Consider the following IVP: x" - 4x' + 4x = 4e2t; x(0) = -1, x'(0) = -4 Find the general solution. A x(t) = e'(212– t-2) B x(1) = e2" (212– 21 – 1) x(1) = -e"(1– 212+ 1)

Q: Prove that if n is a +ive integer,

A:

Q: Theorem 3.59. If T is normal, then the eigen-spaces corresponding to distinct eigenvalues of T are…

A:

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = L, (1, 2, 2)

A: This is a problem of vector calculus.

Q: Solue paramefer methrde ezE

A: Method of Variation of perameters

Q: Give the coordinates of each vertex of the box in the graph. E 8 D 10 A: B: ( C:( D: ( E: F: G: ( H:…

A: In this question, we have to find the coordinates of the points  A, B, C, D, E, F, G and H.

Q: . Verify Stoke's theorem for the vector field F = (2x - y) I- yzJ-y:K ove the upper half surface of…

A:

Q: Find the coordinates of the image. Ry-axis (S) -- -3 Ry-axis (S) = (Type an ordered pair)

A: Given : The coordinates of a point S is (-3, 4) To find : We have to find the image of S under…

Q: Let U= { 1,2,3,...,20}. Let A, B, C be the subsets of U. Let A be the set of all numbers, which are…

A:

Q: converges weakly to x in a normed linear sp

A: We given that ( xn ) is a weakly convergent sequence to x in normed linear space X , then we have to…

Q: At a price of $4.81 per pound, the supply for cherries is 16,130 pounds, and the demand is 10,348…

A:

Q: The functionf:R->R defined by f(x) = (x2+ 1)35 for all x e R is A. One-One but not onto O B. onto…

A:

Q: If x is a continuous random variable, then the total area under the probability distribution f(x)…

A: For a continuous probability distribution, a curve called a probability density function or pdf…

Q: Question 2 In this question we are considering the vector space P2, which is the collection of all…

A:

Q: Which of the following is the general solution to the differential equation (Зх + 2у + 4)dx+ (3x +…

A:

Q: Answer each question correctly. Show your complete solution The complex number 2 + 4i is one of the…

A:

Q: { - (2)*} |리 > 2 z – 2 |리 > 2 z + 2 |리 > 2 z – 2 |리 > 2 z – 2 3.

A: The given problem is to find in which complex expression the given term {-(2k)} will be obtained. We…

Q: Question 12 Compute the orthogonal projection of u onto v. Use the square root symbol 'V' where…

A:

Q: The addition of matrices shown below gives: Гз 7 27 10 0 and [5 3 4] Г2 47 Li 3] А. Зх3 matrix B. 3…

A:

Q: The blue fgure is a diation image of the black figure. The labeled poirt is the center of diaton.…

A: Given:

Q: Given the matrix below and its corresponding rref(A) and rref(A') 1000 2 -1 -3 (10000 8 0100 3 A = -…

A: Use the given information.

Q: In standard normal distribution, what is the area between z = 0 and z = – 2.13 under the normal…

A: Given normal distribution

Q: Assuming that exam score is a normal random variable, determine the corresponding z-score of a exam…

A: Given Raw Score = 178 Mean = μ = 165 Standard Deviation = σ = 8

Q: Verify Stoke's theorem for the vector field F = (2x - y) I- yz*J-yzK over the upper half surface of…

A: Stokes theorem is used

Q: Find the roots using Bairstow's method of the function f (x) = x* – 2x3 + 2x² + 3x – 4. Use u, = 1…

A:

Q: Use Lagrange multipliers to prove that the rectangle with maximum area that has a given perimeter p…

A:

Q: Given the following, determine the solution vector using least norm solution. 2 -1 1 3 3 0 -2 5 1 -2…

A:

Q: 3. Consider the set e = {x = (r1, x2, x3, ...) E C* : i=1 consisting of all absolutely summable…

A:

Q: 8. 2z (z – 1)?

A:

Q: 6s 3 Find the Inverse Laplace Transform of + s²+25 s2+ 25 6 -cos3t – -sin5t 5 3 A B 3cos5t+ - sin3t…

A:

Q: If the cardinality of a set A is 4 and that of a set B is 3, then what is the cardinality of the set…

A:

Q: A vector v is in Null A if and only if A v = 0. Select one: O True O False

A: Given : A vector v and a matrix  A is given. To prove :  A vector v is in  Null(A) if and only if…

Q: Q3/ Assuming that Ø = x?y2 + y² z²+x²z? find AØ At the point (1, -3, 1) And what is a vehicle AØ ?…

A:

Q: Which of the following is NOT a characteristic of a normal curve? A The total area under any normal…

A: Which of the following is not a characteristic of a normal curve :-

Q: Solve by variation of parameters method (h) y" + y' = tan x

A:

Q: 5. when: Let be a relation where R = {(a, b): pair a,b are cross streets in city A}. Sh (a) (a, b) e…

A:

Q: Advanced Math Question

A: In this question, we have to identify the secant line, point of tangency, tangent line, chord, a…

Q: Find the eigen values and eigenfunctions the Sturm-Liouville problem : yu +Aj =o Yco) = 0, Y(7) = 0…

A:

Q: Find the following: A-1 x B-1. 7 -3 5 2 A = B = в -6 4 -5 3 0.11 0.03 A-1 x B-1: 0.21 0.09 0.31 0.03…

A:

Q: There is no clause that, when resolved with itself, yields (after factoring) the clause (¬P∨¬Q).

A: Design a truth table

Q: Find DF of fcxiy)=x²e° at the point (-2,0)-

A: Given function is fx,y=x2ey. We have to find the ∇f at the point -2,0. We know that ∇f=∂f∂xi+∂f∂yj…

Q: In Sl units, the position x of a spring-loaded electromagnetic valve varies over timet in the manner…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 3. f(t) = t cos(5t) + cos(2at) cos (3at)

A:

Q: Let V={(x,y)|x,y∈R}, with addition and scalar multiplication defined as u+v=(u1+v1,u2+v2) and…

A:

Q: Find the area to the

A: Given, the left of z=-1.96 or to the right of z =1.96.

Q: This problem is related to core exercise 31 (module 5) in the textbook, and requires you to do some…

A:

Q: dy What is the general solution to the differential equation -y = (2) sin x ? %3D dx y = x?(2x cos x…

A:

Q: A regular pentagon has sides of 20 cm. An inner pentagon with sides of 10 cm is inside and…

A: We have to find the area inside and concentric to the larger pentagon but outside the smaller…

Q: Consider the real Cartesian plane R^2, with lines and betweenness as before (Example 7.3.1), but…

A: Given, d(A,B)=a1-b1+a2-b2A=a1,a2 B=b1,b2To show:Axiom C1, C2, C3 holds                   As per the…

Q: by f(x) = (x2 + 1)35 for all x e Ris A. One-One but not onto B. onto but not one-one C. neither…

A: Given f(x) = (x2 + 1)35

Q: 8. [Geogebra Question] Let f(r) = VT+2³. Use Geogebra to approximate the area under the graph of…

A: