5. Show that b, is always positive, by establishing the equation (Qn-1,Qn-1) (Qn-2,Qn-2) b,

Q: Find the general solution to the yiven Euler x* j -3xy = 2.

A: Given differential equation is x^2y" - 3xy' + 9y = 0

Q: Find the two smallest positive solutions of 5sin(5x)=3

A: 5sin(5x)=3 sin(5x)=.6 sin(5x)=sin36.87°

Q: 1. If x=27-3k and y = i +5j -4k, express each of the following in terms of i, j, k b) 2(3x+y)-3(4y…

A: Given x→=2i→-3k→ & y→=i→+5j→-4k→To write expression in terms of i→,j→,k→:

Q: Verify that (AB)T = BTAT.

A:

Q: 1. Use Cramer's Rule to show the solution of -24 +7x-10y 1+ (3/7) y = (-5/18)x

A: We have to solve the given system of equation by Cramer's rule

Q: Consider the problem maxx [-(x - 4)]² subject to x21. Use Thus the Kuhn-Tucker conditions to find a…

A: We are given the following problem.       maxx -(x-4)2       Subject to x≥1 Let us simplify the…

Q: 10- Solve the problem: Utt-4uxx = xt, 00 u(x,0) = x, 4(x,0) = 0, u(0, t) = 0, Ux(1,t) = 1+t, t20 %3D

A: Given, utt-4uxx=xt;   0<x<1, t>0 ⋯⋯⋯⋯1ux,0=x,   utx,0=0,   0≤x≤1,⋯⋯2u0,t=0,   ux1,t=1+t,…

Q: The set of of solution of x2 - 5x+ 6 0 in Z12 is (a ).{2,3,4} d){2,3,6,11} (b) {2,3} (c) {.2,3,6}

A: Hence option (b) is correct.

Q: 3) 12 Glven a = Solve for Vo-

A: Given a=vf-votWe now solve for vo

Q: 1 find a- w = +y b- w = tan-¹2 az w a²w ах дуа

A:

Q: Compute Re if z₁ = 5√√2 + 2√3i, and z2 = 3√√√2-5√3i 2

A:

Q: Prove that the equation ! + = 1 has no solutions in positive integers æ, y, z.

A:

Q: Chapter 13, Section 13.6, Question 001 Find Duf at P. S(x, y) = 3(1 + xy); P(1,3); u = Enter the…

A:

Q: Let x = (3,-1,0) and y = (0,1,5). a) Show that no choice of numbers a and b can make ax + by =…

A:

Q: 3. Show that (1+i) = 2i

A:

Q: Use the equations aF OF az ax az ay and ax OF ду OF az az az az and ax to find ду 5yz + 8x In(y) = =…

A: F=5yz+8xln(y)-z2∂F∂x=8ln(y), ∂F∂y=5z+8xy, ∂F∂z=5y-2z∂z∂x=8ln(y)5y-2z, ∂z∂y=5z+8xy5y-2z=5yz+8x5y2-2zy

Q: 5) For what value of µ have the following homogenous equations non trivial solutions? . (1– µ)x1 +…

A:

Q: Solve the problem. 14) If u = -9i – 2j and v = -3i + 7j, find u V.

A: Let us consider two vectors u=ai+bj and v=ci+dj then u-v=(a-c)i + (b-d)j

Q: 5. Find all points at whi

A: 5. Given curve C with parametric equations   C: x(t)=2cost, y(t)=8sint We have to find all points on…

Q: 2. The exact value of sec 57 is O2 2V3 -2 2V3 3

A:

Q: 1. Given that r + px+q and 4x +q have a factor (x-r) where p,q and r are non-zero. Show that 4p…

A: topic - quadratic equations

Q: В. a = lass)-(21-1) given that w= In(6x + 2y³ – 3z).

A:

Q: For which values of a does ax = 1 have a solution in Z5?

