where f(t)= 2: y'−y=f(t), y(0) = 1 0≤t≤1 t>1

Q: a. Find f'(-2) and f"(-2) b. At which value(s) of x does f(x) have a relative extremum on [2,6]?…

A: f' (-2) = 1f'' (-2) = -(1/2)

Q: O Mark the following either true or false. Justification is required. For square matrix A, det (A) =…

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Q: Let A and B be non-empty and bounded subsets of R such that inf A < inf B. Prove the following: ∃a…

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Q: Show that if n is an integer and n^3+5 is odd, then n is even

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Q: Prove that if A is an invertible n x n matrix, then adj A is an invertible matrix and -1 (adj A)-¹ 1…

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Q: list the days during the next 60 days on which megan and michele will see each other in city b

A: Given that:-Megan flies a 21 day schedule( including days off) which then repeats.Michele has a 30…

Q: 7. Use the variation of parameters technique to solve the DE y" − 2 y'+ y = t. You may use the…

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Q: Let y1 (x), y2(x), y3(x), y4(x) be the basic solutions of y(4) +6y"+9y=0. Find the absolute value of…

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Q: 5. Write the differential operator that annihilates the following functions. (a) f(x)=xº sin(√√5x) +…

A: To find the differential operator that annihilates the given functions, we need to determine the…

Q: Problem #8: Let R have the Euclidean inner product. Find a unit vector with a positive first…

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Q: a) Find a matrix B in reduced echelon form such that B is row equivalent to the given matrix A. b)…

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Q: 1. Show that the following functions are convex by verifying the definition, i.e., that f(x + (1…

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Q: Find an equation of the tangent line to the curve (a lemniscate) at the point (3, -1). 2(x² + y²)² =…

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Q: In Exercises 15-20, W is a subspace of R4 consisting of vectors of the form X = XI X2 X3 X4…

A: As per our company guidelines we are advised to solve only the first question. Kindly repost the…

Q: 4. (i) For an odd number n, suppose that 2" # 2 mod n. Can n be a prime? Explain. This is called the…

A: Eulers and fermats little theorem will used

Q: Let A and B be 4 x 4 matrices such that and det (B) = 5. det (A) = -3 Find the following. • det (BT)…

A: If A and B be two square matrices of order n×n. k is a real number. AT is transpose of the matrix…

Q: Use the remainder theorem to find P(-2) for P(x)=-2x^(4)-3x^(3)+5x^(2)-4. Specifically, give the…

A: Given Method(1):           x=- 2  )  -2      -3       5       0         -4…

Q: It is not always possible to construct by ruler and compass, a square equal in area to the area

A: We have to show that It is not always possible to construct by ruler and compass, a square equal in…

Q: Problem #2: Find a 3 × 3 matrix A that has eigenvalues λ = 0, 6, -6, with corresponding eigenvectors…

A: We have to find a  matrix that has eigenvalues , with the corresponding eigenvectorsWe know thatIf A…

Q: Suppose the 9-vector x = (1, 1, 2, 3, 2, 1, 0, -1, 0) represents a time series. (a) We wish to…

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Q: 14. For the pulley system illustrated to the right, when the masses are released, what is the final…

A: From the given figure the net force

Q: Determine the number of permutations (arrangements) possible of 7 things taken 3 at a time.

A: We have to determine the number of possible permutations of 7 things taken  at a time.So,

Q: Use a change of variables to evaluate the following integral. SSS xy dV; D is bounded by the planes…

A: Given information:A triple integral to evaluate: , where  is a region bounded by the following…

Q: 15) How long does it take a Principal of $25,200 at a simple interest rate of 9.5% to become…

A: Given that a principal of $25,200 at a simple interest rate of 9.5%  and interest is $32,500.

Q: (a) Show Σ 1+xn converges for x = [0, 1). xn (b) Show that the series converges uniformly on [0, a]…

A: 25.10 (a)…

Q: Let a, b ∊ R, and suppose that for every ɛ>0 we have a≤b + ɛ. Show that a≤b.

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Q: 16) The amount of $15,700 is deposited into a CD account for 8 years with simple interest. At the…

A: To find the interest rate for a deposit with simple interest, you can use the formula:Simple…

Q: Find a 3 x 3 matrix A that has eigenvalues λ = 0, 12, -12, with corresponding eigenvectors 400…

A: We have to find a  matrix that has eigenvalues , with the corresponding eigenvectorsWe know thatIf A…

Q: Matrix A has 3 rows and 2 columns. Matrix B has 2 rows and 3 columns. Matrix C has 2 rows and 2…

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Q: A graph of -x³+4x²-3x-18 is shown. Use the graph to solve x² + 4x²-3x-1820. YA 20 -A 10 x³+4x²² 3-18…

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Q: What's the conjecture?

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Q: Each elements of a finite field F with p" elements satisfies the equation XP = x. n

A: We have to show that each elements of a finite field F with pn elements satisfies the equation .

Q: K -(x-y-1) dy

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Q: Please use the Laplace transform. I only need help with part c

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Q: Sketch the region enclosed by 2y = 3√x, y = 3, and 2y + 3x = 6. Decide whether to integrate with…

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Q: Mr. and Mrs. Dunn have just purchased a $150000 house and made a down payment of $19000. They can…

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Q: Use the graphs to evaluate the expressions below. (Photo) f(g(5)) = g(f(1)) = f(f(3)) = g(g(2))…

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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: The number of children (in thousands) receiving Social Security benefits for each year from 1988 to…

A: The number of children (in thousands) receiving Social Security benefits for each year from 1988 to…

Q: A solid is bounded from below by the cone z = √x² + y² and from above by the plane z = 1. The…

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Q: MX" + BX' + KX = F(t). (4) so we will also do as much work as we can without specifying the forcing…

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Q: 2. Recall that a number m is said to be square free if d² | m for d ≥ 1 implies that d = 1.…

A: An integer is not square if it is divisible by some square number.

Q: find the general solution by finding the homogeneous solution and a particular solution. please help…

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Q: is a Given vectors U₁, ..., up and w in V, show that w is a linear combination of u₁,..., up if and…

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Q: (Watson 23.2) Consider the following two-country tariff game. There are two countries that are…

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Q: part (b), why is it equal to 0?

A: We have find  why part b is equal to 0

Q: 3. Complete the square and state the vertex, for the following equation=-0.1x² – 0.6x – 0.4.

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Q: Solve the system of linear equations Using the Cramer's Rule. E A) 182 B 8x+6y=1 Sx - 2y = -37 D 691…

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Q: Consider the following tableau for a particular Linear Program (LP) being solved using the M-Method:…

A: Given Information:Tabuleau for particular LPP using big M method is given as…

Q: Let fn(x) = x^n for x ∈ [0,1]. check if it is pointwise convergence. Define where it becomes…

A: Given, fn(x) = xn , x ∈ [0,1].We will check poitwise convergence of fn on [0,1].