Question: Suppose that the radius r and area A = r 2 of a circle are differentiable functions of t. Write an equation that relates dA/dt

Suppose that the radius r and area A = πr2 of a circle are differentiable functions of t. Write an equation that relates dA/dt to dr/dt.

Step by Step Solution

★★★★★

3.34 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

ANSWER We can use the chain rule to relate the derivatives of A and r with respect ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Q:

Suppose that the radius r and surface area S = 4r 2 of a sphere are differentiable functions of t. Write an equation that relates dS/dt to dr/dt.

Q:

Please solve this question Solve the problem. Suppose that the radius r and volume V = 7 7tr of a sphere are differentiable functions of t. Write an equation that relates dV/dt to drdt. Select one: O...

Q:

An outdoor decorative pond in the shape of a hemispherical tank is to be ­lled with water pumped into the tank through an inlet in its bottom. Suppose that the radius ofthe tank is R = 10 ft,...

Q:

\f\f\fDifferentiate the function with respect to the independent variable. 5 f(x) = (4-3x2) 5 f'(x) =Differentiate the function with respect to the independent variable. (1-3x 2) f(x) = (2-x 2)4...

Q:

Please provide explanations for 1, 5, 9. Thank you. Readied the picture = 29 29 ~ 2.9 ft/ sec as the rate at which the weight is being raised when x = 21 ft. EXERCISES 3.8 1. Area Suppose that the...

Q:

1) V is the volume of a cube with edge length x and the cube expands as time passes. a) write an equation with amounts V and x . . . dV dx b t -- ) WI'l e an equation w1th rates (it and dt . dx . dV...

Q:

Hello! Can you help me with these? Please show me the complete solutions. Thanks! 2 12. Given that x + y = 2x + 4y and dx/dt =- 5, find dy/dt when (x, y) = (3, 1). A. 15 B. - 10 C. 3 D. O 13. Let A...

Q:

please show all your work :) Using concepts from the solids of revolution, write out (but do not evaluate!) an integral that computes the volume of a torus with inner radius R = 5 and outer radius =...

Q:

Write complete programs for the below questions and print it out on same sheet. Don't forget to take a screenshot for the output of each question. 1. Write a complete C++ program that will ask the...

Q:

100 ' (x2 )2 . You have 200 meters of fencing to enclose two adjacent rectangular pens for livestock. The total area of the enclosed region is 1400 square meters. What are the dimensions of each pen?...

Q:

lim xyIn(x2 +y?)3 (x.y)-(0,0) Evaluate the limit

Q:

Lucinda Lowery Exports, Inc., is located in Clancy, New Mexico. Lowery is the only company with reliable sources for its imported gifts. The company does a brisk business with specialty stores such...

Q:

The gross profit ratio for Proform, Inc., increased from 4 5 % in 2 0 2 1 to 5 0 % in 2 0 2 2 . Which of the following must be true? Answer Proform had more sales in 2 0 2 2 than in 2 0 2 1 ....

Q:

Problem 7.21. The density of states of an ideal Fermi-Dirac gas is where D is a constant. (a) Compute the Fermi energy. (b) Compute the heat capacity at very low temperature. D 8(E)= if E > 0, if E

Q:

Find the limit. Use 1Hospitals Rule where appropriate. If there is a more elementary method, consider using it. If 1Hospitals Rule doesnt apply, explain why. Alternatively, we could apply 1Hospitals...

Q:

(a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and minimum values of f. (c) Find the intervals of concavity and the inflection points. f (x) = 2x 3 - 9x 2 +...

Q:

Sketch the graph of a function f that is continuous on [1, 5] and has the given properties. Absolute maximum at 2, absolute minimum at 5, 4 is a critical number but there is no local maximum or...

Q:

Chapter 3 6 Saved Help Save & CI 2 Jurvin Enterprises is a manufacturing company that had no beginning Inventories. A subset of the transactions that it recorded during a recent month is shown beloW...

Q:

Rita Arthurs, the sales manager is discussing the possible outcome of the forthcoming election with Paulo Farmer, the production manager. She noted that if one of the major political parties wins the...

Q:

Jarrod receives a scholarship of $35,200 from East State University to be used to pursue a bachelor's degree. He spends $21,120 on tuition, $1,760 on books and supplies, $7,040 for room and board,...