B.C. IC. Solve completely to the final form of the solution as a Fourier Series the heat equation boundary value problem (homogeneous PDE, periodic BC.): xe ,L] L=1 k = 0.2 tzo باد پاپایا Ulo,t) =ull,t) 2u (0₁ t) = ax 2u (Lt) 2x ulx,0) = 1 + 2x 2² μ = 22u 2x² = k du 2t

Q: Find F(w) for f(t)=1 00 Oe-6 O 19 -13 3 9 2²4e-120 16 e-12w 144+x²

A: Let

Q: dy Find eigenvalues & eigenvectors. = [²:2] Y dt 3-2

A:

Q: Show that the following functions are convex by verifying the definition, i.e., that. f(x + (1-A)y)…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: 9. A ball is thrown upward from the roof of a 25 m tall building. The ball reaches a maximum height…

A:

Q: A regional municipality is studying a water supply plan for its tri-city and surrounding area to the…

A: Present worth at year 2030Hence, present worth at year 2030 will be $158.147096 million

Q: 5. Marc is asked to simplify the expression √3-√75. He says that since the radical you -------- ----…

A:

Q: and Consider the subspaces X = U = span{ [-1 −4 −4],[7 −11 −14]} W = span{ [-4 5 3],[5 2-3]} of V =…

A:

Q: A graph of -x³+4x²-3x-18 is shown. Use the graph to solve x² + 4x²-3x-1820. YA 20 -A 10 x³+4x²² 3-18…

A:

Q: Determine the completely factored form of Ax)-x³ +5x²-x-5. O a) (x+5)(x² + 1) b) (x+5)(x+1)(x-1) c)…

A: Determine the completely factored form of f(x) = x^(3) + 5 x^(2) - x -5

Q: 4. (i) For an odd number n, suppose that 2" #2 mod n. Can n be a prime? Explain. This is called the…

A: Eulers and fermats little theorem will used

Q: (14) Find two different reduced systems of residues modulo 8.

A:

Q: a) State the intersecton of an indexed family of sets.

A: According to guidelines we can do only first question thank you .we have to state the intersecton…

Q: Exercise 6.1.10: Find the inverse Laplace transform of 251

A: We have to find the inverse Laplace transformation of the given function.

Q: Find the inverse of the function on the given domain. ƒ-¹ (x) = f(x) = (x6)², [6,∞)

A: Given function is f(x) = (x-6)2 ,[6, ∞).We have to find out the inverse of f.

Q: do you keep flipping inequalities to end up at =2/m? Also, if it Xn - Xm, wouldnt it be (1+1/n) -…

A:

Q: The differential equation y"" + ay" +by" + cy' + dy = 0 has a solution y = -5test - 6e³t cos(2t) for…

A:

Q: Use the Theorem of Pappus to find the volume of the given solid. the solid obtained by rotating the…

A:

Q: 1. Find the Taylor or Laurent expansion of the following functions at zo = 1 Z (1) z²-2z+5² (2) Z…

A:

Q: We learned how the diagonal on the unit square lead Pythagoras to discover not all magnitudes are…

A: We first draw the diagram using ruler and label the figure.

Q: A line cuts the x-axis at A(7, 0) and the y-axis at B(0, -5). A variable line PQ is drawn…

A: A line cuts the x-aris at A(7, 0) and the y-axis at B(0, -5). A variable line PQ is drawn…

Q: Find the particular solution of the differential equation x²y" + 8xy' +12y = 1x 4 y'(1) = 42.…

A: We have to solve the differential equation.

