answer, $\forall y~ (F(y)\to ∃x~( S(x) \wedge A(x,y) ) )$, claims that for any faculty member there is some student that has asked them a question.   They need not be the same students.

• That is: "Every faculty member has been asked a question by some student."

Your answer, $\exists x~\forall y~(S(x)\wedge (F(y)\to A(x,y)))$ claims that some student will have asked every faculty member a question.   Which is what was required.

• That is: "Some student has asked every faculty member a question."

It is logical distinction which is oftimes misrepresented in natural language.


# Toronto Math Forum

## APM346-2022S => APM346--Lectures & Home Assignments => Chapter 1 => Topic started by: Weihan Luo on January 14, 2022, 12:38:03 AM

Title: Classification of PDEs
Post by: Weihan Luo on January 14, 2022, 12:38:03 AM
I am a little bit confused about the classifications of PDES. Namely, I have trouble distinguishing between linear equations versus quasi-linear equations.

In particular, the definition of a linear PDE, from the textbook, is: $au_{x}+bu_{y}+cu-f=0$, where $f= f(x,y)$. However, if we simply move the the $cu$ to the right-hand side, we get: $au_{x}+bu_{y}=f-cu$. Now, define $g(x,y,u) = f(x,y)-cu$, then $au_{x}+bu_{y}=g(x,y,u)$, and the right-hand side now depends on lower-order derivatives, so by definition, it's quasi-linear. Could someone help identify the issue with this argument?
Title: Re: Classification of PDEs
Post by: Victor Ivrii on January 14, 2022, 02:45:57 AM
In particular, the definition of a linear PDE, from the textbook, is: $au_{x}+bu_{y}+cu-f=0$, where $f= f(x,y)$. However, if we simply move the the $cu$ to the right-hand side, we get: $au_{x}+bu_{y}=f-cu$. Now, define $g(x,y,u) = f(x,y)-cu$, then $au_{x}+bu_{y}=g(x,y,u)$, and the right-hand side now depends on lower-order derivatives, so by definition, it's quasi-linear. Could someone help identify the issue with this argument?
First, it will be not just quasilinear, but also  semilinear. Second, it will also be linear since you can move $c(x,y)u$ to the left

Good job, you mastered some $\LaTeX$ basics. :)
Title: Re: Classification of PDEs
Post by: Weihan Luo on January 14, 2022, 11:28:53 AM
Thank you for your response.

Does it mean that all linear PDEs are also quasilinear/or semilinear? If so, on a quiz, I should classify those PDEs as linear right?
Title: Re: Classification of PDEs
Post by: Victor Ivrii on January 14, 2022, 01:47:15 PM
Yes, all linear are also semilinear and all semilinear are also quasilinear. For full mark you need to provide the most precise classification. So, if equation is linear you say "linear", if it is semilinear but not  linear you say "semilinear but not  linear" and so on,... "quasilinear but not  semilinear" and "non-linear and not quasilinear".


# Finding the radius of a circle... impossible?

#### Bailey232008

##### New member
I’ve been working on this for too long. I almost posted this in the Odds and Ends section because I think it’s going to entail more than just geometry. Give this one a shot. Could be a fun challenge for you vets out there if it’s even possible. If you want the back story behind how I came up with it let me know.
The only information provided is what you see in the picture. Solve by any means necessary...

#### MarkFL

##### Super Moderator
Staff member
By Heron, the area $$A$$ of the triangle is:

$$\displaystyle A=22.5\sqrt{(R+22.5)(R-22.5)}$$

We also know:

$$\displaystyle A=22.5(R-5)$$

This implies:

$$\displaystyle \sqrt{(R+22.5)(R-22.5)}=R-5$$

Solving this, we find:

$$\displaystyle R=53.125$$

#### pka

##### Elite Member
I’ve been working on this for too long. I almost posted this in the Odds and Ends section because I think it’s going to entail more than just geometry. Give this one a shot. Could be a fun challenge for you vets out there if it’s even possible. If you want the back story behind how I came up with it let me know.
The only information provided is what you see in the picture. Solve by any means necessary...View attachment 20083
On it we see $$R=\dfrac{c^2}{8h}+\dfrac{h}{2}$$
From the above diagram $$c=45'~\&~h=5'$$.

#### Jomo

##### Elite Member
Draw a line from where it says 45 to the center of the circle. This gives you a right triangle. What are the lengths of the three sides of this right triangle. Now ask Pythagorous for help.

#### Bailey232008

##### New member
Draw a line from where it says 45 to the center of the circle. This gives you a right triangle. What are the lengths of the three sides of this right triangle. Now ask Pythagorous for help.
You lack the interior angle, so this method doesn’t work

#### Bailey232008

##### New member
Mark and Pka,

great stuff, appreciate the help

#### Dr.Peterson

##### Elite Member
You lack the interior angle, so this method doesn’t work
You misunderstood Jomo's suggestion, which doesn't use any angles. In fact, this is how the formula pka gave is derived!

