In Exercises 57-64, factor using the formula for the sum or difference of two cubes. 57. x + 27 58. x + 64 59. x 60. x - 27 62. 27.x – 1 64. &r + 125 64 61. &r 1 63. 64x + 27

Q: Suppose that the piecewise defined function f is defined by [ 1 - 4x, f(x) = Select the correct…

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Q: Find the interest rate needed for $6000 to grow to $8000 in 3 years with continuous compounding.

A: Given data:- Rate of interest = r Final amount, A=$8000 Principle amount, P=$6000 Time, n=3 year

Q: Find the arc length of the curve y = 4x5/4 from x = 0 to x = 4.

A: We have, y=5x5/4  Aim: find arc length from x=0 to x=4

Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: The given function is: fx,y,z=xyz And the constraint is: x2+y2+z2=243   ...(1) Let,…

Q: A boat is anchored so that the anchor is 150 ft below the surface of the water. In the water, the…

A: Given data:- The given anchor is, 150 ft The given anchor weight is, 2000 lb The given chain weighs…

Q: Skill Practice 2 Determine if the relation defines y as a function of x. а. ((8, 4), (3, —1), (5,…

A: A relation is said to be function if every element of domain is connect with exactly one element of…

Q: Find the exact length of the curve. y = ex,   0 ≤ x ≤ 9

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Q: Of the following statements, circle the ones that are TRUE: (-sin x)dx = cos(74) because - sin(0) =…

A: Since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: 1) Rewrite 2ln(x)-3ln(y)+ln(z) as a single logarithm.

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Q: The population of rats, R(t), in a small town's sewage system t years after the beginning of the…

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Q: 3) Solve 62x-1-9.

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Q: Find an explicit description of Nul A by listing vectors that span the null space. 120-4 A= 0 0 1 0…

A: To find the spanning set for nul A .

Q: 7.21

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Q: Define binomial coefficient.

A: Binomial Coefficient:- The binomial coefficient in combinatorics is used to represent the variety…

Q: -10 f(x) = -5 -10 The graph of a piecewise function, f(x), is depicted above. Find its equation:…

A: We know Equation of line passing through point x1,y1 and x2,y2⇒y-y1=y2-y1x2-x1x-x2

Q: 16 = ( V16)³ = (_ = – %3D

A: Given data:- The given expression is,1634=1643=__3=____

Q: Evaluate the limit If the limit does not exist enter DNE. Limit= Number lim x 6 x2 x-6 - 6 x

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Q: Find and simplify an expression for dy/dx. Also evaluate dy/dx at x = a. - (+₂), x+2 y = cos a = 1

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Q: Let Find f(x) = y = f(x) = 5x + 18 cos x. d f(x) =

A: Given query is to find the derivative at indicated point.

Q: Find the angle , in radians, in the given right triangle. The length of the side adjacent to 0 is 16…

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Q: dy Solve the following differential equations. y' = d. dx 3. xy' = yln².

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Q: Use this theorem to find the curvature. r(t) = 3ti + 5 sin(t)j + 5 cos(t) k

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Q: Classify the equation below according to the following Order: Degree: Types: Independent Variable:…

A: Concept: Equations with several unknown variables and their partial derivatives are known as partial…

Q: - h)? + (y – k)? = ?, Skill Practice 4 Write the equation in the form (x and identify the solution…

A: Given data:- The given form of equation is, x-h2+y-k2=r2 And, the given solution set, x2+y2+2x+5=0

Q: ƒ(x) = 2x + 2, 1 2 -x² + ax + b₂ 6 x <-4 x ≥ −4

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Q: 4: Calculate the improper integral if it converges or show that it diverges. L 7 (3x + 1)4 dx

A: Given query is to find integral converging or diverging.

Q: Find dy/dx by implicit differentiation. 7x^2 + 9xy − y^2 = 7

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Q: Determine whether the following statement is true or false, and explain why. The function ƒ(x) = 3x2…

A: Given data:- The given function is, fx=3x2-75x+2

Q: For Exercises 17–32, information about a circle is given. a. Write an equation of the circle in…

A: Hello! thank you for the question but as our honor code, we'll able to solve only the first question…

Q: To help pay for college expenses, Julie Davis borrowed $10,000 at 7% interest compounded…

A: Given data, Principal P=$10,000 Rate r=7%=0.07 Time t=8 years Compounded semi-annually n=6

Q: 8) Find functions f and g such that f(g(x)) = √√2x + 1.

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Q: For Exercises 57–62, find and simplify f(x + h). (See Example 6) 59. f(x) = 7 – 3x 62. f(x) = x – 4x…

A: Hello! thank you for question but as per our honor code, we'll able to solve only the first question…

Q: Solve equation. If necessary, round each answer to the nearest thousandth. log2(5m - 2) - log2(m +…

A: Given data:- log2(5m - 2) - log2(m + 3) = 2

Q: Solve for the particular solution of y = 1/1/1e4x +3 sin 2x when x = 0 and y = 1

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Q: Use the quotient rule to simplify the expressions in Exercises 23-32. Assume that x >0. 1 1 24. 23.…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Q7: Show all your work in this problem. Consider the infinite series a b k=2 k-1 2k + 1 Write down…

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Q: ·S I. Evaluate II. Evaluate x² +6 x³ + 3x SS₁ R dx. 1 (x + y)³ dA, where R is the rectangle [0, 2] ×…

A: Please see the below picture for detailed solution.

Q: Solve for the particular solution of y' = 1/1 e 42 +3 sin 2x when x = 0 and y = 1

A: The differential equation is given by y' = 12e4x+3sin2x The initial condition is  y0 = 1 To…

Q: Given this unit circle, what is the value of y? (-y) y = (1,0) DELL - V[? CALC Enter

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Q: Use the Generalized Power Rule to find the derivative of the function. g(x) = (7x7 — 5x + 3)8

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Q: 5. f(x)=e* cos x + e* sin x

A: We use Product rule  ddxuv=udvdx+vdvdx

Q: Find an equation for the line tangent to the graph of f(x) = -5xe* at the point (2, f(2)). (Round…

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Q: Suppose that f(t) = 1² +4t-3. What is the average rate of change of f(t) over the interval 5 to 6?…

A: Given query is to find average rate of change for the function.

Q: If sin t and is in quadrant I, find the exact value of sin (2 t), cos (2 t), and tan (2 t)…

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Q: Show that for |x| < I, x3 tanhx =x + 5 d Hint: Recall that tanh dx 1 1– x²°

A: It is required to prove that tanh-1x=x+x33+x55+...

Q: Evaluate the expression. 5 = find f"(-1). +81 If f(x)=

A: Given query is to find indicated derivative.

Q: Find the inverse transform of the given function of s. -3s F(s) = ¤~² S A -4₂ (1) B1-4₂ (1) © "₂(1)…

A: Given :- Fs=e-3ss

Q: Skill Practice 4 Graph the equation by plotting points. * + y = 4

A: Given: x2+y=4

Q: Solve the following differential equations. y' = dy = dx 1. 6y2y = xy¹, y(0) = -2.

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Q: Find the average rate of change of the function over the given interval. y = √3x + 1; between x = 1…

A: See this solution in below.