From a certain instant, a right circular cylinder has a radius of 10 cm and altitude of 15 cm.  At this instant the radius is decreasing by 5 cm/sec and the altitude is increasing by 4 cm/sec. How fast is the volume changing at this instant.

Q: Given cost and price (demand) functions C(q) = 150q + 47,100 and p(q) = -2q +890, What price must…

A: This question is related to cost and price functions, we will solve it using given information.

Q: dw dw For the functions w= - 4x² - 2y2, x= cost, and y= sint, express as a function of t, both by…

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Q: 0 7 m We model pumping from spherical containers the way we do from other containers, with the axis…

A: To find the work done.

Q: Evaluate the definite integral. (7x² - 6x +9) dx 0

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Q: Find fx, fy, f₂. fx = f(x,y,z)=x-√√√²+z² (Type an exact answer, using radicals as needed.)

A: topic- partial differentiation

Q: Show that the following series diverges. Which condition of the Alternating Series Test is not…

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Q: Let f(t) Find the Laplace transform F(s) by computing the following integral: 00 [ f(t)e=" dt = […

A: This question is related to integration, we will solve it using given information.

Q: Find the arc length of the curve y = (e²+ e) from x = 0 to z = 2 Length:

A: Given  its derivative

Q: Suppose you go to a company that pays $0.04 for the first day, $0.08 for the second day, $0.16 for…

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Q: The director of the school play has to assign 6 lead roles. If the roles are being chosen from a…

A: Using permutations and combination

Q: The entire graph of the function g is shown in the figure below. Write the domain and range of g as…

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Q: Calculate the value of cos8π° using two terms of the appropriate series. Compare with the value…

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Q: The entire graph of the function g is shown in the figure below. Write the domain and range of g as…

A: We have to find out the domain and range

Q: A solid lies between planes perpendicular to the y-axis at y = 0 and y=2. The cross-sections…

A: A solid lies between planes perpendicular the the y‐axis at y=0 and y=2. The cross‐sections…

Q: Given cost and revenue functions and C(q) = 115q + 31000 and R(q) = -3q² +2500q, how many items must…

A: Let's find how many items must be the company produce and sell to break down.

Q: apn below, state whether Graph 1 2- -8 -2 O Yes Graph 4 8. 4 OYes O No 6. 2+ O No resents a…

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Q: 1. Find the area bounded by: x=y² and y=-x².

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Q: -lving ³4xdx gives 4x b. 4x² c. 2x 1²³ C. 31 d. 2x² 1³

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Q: 2x+1 if x < 2 Let f(x) = x²-1 if x ≥2 Determine the one-sided limit lim f(x). x 2+

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Q: Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the…

A: This is a problem related to area calculation using left hand points. Based on the reimann sum for…

Q: Use the graph of the function y=f(x) below to answer the questions. y 5- # 3- 2+ 1- -5 -4 -3 -2 -1 4…

A: The given graph is:

Q: Find the derivative of the function f(x) = 3 ln(x) + e5ª. df = dx

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Q: It takes 1100 J of work to stretch a spring from its natural length of 1 m to a length of 2 m. Find…

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Q: Find two positive numbers that satisfy the given requirements. The sum of the first number squared…

A: Given :The sum of first number squared and second number is 51

Q: Evaluate the integral: –(9z²+7x) dr %3D (1-1)(z+1)²

A: Given :∫-(9x2+7x)(x-1)(x+1)2dx

Q: 2. Find the volume of solid generated by revolving the area bounded by: y=x²+1, x = 0, y = 0 and x=2…

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Q: Solve each of the following problems completely. Draw the complete figures for each question. 2.…

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Q: S= 4 dx 2 3 X³_4x² +8x 니

A: We need to evaluate integral.

Q: S dx x² √√x²-1²

A: Follow the procedure given below.

Q: If there is no solution, state that there is no solution and explain why.

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Q: Let f(x) = (lnx)7 f’(x) = ƒ' (e¹) =

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Q: 2-[x³.e* dx 3- S x².cosx dx

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Q: Find the first five non-zero terms of the Taylor series for f(x) centered at x = 2. Written…

A: In order to find the first five terms, we need to apply the formula of Tailor's series entered at 2.

Q: The two-dimensional Laplace equation, f(x,y)=-4x+2y-7 Find 2x² 22²4 for the given function. 2²1 2²²…

A: Given function f(x,y)=-4x+2y-7

Q: Consider the following sequence defined by a recurrence relation. Use a calculator, analytical…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = In (√9-x²) dy =

A: Solution: y=ln9-x2 Differentiate both sides

Q: Given f(x) find f'(x) f'(x) = 2 ¹(√2 x² + 3 In =

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Q: Find the area of the region bounded by the graphs of the equations. y = 1+√√x, x=0, x= 8, y = 0…

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Q: Evaluate the following integral, or state that it diverges. S8x² e-x³ dx Select the correct choice…

A: We have to find integral

Q: Find the function f given that the slope of the tangent line at any point (x, f(x)) is f'(x) and…

A: Given query is to find the function.

Q: For each graph below, state whether it represents a function. Graph 1 4 2- Function? Function? -2 O…

A: We have to check the function

Q: Let f(x) = 4ln(4x) f(x) = £' (5)

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Q: Let f(x) = x5. Use logarithmic differentiation to determine the derivative. f(x) = ƒʼ(1) =

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Q: Use the graph of g(x) to answer each question. (a) Find the domain and range of g(x). Write the…

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Q: 2 and x = 6. 4. Find the area bounded by the parabola y² = 4x and the line y = 2x - 4. ² and Find…

A: To find the area of region enclosed by given curves.

Q: Transform each graph as specified below. (a) The graph of y=f(x) is shown. Draw the graph of…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: € 4. If y=u² and u = x³ + 4 determine dx

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Q: Use the method of disks/rings to determine the volume of the solid obtained by rotating the region…

A: Given that the region is bounded by y=2x2 and y=x3 about the x-axis.

Q: Solve each of the following problems completely. Draw the complete figures for each question. 1.…

A: Please see the below picture for detailed solution.

Q: Evaluate the definite integral. 16 (10y√y +9√y) dy 16 jo (10y√y +9√y) dy = (Simplify your answer.) 4

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