Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive.) log3 (172)

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Q: Consider the following function. f(x) = x¹/9+8 (a) Find the critical numbers of f. (Enter your…

A: Solve the following

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A: We have to find the value of c.

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Q: Consider the following function. f(x) = 4x2/3 Find f(-8) and f(8). f(-8) = f(8) = Find all values c…

A: Here, the given function is: f(x)=4-x23

Q: 03) Prove or disprove that y = ce* + de ²x is the solution to y(2) + y(¹) - 2y = 0.

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Q: Susan invested $2,500.00 per year in an IRA each year for 10 years. The interest rate was 7%…

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Q: Question 15 The cost, in dollars, to produce a designer dog leashes is C(z) - 8x +9, and the…

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Q: Consider the solid Q limited by the surfaces: And the planes z = x² + y²₁ z=4-2²-y² y√3= x, y = 0…

A: Given

Q: 6. Without graphing the function on your calculator, find the limit. Use L'Hopital's Rule where…

A: Solution of the problem as follows

Q: Find the indefinite integral. (Use c for the constant of integration.) [ (41²³1 (4t³i + 14tj - 6√tk)…

A: Given that we need to solve the indefinite integral with using integral constant C.

Q: Graph the solution set. 9) y ≤ -2x + 5 3 y2x-2 -1086 ++ 2+ -10+

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Q: A "bead" is formed by removing a cylinder of radius r from the center of a sphere of radius R (see…

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Q: Calculate the following derivative. (Use symbolic notation and fractions where needed.) d6 = dx6 x

A: We have to find the derivative

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) 4x6_ X lim x →∞0 x³ +9

A: We need to evaluate the following limit limx→∞4x6-xx3+9

Q: Solve: (1+x2)dy+ydx=0; y(1)=1, implicit solution Also: a) Determine the value of y if x=e (euler…

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Q: 3) The weekly online sales, S(t), in thousands of dollars, t weeks after online sales began, is…

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Q: The population of a country is modeled by the function P(t) = 15.9e0.01462 where P(t) is the…

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Q: A manufacturer has determined that the total cost C of operating a factory is C = 2x² + 60x + 200,…

A: Given problem:- A manufacturer has determined that the total cost C of operating a factory is   C =…

Q: Find the position and velocity of an object moving along a straight line with the given…

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Q: Follow the steps below to find the nonnegative numbers x and y that satisfy the given requirements.…

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Q: Find the equation of the tangent line to the graph of f(x) = 9 sin(x) + 4 cos(x) at x = in in the…

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Q: 4. sinx 1-sin² x dx

A: integration

Q: Determine the average cost function C(x)= C(x)=x²+2x²-3x+40 Determine the average cost function.…

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Q: Find f. f(x) = f''(x) - 10 + 6x + 24x², f(0) = 5, f(1) = 16

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Q: Find c> 0 such that the area of the region enclosed by the parabolas y = x² − c² and y = c² – x² is…

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Q: 1- Find the area under one arch of y = cos3 x

A: To find the area under the arch we will integrate the given function under the limits of the given…

Q: Use calculus to find the exact absolute maximum and minimum values of f(x) = (x² + 2x - 3)² on…

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Q: The smaller the curvature in the bend of a road, the faster a car can travel. Assume that the…

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Q: Consider the following function. f(x) = x¹/⁹ + 8 (a) Find the critical numbers of f. (Enter your…

A: We will apply f'(x) =0 to get critical number.    If f'(x) > 0 for all x in an interval then f(x)…

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [ (v - x) dx +…

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Q: Direction: Find the integral of the following functions: 1. (5 cos x + 7 sin x) dx 2. f(3tan² x +…

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Q: Find the derivative of f(x) =de 22 Of(x) e (e-2x) ²-e -2x O f'(x)=x²e-2 (-2) O (E) None of these O…

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Q: 5. S COS X 2+3sinx dx

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Q: Express the limit as a definite integral on the given interval. x₁* lim Σ -Ax, [1,4] n10 (x)² + 7 i…

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Q: Q2):- Find Y[Z] of signal Y[n] (Cos wn). U[n]

A: Given

Q: Let R be a plane region with area A whose boundary is a piecewise smooth, simple, closed curve C.…

A: Let's find.

Q: Use logarithmic differentiation to find dy/dx. y = (4 + x)5/x dy dx II

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Q: Find all exact solutions on the interval 0 ≤ 0 < 2T. 4 cos(8) = 2 8 www

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Q: Let C be the curve represented by the equations x = 3t, y = t², (0 ≤ t ≤ 1). In each part, evaluate…

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Q: Example 8 Video Example If it is known that + f²³f(x) dx dx = 12 and Solution By the property of…

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Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. y y = f(x) X…

A: According to the guidelines, I am answering first three subparts. Please repost the remaining.…

Q: Given: xy =tan(x - y). Find dx/dy. tan² (z-y) soc²(z-v) +tan² (z y) sec (x−y) -sec² (2-y)-z 當…

A: find derivative dxdy from equation xy=tanx-y

Q: The sequence given is defined using a recursion formula. Write the first four terms of the sequence.…

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Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: a) Find the distance between two skew lines L1 and L2 such that L1: 1+ 4t, y=5-4t, z=-1+5t  L2:…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: f(x)= x² + 5x + 6 g(x)=x+2 Find (+)(*) (-) (2²) The domain of = (4) (2) is x + [ a

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Q: (D² – D − 2)y - COS X

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Q: Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty…

A: Here we have given a linear programming problem with equations as given below:  x + 3y ≥ 20 7x + y ≥…

Q: 2 1 -2 -4 X -1- -2- Write the factored form of the equation of the most appropriate polynomial. f(x)…

A: Since it is touching at x=-1 It means that there are two roots at x=-1 And one root at x=0