2) P(V,T) = "RT (assume the number of particles/moles n is constant)

Q: 2. Solve the boundary-value problem = 4, y(0,t) = y(5,t) = 0, y(x,0) = 0, y.(x,0) = 5 sin rx. %3D

A:

Q: 2. Solve the general solution for the First Order Linear DE. удх %3D (еУ + 2ху — 2х)dy

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Q: (1) Use the trapezoidal rule and (2) Simpson's rule, with n= 10, to approxima te the integral. Round…

A: Topic : numerical methods

Q: Find a general solution of each reducible second-order differ- ential equation y" + (y')² = yy'

A:

Q: 1 1-xl-x²-y? Evaluate the integral S S [dz dx dy 0 0 0

A: We will evaluate the given integral in this question.

Q: Solve the initial boundary value problem described by = c*u , x>0, t>0 with the data: и(х, 0) — 0,…

A:

Q: 3. Find the solution of the initial boundary value problem (IBVP) Un = Ux for -0 0 (x,0) = xsin(x),…

A:

Q: Suppose that o(x, y) = e"-y and ø(ln 2, In 2) linear approximation to estimate o(ln 2 + 0.1, lIn 2 +…

A: Given that Φ(x,y) = ex-y and Φ(ln2,ln2)=1. Now by using the technique of linear approximation we…

Q: Find the temperature u(x, t) in a rod of length L = 2 if the initial temperature is f(x) (0 < a < 1)…

A: To find - The temperature u(x,t) in a rod whose length is L=2 and if the ends are insulated from 0…

Q: (9) Use Euler's method to estimate y(8) to estimate the solution to y' = y – 2x, y (0) = 1 Use n = 4…

A:

Q: Consider the initial value problem sin(t)y" - ,y + r*y= In -, y(3) = -1, y'(3) = 57. Without solving…

A: Uniqueness and existence theorem: Let p, q, and g be continuous functions on an open interval I such…

Q: 3 Estimate e2* sin(x) dx 1 using the Trapezoidal Rule with n = 1,2,4 and 8 segments 2) using Romberg…

A: Part (1): (a)The trapezoidal rule stats that:

Q: Find the solution to the boundary value problem: dy dy 14- dt + 85y = 0, y(0) = 8, y(7/12) = 2 dt?…

A: We have to find

Q: Use two different methods to calculate dzu/ar if u = /x² + y². = est, and y = 1 + s² cosz. IUse two…

A:

Q: SVEsin(1+ VF )dz 4 Vz sin .3

A:

Q: Suppose that (r, y) = e-v and o(In 2, In 2) = 1. Please use the technique of linear approximation to…

A:

Q: Find a particular solution to y" + 5y' + 6y = lte".

A:

Q: 2z+1 37 Prove the equation through integral calculatipns. dz < 5+z? 2

A: We will do the proof step by step.

Q: (1,0) C is the path from (1, v2) to (1, 0) along line segments as shown in the figure above. Then…

A: The application of line integral is, it represents the work done by a vector function acting along a…

Q: 8 2 1. Reverse order, then integrate Sr) dydx.

A: Given:    Intergral is given

Q: 2 Find つえdy 2 こ( beny s)

A:

Q: (a) Solve the initial boundary value problem by separation of variables : Utt = 4u7z 0 0, u(0, t) =…

A:

Q: 3 by taking n= 6 [In x · dx solution of the integral with Simpson's • method 3. (y, + y2 + y4 + y3 +…

A:

Q: Use Finite-Difference method to approximate the solution of the BVP boundary value problem y" – 3y'…

A: Given,  y''-3y'+4y=sin x, y(0)=9.8, yπ4=15.9  We Use the following approximations,…

Q: Find a general solution of each reducible second-order differ- ential equation y" = 2y(y')3

A: Given the differential equation:

Q: 2 1. The cissoids y : %D а —х

A: Given the equation  of cissoids y2=x3a-x As per our guideline we are supposed to answer only the…

Q: Find a general solution of each reducible second-order differ- ential equation yy" + (y')² = 0

A:

Q: Зуdy 14. 5y 7

A: Consider ∫3y dy5y-7 = 3∫y 5y-7dy= 3∫155y5y-7dy=  3∫155y-7+75y-7dy=  3∫155y-7+755y-7dy=…

Q: If r = (3 cosh 2t)i+ (3 sinh 2t)j+ 6tk and t = In 2 then اخترأحد الخيارات

A:

Q: 2 Suppose that T (x, y, z) represents the temperature at the point (x, y, z), measured in ƏT Kelvin.…

A: Introduction: In differential geometry and vector calculus, the partial derivative is used. The…

Q: 8 Evaluate the integral dx using the two-point Gaussian quadrature rule. 16+z1 -2

A:

Q: -2 Evaluate the integral: ² ft² n s teu du ds dt

A:

Q: 2nd Case (IBVP Summary) (Ut = 1.5uxx, 0 0 Ux(0, t) = 0, ux(6 ft, t) = 0, t > 0 (u(x,0) = 80°F, 0<…

A:

Q: Solve the second order bom boundary value problem : y"+y' +2Y=0 where y(0)s263 and y'lo) =27o.

A: We solve the given initial value problem  y"+y'+2y=0 with initial conditions  y(0)=263,y'(0)=270.

Q: Solve the intial value problem where y(-2) =0: (6e^3y +1)(x+1)dy - xeydx = 0

A:

Q: 4 a2 Calculate the integral: dx (2² + 7)/2 4 Va2 + 7 a) Vz? + 7 +C + 4 ln V7 4 x b) O x + Vx² + 7 +…

A: From the given problem:   I=∫4x2x2+732dx ........(1)   Let,…

Q: 1st Case A 6-ft long rod (laterally insulated) has a thermal diffusivity of 1.5 ft2/hr and initial…

A: For (1), Let us first create the system in both cases and then we will be finding the general…

Q: Use Euler's method to estimate y(8) to estimate the solution to y' = y – 2x, y (0) = 1 %3D Use n = 4…

A: Given differential equation is y'=y-2x, y(0)=1.

Q: 3 In (sec v) 2t Evaluate the integral ex dx dt dv. 00

A: Topic = Integration

Q: Solve the initial value problem Ut + 2uz = 1, x € R, t e R u(0, x) = e¯*, x € R. %3D

A: The differential equation is given as ut+2ux=1 The Lagrange equation is given as dt1 = dx2 = du1 On…

Q: per integral test, (-1)" A) Σ B) none of these en (-1)" dz behaves like

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Q: In - dy + (csct) y = ²n (- + == ), 4(-4)=3 1 -7²-25 dt

A:

Q: Find a general solution of each reducible second-order differ- ential equation y" = (x + y')²

A:

Q: Find the solulion of the intial value problem y=ty, yl=-1

A: Given equation :

Q: Find a general solution of each reducible second-order differ- ential equation y" = (y')2

A: Given, The differential equation y"=(y')2 .               ................(1)

Q: The heat distribution of a long thin rod can be determined by given heat- conduction equation aT OT…

A: In this problem, different conditions are given in the diagram and in the question. so anyone must…

Q: 2. Integral A e3A dA

A:

Q: #3. Solve the fallowing Caucly problem in R" x(0, 0) Uf-Ou t cu =0 on IR"x{t =0}. U = where c is a…

A:

Q: Show that there are infinitely many solutions to the boundary value problem y′′ + 4y = 0, y(0) = 0,…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.