Use the Factor Theorem to solve for k, if P(x) = 2x³ - x² -15x+k and x+2 is a factor of P(x).

Q: Find the radius of convergence, R, of the series. R = 1 00 n = 2 x + 1 5n! Find the interval, I, of…

A: We willuse the ratio test to determine the radius of convergence.

Q: A simple directed graph with vertices A, B,C,D,E,F,G has adjacency matrix . What is the order of the…

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Q: For fe Wm P(R"), assume that the inequality ||¹f|| LPS ||f||LP + ||mf|| LP holds for 1 ≤ i ≤m. Then…

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

A: Ok

Q: Suppose that the series. anx has radius of convergence 5 and (a) n=1 (c) (b) an(x-7)n n=1 (an +…

A: The series ∑n=1∞anxn has radius of convergence  5 and series  ∑n=1∞bnxn has radius of convergence…

Q: 9. Find the first three terms of Laurent series for principal branch. Log(z) in z 1 < 1, where…

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Q: valuate τ (n) and σ(n) for all n such that 40 ≤ n ≤ 50. 2. Verify that 1000! terminates in 249 zero

A: We have to calculate the value of τ(n) and σ(n) for 40 to 50.  And verify that 1000! has 249 zeros.

Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify (see…

A: Given that the  algebraic expression is                         x2-1;    x=secθ.

Q: no need explanation just need final answer

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Q: [50 Cki 3 1 L1 4 Therefore, aijaij : бікскi = = Ckk = [5 c. aijajk = 3 1 L1 4 3 11 [61 33 5 615 3 0…

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Q: V = y = x + 1, y = 0, x = 0, x = 5; Sketch the region. y 7 6 CI 5 H

A: To sketch the region,  y=x+1, y=0, x=0, x=5 .

Q: 1. Let G be the set of all rational numbers. Define the operation in G by a*b = a+b+ab. Is G a group…

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Q: a. Solve the Gompertz equation dy dt =ry In K yini subject to the initial condition y(0) = yo. Hint:…

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Q: 1. Find the general solution of y" - y" -y + y = 0

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Q: 2. Find the general solution of y(4) + 2y"+y=0

A: Given differential equation is y4 + 2y'' + y = 0

Q: For a monopolist's product, the cost function is c = 0.004q+20q+8000 and the demand function is…

A: Given that: The cost function is c=0.004q3+20q+8000.  The demand function is p=450-6q. Profit…

Q: Find the particular antiderivative F(x) of f(x) = x² - x6 Answer that satisfies F(1) = 2. Ke…

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Q: If the population of Quokkas on Rottnest Island in 2007 was estimated at 9700 and in 2017 it was…

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Q: Given the following relations on the set of all integers where (x, y) ER if and only if the…

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Q: 10. Derive CRE in polar coordinates Ur = r-100 uo =-ror Using x = r cos 0 and y = r sine and chain…

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Q: Find the volume of the solid bounded below by the circular paraboloid z = x² + y² and above by the…

A: We want to evaluate volume of solid below by the paraboloid z = x2 +  y2  and above the…

Q: Problem #2: Which of the following sets of polynomials form a basis for P₂? (i) P₁ = 1+x, P₂ = 9x +…

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Q: A farmer has 500 acres of available land and $100,000 to spend. He wants to plant the combination of…

A: Given that a farmer has 500 acres of available land and $100,000 to spend. He wants to plant the…

Q: Suppose that an is defined recursively by an an-1-1 and that a = 2. Find a3. = ao = 2 a₁ = =a² - 1 =…

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Q: Find all complex numbers z satisfying z³ = -27i Z and give your answer as a comma-separated list of…

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Q: ,use properties of the Laplace transform and the table of Laplace transforms to determine L[f].

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Q: i. y" - 4y' + 5y = 39xe* sin(x) + 47e* sin(x)

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Q: 1. Let P,Q, and X be three distinct collinear points and X is between P and Q. (a) If 0 < t < 1 and…

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Q: Find the Laplace transform of sinhot. Recall that coshot = {sinhbt} = | [sinhbt} = {sinhbt} =…

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Q: . Find the complex Fourier series for the fat square wave shown below: f(t) T -3n -2π -T 0 I 5 2π 5…

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Q: Consider the following function: Answer Step 4 of 4: Enter the x-values of any relative minima,…

A: Given function is   Differentiating with respect to x , we get .  Or  f'(x) = -2 x³ +2 x ² .…

Q: Consider the following function: f(x) = (x-6)(x-8)² Step 3 of 4: Determine where the function is…

A: f(x) = x-6x-82  by differentiate with respect to x f'(x) = x-82+2(x-6)(x-8)

Q: Find the Laplace transform of the given function; b is a real constant. f(t) = cos(bt) Your answer…

A: Given: The given function is ft=cosbt, where b is a real constant. To find: We have to find the…

Q: f(x) = x³ + 3x² − 105x + 4. Find = Find x) On what set is f increasing? erval of increase: On what…

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Q: Application of Master Theorem on following recurrences. T(n) = 8T (1) + 10n

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Q: Find the particular antiderivative F(x) of f(x) = x² - x6 that satisfies F(1) = 2.

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Q: An airplane is flying on a compass heading (bearing) of 290° at 330 mph. A wind is blowing with the…

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Q: I se sen5 (t) cos³ (t) dt

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Q: 6. Find the solutions by Inverse Matrix method If AX-Y and D 0, then X-A¹Y (1) (3x, -6x, = 0…

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Q: Find the linearization L(x) of f (x) = ln(1 + x) at a approximate f(0.1). = 0. Use this…

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Q: (b) Let T: R³ R³ be a linear transformation such that: 2 2 0 · (D) - [B] (AD) - [3³] (¦ D-[G] E T 4…

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Q: me Rational Function are shown below. draw the Horizontal Asymptote and write horizontal asymptote…

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Q: Show that the transformation T defined by T(X₁, X₂) = (4x₁ − 2X₂, X₁ + 4, 5x₂) is not linear. If T…

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Q: Consider the following convergent series: Also, consider the partial sums: S • The true mistake of…

A: Given that ∑n=1∞n9n=964 and that SN=∑n=1Nn9n. Then  (a) S5=∑n=15n9n=191+292+393+494+595=830359049.…

Q: 5 Find the general antiderivative of a(x) = = 1 + 16x² Use C for the arbitrary constant. (If…

A: Given that  αx = 51+16 x2        The antiderivative of  αx = 51+16 x2 is  A x = ∫ αx dx…

Q: all the entries of A and of b are integers, and that det A = -1. #1 Let x Consider a system Ax b,…

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Q: Find the general antiderivative of h(x) = 13x²√x. Use C for the arbitrary constant. (If necessary,…

A: Given function whose antiderivative to be found h(x) = 13x2x h(x) = 13x5/2

Q: In this exercise, we suggest the use of technology. Round all answers to two decimal places.…

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Q: Problem 5: How long in years will it takes money to quadruple if it earns (C+D) % compounded…

A: Given:A=1, B=5, C=7, D=6, E=8P=1 (since we're starting with $1)r=C+D%=13% (since the money earns…

Q: Find an antiderivative of v(x) = sec² (4x) + 11x³. Assume that the value of the arbitrary constant…

A: Given: The given function is given by v(x)=sec2(4x)+11x3 To find: We have to find the general…