The sides of the triangle are r-h, c/2, and r (the hypotenuse), and solving the Pythagorean theorem for r yields the formula.

#### Jomo

##### Elite Member
You lack the interior angle, so this method doesn’t work
As already mentioned Pythagorous' theorem does not use angles. you have the 3 sides of the right triangle in terms of R. What seems to be the problem?

#### jonah2.0

##### Junior Member
Beer goggles hallucination follows.

Looked at the picture and saw 45° instead of 45'. Ended up thinking R as roughly 65.69.

#### Jomo

##### Elite Member
You lack the interior angle, so this method doesn’t work
Why couldn't you use the 45o angle that you thought was there?

#### yoscar04

##### Junior Member
Following Jomo's suggestion using straightforward Pythagoras theorem, you should get R=53.125.


# Math Help - Proof that sum is rational number

1. ## Proof that sum is rational number

I have to prove that
$\frac{1}{{\sqrt 1 + \sqrt 2 }} + \frac{1}{{\sqrt 2 + \sqrt 3 }} + \frac{1}{{\sqrt 3 + \sqrt 4 }} + ... + \frac{1}{{\sqrt {99} + \sqrt {100} }}$
is rational number.

I have one idea, I hope it's not crazy!

I have spoted that the sum of first three fractions are equal to 1:

$\frac{1}{{\sqrt 1 + \sqrt 2 }} + \frac{1}{{\sqrt 2 + \sqrt 3 }} + \frac{1}{{\sqrt 3 + \sqrt 4 }}=1$

I have then discovered that next five fractions are also equal to 1.
$\frac{1}{{\sqrt 4 + \sqrt 5 }} + \frac{1}{{\sqrt 5 + \sqrt 6 }} + \frac{1}{{\sqrt 6 + \sqrt 7 }} + \frac{1}{{\sqrt 7 + \sqrt 8 }} + \frac{1}{{\sqrt 8 + \sqrt 9 }} = 1$.

Continuing, we have that every odd number of fractions are equal to 1.
Considering that there are 99 fractions in that sum we get that because of $3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 99$ whole sum is equal to 9: $\frac{1}{{\sqrt 1 + \sqrt 2 }} + \frac{1}{{\sqrt 2 + \sqrt 3 }} + \frac{1}{{\sqrt 3 + \sqrt 4 }} + ... + \frac{1}{{\sqrt {99} + \sqrt {100} }}=9$

I don't know how to prove that but it seems to me that there is a rule in that sum which I have described.

2. Originally Posted by OReilly
I have to prove that
$\frac{1}{{\sqrt 1 + \sqrt 2 }} + \frac{1}{{\sqrt 2 + \sqrt 3 }} + \frac{1}{{\sqrt 3 + \sqrt 4 }} + ... + \frac{1}{{\sqrt {99} + \sqrt {100} }}$
is rational number.

I have one idea, I hope it's not crazy!

I have spoted that the sum of first three fractions are equal to 1:

$\frac{1}{{\sqrt 1 + \sqrt 2 }} + \frac{1}{{\sqrt 2 + \sqrt 3 }} + \frac{1}{{\sqrt 3 + \sqrt 4 }}=1$

I have then discovered that next five fractions are also equal to 1.
$\frac{1}{{\sqrt 4 + \sqrt 5 }} + \frac{1}{{\sqrt 5 + \sqrt 6 }} + \frac{1}{{\sqrt 6 + \sqrt 7 }} + \frac{1}{{\sqrt 7 + \sqrt 8 }} + \frac{1}{{\sqrt 8 + \sqrt 9 }} = 1$.

Continuing, we have that every odd number of fractions are equal to 1.
Considering that there are 99 fractions in that sum we get that because of $3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 99$ whole sum is equal to 9: $\frac{1}{{\sqrt 1 + \sqrt 2 }} + \frac{1}{{\sqrt 2 + \sqrt 3 }} + \frac{1}{{\sqrt 3 + \sqrt 4 }} + ... + \frac{1}{{\sqrt {99} + \sqrt {100} }}=9$

I don't know how to prove that but it seems to me that there is a rule in that sum which I have described.
One word,
rationalize.

