Suppose T is a linear transformation such that [5] 1, T A 5 -1 = 1, T 3 T2 = -6 3 5 2 Find A such that T(x) = Ax.

Q: Determine y(t) y" - 2y' + y = 4e-t + 2et, where y(0) = -1, y'(0) = 2

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Q: Let S {(a,b): a,be R, a 0}. Show that the relation R defined on S by (a, b) R(c,d) if = ad be is an…

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Q: Find the volume of the solid generated by revolving the - area bounded by x² − 2kx − 3ky + k² = 0…

A: The given curves are  x2-2kx-3ky+k2=0                 …13x-3y+k=0                 …2 The given line…

Q: 1. A function f is defined by 1 2 = + 3 4 f(x)= x + 3 32 33 34 for all in the interval of…

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Q: Determine whether the equation is exact. If it is exact, find the solution. If the differential…

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Q: Use modular arithmetic to determine the following:  Disregarding a.m or p.m., if it is now 9…

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Q: 2z 2z x+y Q3 Show that z= satisfies the equation x+y=0 2x 2y x-y

A: Sol

Q: The fifth term of a sixth term is 1215. nine terms. a) 147 615 b) 8100 geometric series is 405 and…

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Q: 2. The Dual model a. Is derived systematically from the Primal model b. provides the decision maker…

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Q: 2) 1 y = ²+² x= cos(t). y = sin² (t).= =-. at t = 3 t

A: Solution of the given problem is below...

Q: woman walks directly tow

A: Given that a wall lamp is positioned /ft up a wall. A oft tall woman walks directly towards the…

Q: In each of Problems 19 through 22, The given differential equation Descr

A: Given,           y'=-y3-ty

Q: [² f(x) dx, where f is the function whose graph is shown. The estimates were 0.7818, 0.8684, 0.8631,…

A: Here is the given graph of the function fx as Also, given as, the left, right, Trapezoidal, and…

Q: Q2-By using Chain Rule, find au/ax, du/dy, du/dz at (x, y, z) = (√√3,2,1) U= p-q q-r p=x+y+z…

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Q: 22) (a) Show that the relation {(0,0), (1,1),(1,2), (2,1), (2,2), (3,3)} is an equivalence relation…

A: We can solve this using given information

Q: Find the value of b for which the differential equation (ye¹0xy + x) dx + (bxe¹0xy) dy = 0 is exact,…

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Q: You deposit $100 each month into an account earning 6.3% interest compounded monthly for 30 years.…

A: Here given  Principle amount P=$100 rate r=6.3% time t=30 years,

Q: 3. Use a straightedge to draw the xy axis for your graph. On the x-axis label the points spaced…

A: Vertical asymptote of a curve: y=f(x) is the line such that the distance between the line and the…

Q: Prove: A bipartite graph with an odd number of vertices does NOT have a Hamilton Circuit.

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Q: b) Consider the following Linear Programming (LP) problem: Maximize z = 3x₁ + 2x2 Subject to 2x₁ +…

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Q: Why is it necessary to get acquainted with the sigma notation's properties?

A: Yes, it is necessary to get aware of sigma properties . It help mathematics to improve itself.

Q: For item 17-18. Let R be the partial ordering on A = {1, 2, 3, 4, 8, 12} defined by xRy if and only…

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Q: 33. Find each interior angle measure of a quadrilateral if its interior angles are represented by x…

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Q: [20 0 -1 1 0 -2 -1] a) Find the characteristic polynomial of A. b) Find the eigenvalues of A. c) For…

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Q: Let n ∈ Z. Prove that if n is divisible by 3, then n = 6k or n = 6k + 3 for some integer k.

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Q: 1. If R is the region in the first quadrant bounded by x-axis, 3x + y = 6 and y evaluate 3x, Jf 3y…

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Q: Q5- Find the Maclaurin series generated by the following function: f(x) = sinh(x)

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Q: 5- y' (sin² 2x) (cos² y)

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Q: Set up the integrals for the mass and center of mass of the tetrahedron bounded by 2x + y + 4z = 4…

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Q: Find the nth root of the matrix B. An nth root of a matrix B is a matrix A such that A = B. 64 0 0 B…

A: The given matrix is                      B=64000-1000343. B is a diagonal matrix matrix. Here we…

Q: 6. Compute the following integrals using Residue Theorem. 5z - 2 a. dz S dz b. So 22(2-1)" z(z-2)4…

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Q: 37. Solve the equation where a, b, c, and d are constants. dy dr ay+b cy + d'

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Q: 2. If Mr. Eugene is the manager's neighbor, then Mr. Eugene lives halfway between Talisay and…

A: We can use formal proof of validity.

Q: Solve the initial value problem. y dy dx = 9x ex, X The solution is y(x) = 9x ex - 5x. y(1)=9e-5

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Q: Solve the equation. dx = 8xt² dt An implicit solution in the form F(t,x) = C is = C, where C is an…

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Q: A relation R is defined on Z by xRy if and only if 8 divides 3x + 5y. Prove that R is an equivalence…

A: This is a question from relation.

Q: Create a third order, non-linear Ordinary Differential Equation with enough initial values to be…

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Q: -kr i) Using the Cartesian position vector r, show that V (1) - ||r||*+2* ii) Consider some…

A: As per the question we have to : Prove the equality involving the gradient of the inverse norm of a…

Q: Q5- Find the Maclaurin series generated by the following function: f(x) = sinh(x)

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Q: 36. The fastest average speed by a cyclist across the continental United States is 15.4 mph, by Pete…

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Q: Consider the following subsets of real plane R² A = {(0,y): ≤ y ≤ 1} B = {(x, y): 0 ≤ x ≤ 1, y =…

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Q: Q2. Let a vector A = [8-463] a) Compute the square of each element. b) Compute the square root of…

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Q: Homework 4. Show that the following are metric on R": d₁(x, y) = max₁sisn |X₁-yil; d₂(x, y) = -1 |x₁…

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Q: lim-2 x³-x²-√2x x²-11x+18

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Q: 2 A sales representative's orders for May were 16% less than her April orders, 3 which amounted to…

A: Here we have given that, Sale for April is $51120. Sale for May is 1623% less than April. a) So, we…

Q: a) Make a b) Show that if with |K| list of all subgroups of Q8 K is is a subgroup of Qs. k is…

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Q: CQ 13 A hot metal bar has temperature 260°C. The metal bar is placed in a 20°C room where it cools…

A: Given that a hot metal has a temperature of 260°C. It is placed in a room where it is cooled down…

Q: Prove that sin²x x cos²x x = csc²x-cot²x 4csc²2x

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Q: Please help with this question: Find the equation of the line or plane  a) Plane parallel to the…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 4. Express each of these statements using predicates, quantifiers, logical connectives, and…

A: We know that ,  A Predicates is an expression of one or more variables defined on a some specific…