This is all there is to the question.
This is all there is to the question. 1.11. Find all polynomial solutions p(t, x) of...
Question 1: The separated solutions of the o fom u(x.t) -X(x)T(t), with the following solutions: ne-dimensional heat equation dtt lu solutions of are - X(x)-Ax +B and T(t) E X(x) = A cos kx + B sin kx and T(t)=Ee-Det The boundary conditions for a metal rod insulated from both sides arex aum = 0 when x =0, and dx (e) Using the boundary conditions for u(x.t) wrie the boundary conditions for XCx), explain for full marks. (b) Find the...
A polynomial P is given.
P(x) =
x3 + 64
(a) Find all zeros of P, real and complex. (Enter your
answers as a comma-separated list.
(b) Factor P completely
A polynomial P is given. P(x) = x364 (a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. Enter your answers as comma-separated list.) -4.2 +2i 3 .2-2i 3 X = (b) Factor P completely. P(x) (x-4)(x - 2+ 2i/ 3 ) (x -2-2/V3...
11. (adapted from 1.6 8) Prove the characteristic polynomial of matrix A - is p(x) = 12 - (a+d)X + ad-bc = 0. Show that p(A) = A - (a + d) A+ (ad - bc)1 = 0. 12. (adapted from 1.6 14) Suppose A has eigenvalues 0,0,3 with independent eigenvectors u, v,w. (a) Give the vectors span the nullspace and the column space. (b) Find a particular solution to Ax=w. Find all solutions. (c) Does w + u in...
Question on #2 parts a and b (second photo has
definitions).
2a. Write out A3+3 explicitly as a polynomial in r, s ,t 13 + u as a polynomial in the three elementary symmetric funetions in r, s, t the matrix 82 Let σ be a permutation in Sym({r,s,t) Lemma 10.1. then If σ has order 2, then σ interchanges A3 and μ that every permutation in Sym(ir,,t) fixes both 3,pe, every In any case, it follows Аз + 3...
State the degree of the polynomial equation. 31) 3(x + 6)2(x - 6)3 = 0 Find all of the real and imaginary roots, stating the multiplicity of each. 32) (x + 5)2(x - 1) = 0 Find the product. 33) (x - 7i)(x + 7i) Find all real solutions to the equation. 34) Vx + 13 = x - 7 Find all real and imaginary solutions. 35) -2x3 + 2x2 + 8x - 8 = 0
Question 2 ul lu (a) Find the solution u(x,t) for the 1-D wave equationfor -oo < x < oo with initial conditions u (x,0)-A(x) , where A(x) s presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and t, somewhat similar to f(x) on page 85 of the Notes Part 2. di+10 dı+15di+20 (b) Check for the wave equation in (a) that if f(xtct) (use appropriate value...
Find x intercepts of the polynomial: p(x)=(x-5)(x+2)(x-1)-30; . Show all steps
Fourier Wave Equation
Question 2 The function u(x,t) is governed by the wave equation 82u 182u 8x2 c2 8t2 Subject to the following conditions having c2 3 i. At x 0 and x-1, u 0 for all t 2 0. i. Whent 0, for sx s 1 Use the method of separation of variables to establish that the solution for u(x, t). From the solution established, given a condition t0, usinx(1 + cosx) for 0 s x s1. Find the...
Find the constant a and all the similarity solutions of the form х u (x, t) = F ta Ut = de 0 дх и
For the following polynomial function, find (A) the degree of the polynomial, (B) all x-intercepts, and (C) the y-intercept. f(x) = (5x + 3)*(x-1,5 (A) The degree of the polynomial is