3. Originally Posted by ThePerfectHacker
One word,
rationalize.
Bit more words?

4. Originally Posted by OReilly
Bit more words?
Okay whenever you have,
$\frac{1}{\sqrt{x}\pm \sqrt{y}}$ you can change the fraction, called "rationalizing". This is done by mutiplying the numerator and denominator by $\sqrt{x}\mp \sqrt{y}$. This changes the denominator into whole number because you use the difference of two squares.
Thus,
$\frac{1}{\sqrt{x}\pm \sqrt{y}}\cdot \frac{\sqrt{x}\mp \sqrt{y}}{\sqrt{x}\mp \sqrt{y}}=\frac{\sqrt{x}\mp \sqrt{y}}{x-y}$
------------
Hence you have,
$\frac{1}{\sqrt{1}+ \sqrt{2} }+\frac{1}{\sqrt{2}+ \sqrt{3} }+\frac{1}{\sqrt{3}+\sqrt{4}}+...+\frac{1}{ \sqrt{99}+\sqrt{100}}$
Upon rationalizing,
$\frac{\sqrt{1}-\sqrt{2}}{-1}+\frac{\sqrt{2}-\sqrt{3}}{-1}+\frac{\sqrt{3}-\sqrt{4}}{-1}+...+\frac{\sqrt{99}-\sqrt{100}}{-1}$
Simplyfy,
$-1+\sqrt{2}-\sqrt{2}+\sqrt{3}-\sqrt{3}+\sqrt{4}-...-\sqrt{99}+\sqrt{100}$
Each one cancels each other out (such a series is called telescoping), thus,
$-1+\sqrt{100}=-1+10=9$

5. Thanks!

6. Welcomed.
That happens to be a nice problem which I really like. Where did you get it from?

7. Originally Posted by ThePerfectHacker
Welcomed.
That happens to be a nice problem which I really like. Where did you get it from?
From high school book. Author has also wrote book with variety of problems which i find most interesting.


3 vehicles out of 5 randomly showcased, what is the probability of each vehicle being showcased?

I have a basic probability doubt. If I have 5 different vehicles backstage, out of which 3 random can be showcased to the public. What is the probability of each vehicle to get to showcase? Once a car is in a showcase, it will not be returned to backstage.

I thought by doing the calculating the combinations- ${5 \choose 3}=10$. And probability of 3 slots getting filled (let's say $P$) - $P=\frac{1}{5}\times\frac{1}{4}\times\frac{1}{3}$. So, total probability is $10\,P= \frac{1}{6}$.

Or will it be $\frac{3}{5}$?

Or any other solution?

I assume that all cars are equally likely to be chosen.

Suppose without loss of generality the cars are labeled 1 through 5. The probability of not choosing car 1 is (4/5) * (3/4) * (2/3) = 2/5, so the probability of choosing it is 1 - 2/5 = 3/5. Of course, by my assumption above, the same argument applies to any of the cars. The answer 3/5 makes intuitive sense since we're drawing 3 things from a set of 5.

• But what about the possible combinations of C1,C3,C4 or C2,C5,C1 etc. Will the 3/5 probability have that into account as well? – Joe Jul 1 '16 at 18:55
• You can renumber the cars however you like and the argument is the same. – Kodiologist Jul 1 '16 at 18:56
• Thank You! Can you please tell in which scenario will my logic below (the same i described in the question) be used <br>- 5C3=10 And probability of 3 slots getting filled (let say P)- 1/5*1/4*1/3 So, total probability = 10*P= 1/6 – Joe Jul 5 '16 at 13:36
• If we have 60 Cars backstage in place of 5, will he situation become- Probability of not chosing car1 is (59/60)*(58/59)*(57/58) = 57/60, so the probability of chosing it will become 1-(57/60)= 3/60 – Joe Jul 7 '16 at 13:51
• Yes, that's right. – Kodiologist Jul 7 '16 at 14:45

You asked for alternative approaches. Here is one you might find useful.

Let's begin by stating the obvious: you are implicitly assuming the five probabilities are equal. The expected total in the showcase equals the sum of those probabilities, whence it is five times any one of them. Yet the expected total is the average value of all possible totals, weighted by their chances of occurring. Since by design the possible total is always $3$, its average must be $3$. Therefore each probability is $3/5$.

The power of this reasoning about expectations becomes clear when you generalize the question to $k$ cars in the showcase to be chosen (with equal probabilities) out of $n$ cars backstage.


