22 32 S[ (4-y ) dydx 1. ans:- 3 0 0

Q: Sum of seriy n=1 2"+1 4ª

A: Explanation of the answer is as follows

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 1 + e2t L{f(t)} =

A:

Q: fraluate |-S)t

A:

Q: Solve for a A/20 + 4/15 = 9/15 Leave as improper fraction

A:

Q: Let W be a plane in R³. Let P be the matrix of the projection onto W and let R be the matrix of the…

A:

Q: b. y = 4x (2x-1)⁹

A:

Q: Recall that X = 0(t)-1(to)X, + (t) -(s)F(s) ds solves the initial value problem X' = AX + F(t), X(t)…

A:

Q: Use X = eAtC to find the general solution of the given system. %3D 0 0 0 X' =5 0 0X 7 10 X(t) = %3D

A: We will find eigen values and corresponding eigen vectors  of the equation to get general solution

Q: 3 LS 2dydx = 4 %3D О 20 30 О 30 О 15

A: Integrate the given double integration in given order. First Integrate with respect to y and than…

Q: Suppose that dP/dt- 0.14P(t) represents a mathematical model for the growth of a certain cell…

A: Given:the growth of a culture at time t is dPdt = 0.14P(t)P = 2 million cells

Q: S sec4e tan30 de

A:

Q: The matrix: A = B a11 a21 is the inverse of the matrix given by: b (a (²5) C d ie: A = B-1 || a12…

A:

Q: Use (1) in Section 8.4 X = eAtc (1) to find the general solution of the given system. 1 0 X' = X(t)…

A:

Q: 4. Sdx

A:

Q: Use the Laplace transform to solve the given initial-value problem. y' + 5y = e3t, y(0) = 2 y(t) %3D

A:

Q: integral 2200e0,024t

A: To find: The integral of ∫2200e0.024tdt. Formula used: Integration formula: ∫ea·tdt=ea·ta+C…

Q: tion 10 37 = 1 8z + 9 or z:

A:

Q: QUESTION 2 Two random variables X and Y have the following joint probability density function. f(x,…

A: As mentioned I have done 4th part using the concept of variance.

Q: Express the quantity S².

A:

Q: For the samples r(tk) = 4,2,6, –1, plot the "sinc" interpolation function. In your %3D opinion, does…

A: The basis function used in 'sinc' interpolation is : sinc(t) = sin(πt)/(πt)  when t≠0  and  1  when…

Q: 12X dx (x+9)0

A: We know, ∫xndx= x(n+1)/(n+1) Let I= ∫12x/(x+9)⁶ dx

Q: Suppose that dP/dt - 0.18P(t) represents a mathematical model for the growth of a certain cell…

A: Given that dP/dt = 0.18 P(t)  Where P(t) is the size of culture at time t.

Q: Solve the differential equation by variation of parameters. 4y"-y = ex/2 + 6 y(x) =

A:

Q: October 7, 2021

A:

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A:

Q: SeC secfe de

A: The given integral is: I=∫24 sec-2θ dθ

Q: Integrate X dx 1+ x²

A: Given, I=∫x51+x12dxOrI=∫x51+x62dx

Q: In a factory,that produces glass bottles, HH number of bottles are defected in 1000 bottles…

A: Given, Number of defective bottles = 2 (N) Total no. of bottles = 1000

Q: Se ſe2**** dx 2x+e* vii.

A:

Q: Find the general solution of the given second-order differential equation. y"- 10y' + 26y = 0 %3D…

A:

Q: 2 水 -4x (lx

A:

Q: Vz? – 25 4. -dz

A: use substitution method for solving the integral.

Q: Q: Evalunte 5 x²-2 up (x-2)² 3

A: Given