Solve the following problem and show your complete solutions. Explain your answers for better understanding.

Q: 4. It costs C(x) = 112 + 1.4x dollars to produce x Specialty Hair Ribbons. To sell x Specialty Hair…

A: It costs  dollars to produce x Specialty Hair Ribbons.To sell x Specialty Hair Ribbons, the price…

Q: t (seconds) v (t) (feet/second) a (t) (feet/second 2) -20 -30 15 1 No. Since v (0) = V a (t) = v1…

A: Given that a car travels on a straight track, during that time interval seconds ,the car's velocity…

Q: 8) Find two positive numbers such that the sum of twice the first number and three times the second…

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Q: Use partial fractions to find the power series of the function: 18 n=0 x +42 (x − 2)(x + 9)

A: The given function .The aim is to find the power series of the function.

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

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Q: Find the total mass of two turns of a spring with density p in the shape of the circular helix…

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Q: Degree: 4 ; zeros: 2i and -5i Form a polynomial f(x) with real coefficients

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Q: Is the series convergent or divergent? If convergent, is it absolutely convergent? M8 n=1 (−1)n √n

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Q: Find the arc length of the following curve on the given interval. x = 7 sint - 7t cos t, y = 7 cost…

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Q: Express the Cartesian coordinates (1,-1) in polar coordinates in at least two different ways. Write…

A: The given cartesian coordinates is .The aim is to find the polar coordinate in two different ways.

Q: Solve y(t)= dy dt = 4(y - 9), y(0) = 4

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Q: Evaluate the integral and check your answer by differentiating. NOTE: Enter the exact answer. 6 [[P+…

A: Let assume,

Q: =(x, y) = (2xy³)î + (1 + 3x²y²)ĵ. Show that is a conservative vector field on R². Find a potential…

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Q: Analyze the equation. That is, find the center, vertices, and foci of the ellipse and graph it. 2 2…

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Q: Find the mean value of y = x + x³ + x² 5 over the range 0 < x < 2. Enter your answer as a decimal in…

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Q: The function h defined by h(x) = Select one: True False 3x² +5x-1 x³ = x+2 has a vertical asymptote.

A: The objective of the question is to determine whether the equation x³ = x+2 has a vertical…

Q: What is the domain of the radical function f(x)=√2x²-5x-12? D: (-∞0, ∞0) D: [-1.5, 4] D: [-1.5, ⁰⁰)…

A: The function is given byTo determine: The domain of the the function.Domain Restrictions for Square…

Q: Current Attempt in Progress Evaluate the integral using an appropriate substitution. NOTE: Enter the…

A: The given integral is x3+5)3

Q: a = 6, b=1, C= 20° C≈ (Round to two decimal places as needed.)

A: a=6b=1C=20°

Q: What is the radius of convergence (x-4)" Ση=1 n m

A: Given

Q: 5. Evaluate the given improper integral or show that it diverges: π/4 (a) 0 1₂³² x² ex dx (b) 0 tan…

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Q: Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers…

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Q: function given 6x^2 ln(x), x>0  use interval notation to indicate where f(x) is concave up. use…

A: We need to find concavity intervals and inflection points.

Q: Find the integral. √ ³√x¹¹ dx 3 11 √ ³√x¹¹ dx= 11

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Q: Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose…

A: We have given an integral. We have to use the given theorems and power rules to evaluate the…

Q: 4) Determine whether the series is convergent or divergent. If it is convergent, find its sum. 1 a)…

A: Nth term divergence test:Geometric series :

Q: A measure of the adhesiveness of honey can be modeled as f(x, y) = −125.48 + 4.26x + 4.85y − 0.05x2…

A: A measure of the adhesiveness of honey can be modeled aswhere,x is the percentage of glucose and…

Q: hate the following definite in 0 π sin5x dx

A: According to our guidelines, we are supposed to answer only one question if multiple questions are…

Q: USE LIMIT COMPARISON TEST TO DETERMINE CONVERGENCE/ DIVERGENCE OF THE SERIES E n+2 3n²+2n²+n+1 n=1

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Q: r(t) = (8et sin t,8et cos t,8et) Find the tangential component of the acceleration. at = (Type an…

A: r(t)=&lt;8etcost, 8et&gt;

Q: roximate f by a Taylor polynomial with degree n at the numbe Talor’s Inequality to estimate the…

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Q: Use Stokes' Theorem to evaluate [F·dr where F = (x + 7z)i + (10x + y)j + (8y − z) k and C is the cur…

A: Given that  To find  ,where C is the curve of intersection of the plane  with the coordinate…

Q: Estimate the area under the graph of f(x) = 25-² over the interval [-1,4] using four approximating…

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Q: dy dx = 6x5y, which satisfies the initial Find the solution of the differential equation, condition…

A: dydx=6x5y,y(0)=1

Q: O 16xsec²(4x²)tan(4x²)

A: Given that the function

Q: Test the series below for convergence using the Ratio Test. gn n=1 n! The limit of the ratio test…

A: The series is given bywhere Ratio Test for series convergence:

Q: Differentiate y with respect to x given y = √x(2+bx³) 7bx3+2 2√x 0 36х 2 6bx+2 Vx 6b5x+1 2

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Q: given f(x)=(8-6x)e^x  use interval notation to indicate where f(x) is concave up and use interval…

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Q: Determine the slope of the tangent line, then find the equation of the tangent line at t = -1. x =…

A: The given curve .The aim is to find the equation of the tangent line at .

Q: Estimate the slope of the line. y 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 X Ⓒ

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Q: Determine all critical numbers of the function f(x) = 8x4 - 25x² + 15 Note: For this problem, we are…

A: The objective of the question is to find the critical numbers of the function f(x) = 8x^4 - 25x^2 +…

Q: Find both the vector equation and the parametric equations of the line through (3,1,2) that is…

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Q: If P= log 2 * and Q = log 5², plot the inverse of P*Q

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Q: Let f(x) = Find the intervals of convergence for f. (Enter your answers using interval notation.)…

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Q: Consider the following. | 12 (a) Perform the integration in two ways: once using the Simple Power…

A: Power rule: +C

Q: Consider the solid bounded by the coordinate planes and the plane 3x + 6y + 2z - 6 = 0. (a) Set-up…

A: The solid is enclosed by plane 3x+6y+2z-6=0 and coordinate planes.

Q: Suppose that the variables and y are related by the implicit equation V = -3.6x-2.7 ln(x)+1.2y- 2…

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Q: Find all holes of the following function. If a hole exists, write your answer as a coordinate point…

A: The given function .The aim is to find the holes in the function.

Q: evaluate the integral dx 8+2x-X² S

A: The given integral is 1/sqrt(8+2x-x2)

Q: A company has the linear total cost function C(x) = 22x + 2109. (a) What is the company's marginal…

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