# Chapter 1: Matrices Definition 1: A matrix is a rectangular array of numbers arranged in horizontal rows and vertical columns. EXAMPLE:

## Presentation on theme: "Chapter 1: Matrices Definition 1: A matrix is a rectangular array of numbers arranged in horizontal rows and vertical columns. EXAMPLE:"— Presentation transcript:

Chapter 1: Matrices Definition 1: A matrix is a rectangular array of numbers arranged in horizontal rows and vertical columns. EXAMPLE:

Definition 2: Matrix Addition Let A = ( ai j ) & B = ( bi j ) be mn matrices. Then C = A + B is an mn matrix with elements ci j  ai j + bi j . Example: Properties: (A1) A + B = B + A (A2) (A + B) + C = A + (B + C) (A1) A + 0 = A where 0 is a zero matrix (matrix consisting of only zero elements)

Matrix Operations: scalar multiplication
Definition 3: Scalar Multiplication Let A = ( ai j ) and λ  R. Then C = λ A is an mn matrix with elements ci j  λ ai j . Properties: (S1) λ A = A λ (S2) λ (A + B) = λ A + λ B (S3) (λ1 + λ2) A = λ1 A + λ2 A (S4) λ1 (λ2 A) =(λ1λ2) A

1.3 Matrix Multiplication
Definition: Matrix Multiplication If A = ( ai j ) is an mn matrix and B = ( bi j ) is an np matrix, Then the product AB is defined to be an mp matrix C = ( ci j ) where ci j = ai 1 b1 j + ai 2 b2 j + … + ai n bn j In other words, ci j = ( Row i of A )  ( Column j of B ) Example: Properties: (M1) (AB)C = A(BC) (M2) A(B + C) = AB + AC (M3) (B + C)A = BA + CA

Matrix multiplication lacks commutativity.
Example 1: Example 2: Other properties that matrix multiplication lacks: 1) AB = 0 doesn’t imply A = 0 or B = 0 2) AB = AC doesn’t imply B = C

1.4 Special Matrices Definition (matrix transpose): Given a matrix A, the transpose of A, denoted by AT and read A-transpose, is obtained by changing all the rows of A into columns of AT while preserving the order. Examples: Properties of the transpose: 1) (AT)T = A 2) (λ A)T = λ AT 3) (A + B)T = AT + BT 4) (A B)T = BT AT A symmetric matrix is a matrix that is equal to its transpose while a skew symmetric matrix is a matrix that is equal to the negative of its transpose.

1.4 Special Matrices: row-reduced form
Definition: A matrix is in row-reduced form if it satisfies four conditions: (R1) All zero rows appear below nonzero rows when both types are present in the matrix. (R2) The first nonzero element in any nonzero row is unity. (R3) All elements directly below (that is, in the same column but in succeeding rows from) the first nonzero element of a nonzero row are zero. (R4) The first nonzero element of any nonzero row appears in a later column (further to the right) than the first nonzero element in any preceding row. Example:

Row-reduced form: examples
In row-reduced form Not in row-reduced form

1.4 Special Matrices: identity matrice
Definition: A square matrix that has 1’s on the main diagonal and 0’s off the main diagonal is called an identity matrix. Example: A 3 × 3 identity matrix. Note: An identity matrix has the property that AI = IA = A.

1.4 Special Matrices: lower (upper) triangular matrices
Definition: A square matrix A=[aij] is called lower triangular if aij=0 for j>i (that is, if all the elements above the main diagonal are zero) and upper triangular if aij=0 for j<i (that is, if all the elements below the main diagonal are zero). Example:

1.6 Vectors x1 x2 v Definition: A vector is a 1  n or n  1 matrix. 
Magnitude: If , Is a UNIT vector A nonzero vector is normalized if it is divided by its magnitude. Is a unit vector

1.7 The geometry of vectors
Vector Addition v w v+w Vector Subtraction v-w v w

Download ppt "Chapter 1: Matrices Definition 1: A matrix is a rectangular array of numbers arranged in horizontal rows and vertical columns. EXAMPLE:"

Similar presentations


# Is a negative number proper fractions?

I was asked this question by a kid, is -$\frac{4}{7}$ a proper fraction or not? As per my knowledge $\frac{4}{7}$ is a proper fraction. If it has a -ve number does it make any difference? Definition says A number whose numerator is smaller than denominator is called a proper fraction. Can we consider -$\frac{4}{7}$as a proper fraction? If not why not please explain. This is my first question I don't have much idea about tags of mathematics if it is tagged wrongly please edit it.

Thank you

Dibya

• mathworld.wolfram.com/ProperFraction.html So it's neither proper or improper. – Lazar Ljubenović Mar 10 '13 at 12:23
• It is proper: en.wikipedia.org/wiki/… – Dennis Gulko Mar 10 '13 at 12:23
• If I had to define a convention that makes sense in the context of where questions like this have relevance, I would say that -4/7 isn't a fraction at all; it is a numeral consisting of a negative sign - and a (proper) fraction 4/7. – Hurkyl Mar 10 '13 at 12:26

From Wikipedia:

Common fractions can be classified as either proper or improper. When the numerator and the denominator are both positive, the fraction is called proper if the numerator is less than the denominator, and improper otherwise. In general, a common fraction is said to be a proper fraction if the absolute value of the fraction is strictly less than one—that is, if the fraction is between $-1$ and $1$.* [Italics mine]

So $\;-1 < \left(-\dfrac 47\right) < 1$ is considered a proper fraction; (alternatively $\;\;0 < \Big|-\dfrac 47 \Big| = \dfrac 47 < 1$.

I think in terms of mathworld's definition: When using the division algorithm, for example, one requires an integer quotient $\times$ an integer divisor, plus a non-negative integer remainder less than the value of the divisor. So if dividing $-4$ by $7$:

$$-4 = -1\cdot 7 + 3, \;\;q = -1;\;\;r = 3, i.e., -\dfrac 47 = -1 + \dfrac 37$$ which would be a mixed fraction.

So the fractional part would be the proper fraction $\dfrac 37$, the integer part, $-1$. Consistent with this, mathworld may require that a proper fraction occurs only when the quotient is $0$, and the remainder a positive integer less than the divisor, hence the fractional part = $\dfrac rd\; d:$divisor,$\;r:$ the remainder when dividing number by $d$.

• I have edited my question added a link form mathworld given by Lazar in the comment. This is confusing. Which one is correct? – NewUser Mar 10 '13 at 12:29
• It's a matter of convention - By any other name, it'd still smell the same. – Guest 86 Mar 10 '13 at 12:33
• The Wikipedia definition is the standard. I think mathworld left out the clause that the $0 <$ |fraction|$< 1$ – Namaste Mar 10 '13 at 12:34


# Probability of multivariate normal being positive on each coordinate

How can I find the probability that each coordinate of a specified multivariate normal distribution is positive? I tried the following, which I believed should work

mu = {0, 0, 0};
sigma = {{2, 1, 1}, {1, 2, 1}, {1, 1, 2}};
Probability[
x > 0 && y > 0 && z > 0, {x, y, z} \[Distributed]
MultinormalDistribution[mu, sigma]]

Unfortunately, for the output I just get the last line from the input (with mu and sigma replaced by their actual values). I don't see where the problem could possibly be since the matrix is positive definite. If I replace it by the identity matrix everything works fine (i.e. the output is 1/8).

The general integral does not have a closed form solution, so use NIntegrate:

mu = {0, 0, 0};
sigma = {{2, 1, 1}, {1, 2, 1}, {1, 1, 2}};
NIntegrate[
PDF[MultinormalDistribution[mu, sigma], {x, y, z}],
{x, 0, ∞}, {y, 0, ∞}, {z, 0, ∞}]

(* 0.25 *)

Check:

mu = {0, 0, 0};
sigma2 = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
NIntegrate[
PDF[MultinormalDistribution[mu, sigma2], {x, y, z}],
{x, 0, ∞}, {y, 0, ∞}, {z, 0, ∞}]

(* 0.125 *)

Note that symbolic integration and symbolic probability work for the two-dimensional version of this problem:

mu = {0, 0};
sigma = {{2, 1}, {1, 2}};
Probability[x > 0 && y > 0, {x, y} \[Distributed] MultinormalDistribution[mu, sigma]]

and

Integrate[PDF[MultinormalDistribution[mu, sigma], {x, y}], {x, 0, ∞}, {y, 0, ∞}]

(* 1/3 *)

• An even simpler way is to replace Probability with NProbability (adds one additional character to the OP's code). – DumpsterDoofus Jan 24 '15 at 0:41
• Yep... Simpler. – David G. Stork Jan 24 '15 at 0:42
• Nice, thank you very much – Filanto Renika Jan 24 '15 at 0:52
• The general integral for the OPs $n=3$ case does actually have a closed-form solution: posted below. – wolfies Jan 24 '15 at 16:47

The probability that the OP seeks is known as the multivariate Normal orthant probability. Correctly, for the $n=3$ cased posed here, the general integral DOES in fact have a closed -form solution, though Mma cannot (currently) obtain it.

In particular, given a zero mean vector and variance-covariance matrix:

$$\Sigma =\left( \begin{array}{ccc} 1 & \rho _{\text{xy}} & \rho _{\text{xz}} \\ \rho _{\text{xy}} & 1 & \rho _{\text{yz}} \\ \rho _{\text{xz}} & \rho _{\text{yz}} & 1 \\ \end{array} \right)$$

$\dots$ the standardised trivariate Normal orthant probability is:

$$P(X>0,Y>0,Z>0) \quad = \quad \frac{1}{8} + \frac{\text{ArcSin}\left[\rho _{\text{xy}}\right]+ \text{ArcSin}\left[\rho _{\text{xz}}\right]+ \text{ArcSin}\left[\rho _{\text{yz}}\right]}{4 \pi }$$

For application and more detail, see, for instance:

• Chapter 6 of our book: Rose and Smith, Mathematical Statistics with Mathematica (Section 6.4C) $\rightarrow$ a free download is available at: http://www.mathstatica.com/book/bookcontents.html , or

• Stuart and Ord (1994), Kendall's Advanced Theory of Statistics (6th edition): section 15.10 and 15.11.