Q: Let y = -6 0 d U₁ 6 -6 -1 142 = -2 4 -36 Compute the distance d from y to the plane in R³ spanned by…

A: Given That: First find the closest point in the plane spanned by this is given by Now:

Q: Assume that the sequence shown below converges and find its limit. √3, √3+√3,√√3+√3+√3 √3+₁ " 3 +…

A:

Q: 3 2 7. ty'-2y=t³ sin(2t) − t³ +4tª; y(n)= · Use a graphing utility to draw a graph of the solution…

A:

Q: Find the null space for the given matrix. (A graphing calculator is recommended.) 20 4 2 3 3 -1 4 1…

A:

Q: Find all the zeros. Write the answer in exact form. 4 q (x) = 2x² - 7x² + 3x² +8x-4 If there is more…

A: In this question we will find the zeros of the polynomial.

Q: The number of elements in a finite field of characteristic p is of the form p\power{n}, where n…

A: We have to prove given statement , which is that "The number of elements in a finite field of…

Q: 4. Consider the matrix -a -a (a² + a) 0 0 0 -2a 0 -(2-a²) 2+4a-a² -2a Find all values of a for which…

A:

Q: Find the least squares solution of the inconsistent linear system x₁ + x₂ + x3 = 3, X3 = 1, + x3 =…

A:

Q: Find Q for the QR factorization of A Q = Ex: 1.23 V1 = J]-[ 1 0 -3 0 2 -30 0 -10 3 -30, V3 = -2]…

A: Given  and the orthogonal vectors are                 ,     ,            Now normalized the above…

Q: Let A, B,C M.(R) be three square invertible matrices with real coefficients. Solve the following…

A:

Q: y" + y = secx tan x

A:

Q: Prove there is no real number a such that 28 + x6 + 1 = 2x³

A: The given equation .The aim is to prove the equation has no real solutions.

Q: This problem mainly tests your calculator skill. I would like you to do as much as you can on the…

A: A point of inflection on the curve at which the concavity change. i.e., the sign of the curvature…

Q: Suppose f(x, y) = x² + 2xy + y². Which field plot is Vf? Justify your answer. 7

A: We have to find the field plot of  where

Q: 40 -40 y²2√6400 – 4y²dy

A:

Q: Supose you have a number 12340 that has a prime factorization of 22*5*617. What are the solutions to…

A:

Q: Let p be a given Natural Number. Give a sequence (XN) that is not a Cauchy sequence, but it…

A:

Q: Use traces to sketch the surface: x² = 36y² + z²

A: Given surface :Use the traces to sketch the given surface

Q: Let f(x) := x² for x∊R, and let E := {x∊R : -1≤x≤0} and F := {x∊R : 0≤x≤1}. Show that E∩F = {0} and…

A:

Q: Let f(x) := x² for x∊R, and let E := {x∊R : -1≤x≤0} and F := {x∊R : 0≤x≤1}. Find the sets E\F and…

A: Given, f(x) := x² for x∊ R,  E := {x∊ R : -1≤x≤0} and F := {x∊ R : 0≤x≤1}.

Q: One root of the equation 2x + x³ + 4x + 2 = 0 is O a) 1/1/2 Ob) -2 Oc) - 1/12 d) 2

A:

Q: Determine the value of k so that 3x - 1 is a factor of 3x³ + 8x² + kx-2. a) k = 3 b) k = 1 c) k=-1…

A:

Q: Find a basis for the orthogonal complement of the subspace of Rª spanned by the following vectors.…

A:

Q: The table to the right categorizes 25 senators as to political party and gender. One member is…

A: .

Q: Let L₁ be the line passing through the points Q₁=(4, -2,-4) and Q₂=(3, 1, -7) and let L₂ be the line…

A:

Q: Consider the following Linear Programming model: Z Except the right hand side values, the optimal…

A:

Q: Problem 26. Consider the following equivalence relation on the set A = {1, 2, 3, 4, 5, 6): Find the…

A:

Q: Find y'(0) and y"(0) from the following table ofvalues: X 0 1 2 y 4 8 15 3 4 7 6 5 2

A: From the given table upper digits are values of X and lower digits are values of Y(X).

Q: The total body surface area, or BSA, of a human is difficult to calculate. There are various models…

A: