The radius r of a circle is increasing at a rate of 4 centimeters per minute. Find
Question:
The radius r of a circle is increasing at a rate of 4 centimeters per minute. Find the rates of change of the area when r = 37 centimeters.
Step by Step Answer:
29...View the full answer
Calculus Of A Single Variable
ISBN: 9781337275361
11th Edition
Authors: Ron Larson, Bruce H. Edwards
Related Video
The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.
Students also viewed these Mathematics questions
-
The radius r of a circle is increasing at a rate of 4 centimeters per minute. Find the rates of change of the area when (a) r = 8 centimeters (b) r = 32 centimeters
-
The radius of a circle is increasing at a rate of 2 ft min. At what rate is its area changing when the radius is 3 ft? (Recall that for a circle, A = r2.)
-
Construct the general solution of x ' = Ax involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories. =[ A = 3. -2 1]
-
Each of the following surveys has bias. Determine the type of bias and suggest a remedy. (a) A politician sends a survey about tax issues to a random sample of subscribers to a literary magazine. (b)...
-
Use the linearity properties of the Laplace transform and the basic functions to calculate L {f (t)}. a) f(t) = 4t 10 b) f(t) = t2 + 6t 3 c) f(t) = (t+1)3 d) f(t) = 1+et e) f(t) = (1+ e24) f) f(t)...
-
Fill in the Blank. Univariate distributions describe the probability distributions of __________ random variables.
-
The demand for subassembly S is 100 units in week 7. Each unit of S requires 1 unit of T and 2 units of U. Each unit of T requires 1 unit of V, 2 units of W, and 1 unit of X. Finally each unit of U...
-
A. Consumers' decisions are impacted by several factors including antecedent factors, the purchase environment factors and post-purchase process factors. Describe each of these factors or issues, the...
-
Shibby Shades Inc. manufactures artistic frames for sunglasses. Talia Demarest, controller, is responsible for preparing the companys master budget. In compiling the budget data for 20x1, Demarest...
-
Use the rules of differentiation to find the derivative of the function. g(s) = 3s 5 2s 4
-
Use the rules of differentiation to find the derivative of the function. f(x) = x 3 11x 2
-
A tradition in the United States is to drape an American flag over the casket of a deceased U.S. Forces veteran. At the burial, the flag is removed, folded into a triangle, and presented to the...
-
Dallas (UK) Ltd is a wholly owned subsidiary of a US parent and has been set up as a new manufacturing facility in the UK. The projected capital costs and sources of funds are as follows: Costs...
-
Define current liabilities and give three examples.
-
The purchasing manager of a manufacturing business knows that its total production requirement for raw materials will be 7,200 units per month. Each unit has a price of 10. The cost of holding stocks...
-
Explain, in terms of divisional performance evaluation, the difference between using profit and profitability.
-
AB Ltd manufactures units for drills. All units are identical. The following working capital requirements are budgeted: Notes: 1 Each month is assumed to consist of four working weeks. 2 Wages are...
-
Nickel(II) chloride reacts with sodium phosphate to precipitate nickel(II) phosphate. 3NiCl2(aq) + 2Na3PO4(aq) Ni3(PO4)2(s) + 6NaCl(aq) How many moles of nickel(II) chloride are needed to produce...
-
Cornell and Roberts are partners who agree to admit Stanley to their partnership. Cornell has a capital balance of $80,000 and Roberts has a capital balance of $120,000. Cornell and Roberts share net...
-
In Exercises use the properties of summation and Theorem 4.2 to evaluate the sum. Use the summation capabilities of a graphing utility to verify your result. Data from in Theorem 4.2 12 i=1
-
In Exercises, set up a definite integral that yields the area of the region. (Do not evaluate the integral.) f(x) = 5 y 5 4 3 2 1 1 2 3 4 5 X
-
In Exercises, set up a definite integral that yields the area of the region. (Do not evaluate the integral.) f(x) = 6 - 3x 6 543 4 -2-1 2 1 y 11 1 2 3 4 5 X
-
In Year 1 , Stallman Co . had a break - even point of 8 0 , 0 0 0 units, a selling price of $ 1 9 per unit, and fixed costs of $ 2 0 0 , 0 0 0 . What is Stallman Co . s variable cost per unit? (...
-
Margarita's interest and gains on investments for the current year are as follows: Interest on Madison County school bonds $ 6 0 0 Interest on U . S . government bonds 7 0 0 Interest on a Federal...
-
Taylor, an unmarried taxpayer, had $90,000 in adjusted gross income for Year 13. During Year 13, Taylor donated land to a church and made no other contributions. Taylor purchased the land in Year 1...
Study smarter with the SolutionInn App