A circle has an initial radius of 50 ft when the radius begins decreasing at a rate
Question:
A circle has an initial radius of 50 ft when the radius begins decreasing at a rate of 2 ft/min. What is the rate of change of the area at the instant the radius is 10 ft?
Step by Step Answer:
dx Ax x so 2x At ...View the full answer
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
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 distance formula, midpoint formula, and center radius form of the equation of a circle are closely related in the following problem. A circle has a diameter with endpoints (-1, 3) and (5, -9)....
-
A circle of radius I? is placed in the first quadrant as shown in Figure 18. What is the radius r of the largest circle that can be placed between the original circle and the origin? R
-
A circle of radius r is inscribed in a square. See the figure. (a) Express the area A of the square as a function of the radius r of the circle. (b) Express the perimeter p of the square as a...
-
The following is the ending balances of accounts at December 31, 2018, for the Weismuller Publishing Company. Additional Information: 1. Prepaid expenses include $120,000 paid on December 31, 2018,...
-
Outline the purpose and content of (a) An invoice; (b) A debit note; (c) A credit note.
-
Suppose a least-squares regression line is given by y = 4.302x - 3.293. What is the mean value of the response variable if x = 20?
-
What is the difference between interpersonal and organizational communication?
-
Calculating Annuity Values an All-Pro defensive lineman is in contract negotiations. The team has offered the following salary structure: All salaries are to be paid in lump sums. The player has...
-
Information about Kroger Company and four industry competitors in 2017 is shown below (dollar values in millions). a. Estimate the industry asset beta, weighting each competitor by its proportion in...
-
Sunburst sells a snowboard, Xpert, that is popular with snowboard enthusiasts. Below is information relating to Sunburst's purchases of Xpert snowboards during September. During the same month, 116...
-
Use the definition of the derivative to do the following. Verify that where g(x) = 2x - 3. g'(x) V2r 3'
-
Carry out the following steps. a. Use implicit differentiation to find dy/dx. b. Find the slope of the curve at the given point. tan xy = x + y; (0, 0)
-
The table shows results of whether the death penalty was imposed in murder trials in Florida between 1976 and 1987. For instance, the death penalty was given in 53 out of 467 cases in which a white...
-
Identify a public conflict (such as a recent Congressional debate or even a celebrity breakup) that has come to the forefront in the media (or public's attention) in the last thirty days. You have...
-
Performance Management Issues You have been asked to return to your alma mater and speak to current students about performance management issues. To make the most of this experience for yourself and...
-
Analysis of competitor organization of our selected organization Walmart and its competitor Safeway. 1. Complete analysis of competitor organization; addresses all relevant factors and typically uses...
-
Defining Program Objectives of Youth centers Clearly define the objectives of your program or center. What specific outcomes do you hope to achieve? Examples may include promoting physical fitness,...
-
Identify a local or regional organization and analyze how they demonstrate servant leadership in their operations. You will want to review their website, social media, news, and other resources to...
-
Can a moving body have constant speed but variable velocity? Nonzero acceleration?
-
If there is an unrealized holding gain on available-for-sale investments, it is reported as?
-
(a) A lamina has constant density p and takes the shape of a disk with center the origin and radius R. Use Newtons Law of Gravitation (see Section 13.4) to show that the magnitude of the force of...
-
If f is continuous, show that ESI0 dt dz dy - S (x tf() dt Jo Jo Jo
-
Evaluate lim n- i=1 j=l Vn2 + ni + j
-
Suppose the S&P 500 currently has a level of 960. One contract of S&P 500 index futures has a size of $250 S&P 500 index. You wish to hedge an $800,000-portfolio that has a beta of 1.2. (A)In order...
-
Exhibit 4.1 The balance sheet and income statement shown below are for Koski Inc. Note that the firm has no amortization charges, it does not lease any assets, none of its debt must be retired during...
-
Haley is 57 years of age. She is planning for future long-term care needs. She knows that yearly nursing home costs in her area are currently $69,000, with prices increased by 5 percent annually....
Study smarter with the SolutionInn App