A:

Q: 1 Show that xn-m)}-2X(2). assu me. Zera 1c

A: As per the company's rule, we are supposed to solve one problem or three subparts. As there are two…

Q: 12. Solve the problem: Utt = c*upx + Ax, 0 0, A= constant, и (х,0) — 0, и (0, t) — 0, Ut (x, 0) =…

A:

Q: 1. Show that (a) exp(2±3лi) = -e²; (c) exp(z+лi) = - expz. πί p ( ² + 7² ) = √ = (1 + i); 4 (b) exp

A:

Q: 6. Show that (1) Cou(B1, g) = 0 (2) Cov(3o, B1) %3D

A:

Q: 38) - con A) 0 sec B) 5π T, 13л 5т D) 0 3 12 12

A: Find the value of x which satisfy sec(x/2)=cos(x/2)

Q: 4) To find the root of the equation x² - 3 = 0 using the fixed point method in [1,2], one of the…

A: The given problem is to find the iteration formula for finding the root of the given equation x2-3=0…

Q: Find the value of m that makes: Show that the equation  xex-1=0 has a unique solution on [0,1].

A:

Q: 8. Solve the Cauchy-Euler equation 4x²y" + 8xy' + y = 0.

A:

Q: 1d. Show that the given equation x- In xX= 0, has a root in the interval [4, 5].

A:

Q: 5] compute: 7A -5B where: 2+3i itqi -si A = 3+7i -4 ?b-8 7 3ti 2+si ?5-8 5-2i -4-3i 8ミ チ+

A:

Q: show that x'-15x +C= O has at most root on E2,2] one

A:

Q: :Use inverse matsix (by Gauss Jordan an Elimination) to solve the syálem 2x + By +3 = - 1 %3D 2x…

A: Consider the given equations 2x+3y+z=-13x+3y+z=12x+4y+z=-2 The given equation can be written as AX=B…

Q: Show that the equation In(x + 1) = In(x²) has at least two real solutions.

A: we need to show that ln(x+1)=ln(x2) has at least  two real solutions.

Q: 3 If A = 1] show that A² - 5A + 7I = 0. %3D %3D -1 2

A:

Q: 5. Solve the problem kuxx = xt, u(x,0) = 0, u₁(x,0) = e, Utt - kuxx -∞ 0 ∞ < x < ∞ ∞<x<∞ -

A: Given is the pde. The objective is to find the solution. The solution is for this type of pde is…

Q: For which values of a and m does ax = 1 have a solutionin Z m?

A: To find for which values of a and m does ax=1 have a solution in Zm. Zm=0,1,2,....,m-1 when a=0,…

Q: Prove Equationally that A, B H A = B.

A: Given:                       A, B ⊢ A≡B To do: Prove the given statement equationally.

Q: #9a using Descartes's rule of sign

A: Given equation is,

Q: 9. In OP, QR = 7x – 20 and TS = 3x. What is x? -

A: Joining QP and TP, we get the radius of the circle.

Q: The set of solutions to z^6=−i is?

A: We have to find The set of solutions to z^6=−i.

Q: 1. (a) Let 5 -6 -6 B = |-1 4 2 3 -6 -4 Find oigon nigon un imil to D

A: To finding the eigenvalues and eigenvectors to the given matrix we use Gaussian elimination method.…

Q: 2. Sketch 0 in standard position if cose = 8. and deter %3D

A: Given that: cosθ=-817

Q: of dr? e-ex

A:

Q: dt 7) /2-t

A: 7).∫-∞-2dt/2-t                         = ∫-∞-2(2-t)-1/2dt

Q: Find a number 8 such that if |x – 2| < 8, then |4x – 8| < ɛ, 11) where ɛ %3D 0.01.

A: Ffind the delta

Q: 4. Find the solution to the IVP in explicit form and determine the interval in which the solution is…

A: y'=3x2-ex2y-5dydx=3x2-ex2y-5(2y-5)dy=3x2-exdx Integrate both sides