Solve the initial-value problem where f(t)= = 2: y'-y = f(t), y(0) = 1 0 ≤t≤1 t≥1 1: in the following two ways: a) Using the Laplace transform b) By directly solving the first-order linear differential equation techniques discussed in previous chapters.

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A: (a) Area at We have given that now evaluated r and  at The initial area is

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

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Q: 3. Consider the curve which is the graph of the equation x³ + y³ − 3xy = 0. Graph this curve using…

A: Let f(x,y)=x3+y3−3xy=0Thendf=0∂f∂xdx+∂f∂ydy=0dydx=−∂f∂x∂f∂y

Q: Prove that if a = b (mod m) and if c = d (mod m), then a+c=b+d (mod m).

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

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Q: Why isn't region B -4 instead of positive 4?

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Q: Find the maximum value of f(x,y) = 31-x² - y² on the line x + 5y = 26.

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Q: Laplace transform of t² sin2t. [12s²-16] [2323 .(s²+4)². 35²-4 [(s²+4)³. [12s²-16 .(s²+4)6 O [12…

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Q: (b) Prove that if a = b (mod m) and if b = c (mod m), then a = c (mod m).

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

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Q: Compute the indicated 3 x 3 determinant. ab 0 0 a b a 0 b

A: The given problem is to find the determinant of the given 3*3 matrix.

Q: Use properties of determinants to evaluate the given determinant by inspection. 0 1 0 0 1000 0 0 1 0…

A: .

Q: Solve (y - 3)² = -54 for y y=3± √6i y = 3±3i y=3±3√6i y = 3+ 6i

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Q: Which statement isnt and can never be true? MA Sinx = COS X B COSX = 0944 sinx + cosx = tan x So 0 -…

A: We choose a statement which can never be true.

Q: 3. Find the lengths of the following curves. (a) x²/3 + y²/3 = 1. 1 (b) x = y√/y² − 1 − 1⁄2 ln (y +…

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Q: If X₁ >0 and X₁+₁=2 + x for N> 1, show that is a contractive sequence. Find the limit.

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Q: Compute the determinant using cofactor expansion along the first row and along the first column. 102…

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Q: Let F be a field and let n be a positive integer. Then There exists a primitive nth root of unity in…

A: Suppose that F be a field and let n be a positive integer. Then there exists a primitive nth root of…

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

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Q: Use the eighteen rules of inference to derive the conclusions of the symbolized argument below. Q S…

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Q: Find the least-squares line given the matrix products ATA 608.4 5942.2 A¹b- = y = Ex: 1.2 +Ex: 1.2 €…

A: Let us to find a least square line for the set of values {(xi,yi):i=1,2,⋯,n}Let the equation of line…

Q: 5. Consider X with the discrete metric. (a) Show that every subset of X is open and closed. (b) Show…

A: Consider X with the discrete metric. (a) Show that every subset of X is open and closed. (b) Show…

Q: . Let C be the curve parameterized by r(t) = (t(1 – t)(1+t), t(1 – t)(2 − t)) where t = [0, 1].…

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Q: Determine whether the matrix 024 A = 2 4 2 331 is invertible, and if it is, compute its inverse.

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Q: 2. Formulate the logical constraint for the following statements. (Where A, B, C, and D are all…

A: A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra,…

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A: Given that  be a linear combination of .

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Q: 3. Use the definition of a convex set to show that if S₁ and S₂ are convex sets in R+", then so is…

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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: Find the approximations Tn. Mn, and S, for n = 6 and 12. Then compute the corresponding errors ET,…

A: Thus, the integral value is 36.Let us assume..

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: Consider the set S composed of the points on the line segment S₁ between points (-1,0) and (2,0) and…

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Q: Problem 2 True or false? Justify your answer. Give a counterexample if it is false. (a) If limx→a…

A: Let us solve above problem

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Q: 1) A) Show that the set of all odd integers is countable, by producing a 1-1 Function F From J onto…

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Q: ove the following corollary of the projection theorem: Given a linear variety VC R* associated with…

A: Projection Theorem: Given a Hilbert space H and a closed subspace M of H, for any x in H, there…

Q: Consider the matrix A 00 1 -2 0 0 24 0 6 8 -3 48 -1 14 16 1 2 1 1 4 0 -9 -6-18 -1 -3 a) Determine a…

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Q: The Little Bookshop recorded books sold in a book sale.  Calculate the mean cost of the books sold.…

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

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Q: 6. Explain why a quadratic function needs to be in vertex form in order to determine the inverse.

A: A quadratic function is given.To Explain:Why does a quadratic function need to be in vertex form in…

Q: Olivia plans to secure a 5-year balloon mortgage of $210,000 toward the purchase of a condominium.…

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Q: The sentence (3x) (x ≥ 0 ^ x ≤ 0) (the universe is R) translates into an English sentence as "There…

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Q: 88 MULTIPLE CHOICE The bar graph below shows the average number of vehicles (rounded to the nearest…

A: We solve the given problem by using data of bar graph.

Q: Evaluate b.) D te-2t cost dt

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Q: lim s n where s₁ = 1, and S n+1 = (1 – = -)Sn n+31 for n ≥ 1.

A: We first evaluate the first few values of the sequence

Q: The iterated integral (fr Cos[0], r Sin[0]]r do) dr equals the 2D area-weighted integral f(x, y] da…

A: Given iterated integral .We have to find the domain for