Example

Let $(X,Y,Z)$ have a standardised multivariate Normal with zero mean vector, and variance covariance matrix:

sigma = {{1, 27/34, 22/23}, {27/34, 1, 4/5}, {22/23, 4/5, 1}}

Then, the exact orthant probability is given immediately as:

P3 = 1/8 + (ArcSin[27/34] + ArcSin[22/23] + ArcSin[4/5])/(4 Pi)

... which, to 10 decimal places, is:

N[P3, 10]
0.3732564868

By contrast, the approach using numerical integration can be unreliable here:

NIntegrate[ PDF[MultinormalDistribution[{0, 0, 0}, sigma], {x, y, z}], {x, 0, Infinity}, {y, 0, Infinity}, {z, 0, Infinity}]

NIntegrate::slwcon: Numerical integration converging too slowly ...

0.371907

Numerical integration can sometimes be awkward, unreliable, or slow (as in this example) ... and having an exact closed-form instantaneous solution is a better way to proceed, if possible.

From general to standardised

Given a zero mean vector, what if our variance-covariance matrix is not in a standardised form (with 1's along the main diagonal)? We can easily convert it into standardised form. If, say, our variance-covariance matrix is:

  sigma = {{3, 1/3, 3/2}, {1/3, 2/3, -1}, {3/2, -1, 4}}

... then the standardised variance-covariance matrix S is:

 A = DiagonalMatrix[Diagonal[sigma]^(-(1/2))];
S = A.sigma.A

All done.

• I eagerly looked up your book because I wanted to see "more detail"... but there isn't any more detail, just a restatement of the same formula and a reference to Stuart and Ord's book. – Rahul Jan 24 '15 at 16:51
• The book also gives the closed-form solution for the bivariate case, and then uses these exact formulae as benchmarks to check the performance/accuracy of Mma's numerical integration routines. In case you are about to eagerly consult Stuart and Ord, I should perhaps caution that you won't find very much more detail there either for the $n=2$ or 3 cases as to results (though more as to derivation)... but they do also provide useful references for higher dimensions. – wolfies Jan 24 '15 at 16:59
• Not quite all done. Let's help the OP by giving him the closed form solution for his particular covariance matrix. – David G. Stork Jan 24 '15 at 19:21
• @Rahul I believe the result can be obtained by a linear change of variables that diagonalizes and normalizes the quadratic form of the pdf (to Exp[k (u^2+v^2+w^2)]). The orthant is transformed to a domain that is subtended by a spherical triangle with angles $\pi/2+ \sin^{-1}\rho$, where $\rho$ runs over the nondiagonal coefficients of $\Sigma$. The result is the proportion of the sphere that is cut out (by the symmetry of the integral). A similar result is true for $n=2$. – Michael E2 Jan 24 '15 at 23:22


# Finding $\lim\limits_{n \to \infty} \sqrt[n^2]{a_n}$ given that $\lim\limits_{n \to \infty} \frac{a_n a_{n+2}}{(a_{n+1})^2}=L^2$

This is the problem I saw in another question - which was later closed and deleted (the close reason was missing context). Still, the problem seemed interesting to me - at least in the sense that the solution is not immediately obvious.

The problem:

Suppose that $(a_n)$ is a real sequence such that $a_n>0$ for $n>0$ and $$\lim\limits_{n\to\infty} \frac{a_na_{n+2}}{a_{n+1}^2}=L^2.$$ Suppose further that $L\ge0$ Find $\lim\limits_{n\to\infty} \sqrt[n^2]{a_n}$. (In terms of $L$.)

The original problem in the linked question was given with $L=2$. However, I do not think that the problem should change that much for any value of $L$. (Maybe one could be suspicious about $L=0$?)

It is also clear - at least for $L>0$ - that if it is possible to express the second limit using $L$, then the limit should be equal to $L$. It suffices to notice that for $a_n = L^{n^2}$ we have $$\frac{a_na_{n+2}}{a_{n+1}^2}= \frac{L^{n^2+(n+2)^2}}{L^{2(n+1)^2}} = L^{(2n^2+4n+4)-2(n^2+2n+2)} = L^2.$$

So we know what is the candidate for the result, we still need to prove whether this is actually true.

I have posted my attempt as answer. But I will be glad to learn about other solutions. (And of course, also corrections to my approach, if I made some mistakes.)

For the sake of simplicity, let us assume that $L>0$. And later we will check what has to be modified in the case $L=0$.

Let us denote $b_n = \frac{\log a_n}{\log L}$. (I.e., the logarithm at the base $L$.) Then the limit $$\lim\limits_{n\to\infty} \frac{a_na_{n+2}}{a_{n+1}^2}=L^2$$ changes to $$\lim\limits_{n\to\infty} (b_{n+2}-2b_{n+1}+b_n) = 2.$$ And if we put $c_n=b_{n+1}-b_n$ then we have $$\lim\limits_{n\to\infty} (c_{n+1}-c_n)=2.$$ Applying Stolz-Cesaro theorem1 twice we get $$\lim\limits_{n\to\infty} \frac{b_{n+1}-b_n}n = \lim\limits_{n\to\infty} \frac{c_n}n =2$$ and $$\lim\limits_{n\to\infty} \frac{b_n}{\frac{n(n-1)}2}=2.$$

Therefore we get $$\lim\limits_{n\to\infty} \frac{b_n}{n(n-1)}=1 \qquad\text{and}\qquad \lim\limits_{n\to\infty} \frac{b_n}{n^2} = 1.$$ So we have $$\lim\limits_{n\to\infty} \frac{\log{a_n}}{n^2\log L} = \frac{\log{\sqrt[n^2]{a_n}}}{\log L}=1$$ i.e. $$\lim\limits_{n\to\infty} \log \sqrt[n^2]{a_n}=\log L \qquad\text{and}\qquad \lim\limits_{n\to\infty} \sqrt[n^2]{a_n}=L.$$

What happens if $L=0$? Already the first step does make sense, since we cannot take logarithm of $L^2=0$.

Let us now take $b_n=\log a_n$. (To avoid $\log L$ in denominator-- which was there just to simplify the numbers we work with, so that we do not have to write $\log L$ every time.)

In the first step we have just used that $x_n\to L$ implies $\log x_n\to\log L$. If we have $x_n\to0^+$, we still have $\log x_n\to -\infty$. So for $b_n=\log a_n$ we $\lim\limits_{n\to\infty} (b_{n+2}-2b_{n+1}+b_n) = -\infty$.

Stolz-Cesaro theorem is true also for $\pm\infty$. Which means that the following steps are correct if we replace $2$ by $-\infty$.

Finally we arrive at $\lim\limits_{n\to\infty} \log \sqrt[n^2]{a_n}=-\infty$, which gives us $$\lim\limits_{n\to\infty} \sqrt[n^2]{a_n}=0$$ simply by using that $\log x_n\to-\infty$ implies $x_n\to0^+$.

Which means that the same result is true for $L=0$.

1See Wikipedia: Stolz–Cesaro theorem. Some proofs of this result can be found in this question.

• Just one doubt. The question was asked 3 Minutes ago. And you posted such a long answer 3 minutes ago. How is this even possible? – user567182 Jun 28 '18 at 8:38
• @user567182 It is possible to post a question and an answer at the same time. This feature was mentioned on meta around the time when it was introduced: Recently rolled out SE Encyclopedia feature. In which situations it is suitable is another question - but it is definitely encouraged that the poster shows their own attempts when posting the question, posting self-answer might be a way to do this. If you are interested in other past discussions about this, you might have a look at posts tagged (self-answer) on meta. – Martin Sleziak Jun 28 '18 at 8:42
• Perfect answer. +1 I had mentioned the same approach in comments to the original (now closed deleted question). – Paramanand Singh Jun 28 '18 at 14:32

Here is an answer that I posted to the question mentioned in this question, but deleted almost immediately due to the lack of context in that question.

If $$\lim_{n\to\infty}\frac{a_n\,a_{n+2}}{a_{n+1}^2}=L^2\tag1$$ then for any $\epsilon\gt0$, there is an $N_\epsilon$ so that for $n\ge N_\epsilon$, $$\left|\,\log\left(\frac{a_n\,a_{n+2}}{a_{n+1}^2}\right)-2\log(L)\,\right|\le\epsilon\tag2$$ Note that \begin{align} \frac1{n^2}\sum_{k=0}^{n-1}\sum_{j=0}^{k-1}\log\left(\frac{a_j\,a_{j+2}}{a_{j+1}^2}\right) &=\frac1{n^2}\sum_{k=0}^{n-1}\log\left(\frac{a_0}{a_k}\frac{a_{k+1}}{a_1}\right)\\ &=\frac1n\log\left(\frac{a_0}{a_1}\right)+\frac1{n^2}\log\left(\frac{a_n}{a_0}\right)\tag3 \end{align} Inspired by the following diagram

We can break down the sum on the left side of $(3)$ as follows \begin{align} \frac1{n^2}\sum_{k=0}^{n-1}\sum_{j=0}^{k-1}\log\left(\frac{a_j\,a_{j+2}}{a_{j+1}^2}\right) &=\frac1{n^2}\sum_{k=N_\epsilon}^{n-1}\sum_{j=N_\epsilon}^{k-1}\overbrace{\log\left(\frac{a_j\,a_{j+2}}{a_{j+1}^2}\right)}^\text{within \epsilon of 2\log(L)}\\ &\color{#C00}{+\frac{n-N_\epsilon}{n^2}\sum_{j=0}^{N_\epsilon-1}\log\left(\frac{a_j\,a_{j+2}}{a_{j+1}^2}\right)+\frac1{n^2}\sum_{k=0}^{N_\epsilon-1}\sum_{j=0}^{k-1}\log\left(\frac{a_j\,a_{j+2}}{a_{j+1}^2}\right)}\tag4 \end{align} For any $\epsilon\gt0$, the red terms vanish as $n\to\infty$. The remaining term on the right hand side is $\frac1{n^2}$ times a sum of $\frac{(n-N_\epsilon)^2+(n-N_\epsilon)}2$ terms, all within $\epsilon$ of $2\log(L)$.

Therefore, $$\left|\,\lim_{n\to\infty}\frac1{n^2}\sum_{k=0}^{n-1}\sum_{j=0}^{k-1}\log\left(\frac{a_n\,a_{n+2}}{a_{n+1}^2}\right)-\log(L)\,\right|\le\frac\epsilon2\tag5$$ Since $(5)$ is true for any $\epsilon\gt0$, we have $$\lim_{n\to\infty}\frac1{n^2}\sum_{k=0}^{n-1}\sum_{j=0}^{k-1}\log\left(\frac{a_n\,a_{n+2}}{a_{n+1}^2}\right)=\log(L)\tag6$$ Taking the limit of the right hand side of $(3)$ as $n\to\infty$, we get $$\lim_{n\to\infty}\frac{\log(a_n)}{n^2}=\log(L)\tag7$$ which implies $$\lim_{n\to\infty}\sqrt[n^2]{a_n}=L\tag8$$

• It's great that you posted your answer here. By the time I saw your answer (to the old deleted question) it was in deleted state. +1 – Paramanand Singh Jun 29 '18 at 8:47
• Not surprising, since it was only there for 18 seconds. – robjohn Jun 29 '18 at 11:50

This is not another solution, but is the essence of your solution worked out by me individually.

If $L>0$,

By two applications of Stolz-Cesaro theorem,

\begin{align*} \lim_{n\to\infty}{{\ln a_n}\over{n^2}} &=\lim_{n\to\infty}{\ln{\frac{a_{n+1}}{a_n}}\over{2n+1}}\\ &=\frac{1}{2}\lim_{n\to\infty}{\ln{\frac{a_{n+1}}{a_n}}\over{n}}\\ &=\frac{1}{2}\lim_{n\to\infty}{\ln{\frac{a_{n+2}}{a_{n+1}}-\ln{\frac{a_{n+1}}{a_n}}}\over1}\\ &=\frac{1}{2}\lim_{n\to\infty}\ln\Bigg(\frac{\big(\frac{a_{n+2}}{a_{n+1}}\big)}{\big(\frac{a_{n+1}}{a_{n}}\big)}\Bigg)\\ &=\frac{1}{2}\lim_{n\to\infty}\ln\frac{a_na_{n+2}}{{a_{n+1}}^2}\\ &=\frac{1}{2}\ln(L^2)\\ &=\ln L\\ \therefore\lim_{n\to\infty}\sqrt[n^2]{a_n}&=L \end{align*}

If $L=0$, \begin{align*} \lim_{n\to\infty}{{\ln a_n}\over{n^2}} &=\lim_{n\to\infty}{\ln{\frac{a_{n+1}}{a_n}}\over{2n+1}}\\ &=\lim_{n\to\infty}{\ln{\frac{a_{n+1}}{a_n}}\over{n}}\\ &=\lim_{n\to\infty}{\ln{\frac{a_{n+2}}{a_{n+1}}-\ln{\frac{a_{n+1}}{a_n}}}\over1}\\ &=\lim_{n\to\infty}\ln\Bigg(\frac{\big(\frac{a_{n+2}}{a_{n+1}}\big)}{\big(\frac{a_{n+1}}{a_{n}}\big)}\Bigg)\\ &=\lim_{n\to\infty}\ln\frac{a_na_{n+2}}{{a_{n+1}}^2}\\ &=-\infty\\ \therefore\lim_{n\to\infty}\sqrt[n^2]{a_n}&=0 \end{align*}