A circle has radius r cm and area Acm 2 . The radius is increasing at a
Question:
A circle has radius r cm and area Acm2.
The radius is increasing at a rate of 0.1cms−1.
Find the rate of increase of A when r = 4.
Step by Step Answer:
The area A of a circle is given by the formula A r2 Taking the derivative of both sides w...View the full answer
Cambridge International AS And A Level Mathematics Pure Mathematics 1 Coursebook
ISBN: 9781108407144
1st Edition
Authors: Sue Pemberton, Julian Gilbey
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
-
Determine the matrix in homogeneous form that produced the image of the semicircle depicted in the following figure: Original fiure -4 -32 0 2 34 Image 1 -4 -32 0 12 3 4
-
A population of bacteria is increasing at a rate of 1000 / (2 + 3t)0.75 bacteria per hour, starting from a population of 106. Could this sort of growth be maintained indefinitely? When would the...
-
A population of bacteria is increasing at a rate of 1000 / (2 + 3t)1.5 bacteria per hour, starting from a population of 1000. Could this sort of growth be maintained indefinitely? Would the...
-
As a brand manager, for a product of your choice, develop a strategy for launching the product in a manner most likely to capture the attention of the product's primary target market. Write a...
-
Identify several brand logos other than those illustrated in this chapter and indicate why, in your view, these are effective logos.
-
Evaluate theory and research about this in social work education and the workplace.
-
C2.5. Explain why firms havedifferent price-earnings (PIE) ratios.
-
A study on motivated skepticism examined whether participants were more likely to be skeptical when it served their self-interest (Ditto & Lopez, 1992). Ninety-three participants completed a...
-
A company uses the perpetual inventory method. Which of the following entries would be made to record a $1,200 purchase of merchandise Inventory on account? The accounting entry would be a $1,200...
-
QUESTION 1 ABCL .., a Canadian-controlled private corporation, has a fiscal year end of October 31, 2018. ABC Ltd.'s bookkeeper has compiled the following information and has told you she followed...
-
A sphere has radius r cm and volume V cm3. The radius is increasing at a rate of Find the rate of increase of the volume when V = 36. 2 cm s-.
-
The sum of two real numbers, x and y, is 9. a. Express y in terms of x. b. i Given that P = x 2 y, write down an expression for P, in terms of x. ii. Find the maximum value of P. c. i Given that Q =...
-
Describe the decision-making process at the Denver Bronco's marketing group. Why is the group decision process beneficial for this organization?
-
1.A woman eats 65g of protein per day. She weighs 156 lbs. How much protein is she getting per kg of body weight? Explain briefly both question 2.152 lbs = ________________kg. [2.2 lbs = 1 kg] explain
-
The concrete slab shown in Figure is 7m x 5m. The slab is not supported along one of the 7m long edges (free edge). The other three edges are supported and continuous over the supports, and therefore...
-
1. If possible, find 4-B -[{3}][{3}] A=
-
Georgi owns 50% of Forbes, Inc., an S corporation. At the beginning of the current tax year, Georgi had zero basis and an unused net business loss carryover of $10,000. During the tax year, she...
-
luation, of Fundamental Managerial Accounting Concepts. Use Excelshowing all work and formulasto complete the following: Prepare a flexible budget. Compute the sales volume variance and the...
-
Suppose you are given an array, A, containing n distinct integers that are listed in increasing order. Given a number k, describe a recursive algorithm to find two integers in A that sum to k, if...
-
What are the principal differences among asset liquidity management, liability management, and balanced liquidity management?
-
Consider the nutrients saturated fat, total fat, and total calories. Plot the distribution of each nutrient for both the diet record and the food-frequency questionnaire. Do you think a normal...
-
Suppose an average woman did not gain any weight from age 18 to 50. What average SBP for 50-year-old women would be expected under these assumptions? Cardiovascular Disease Obesity is an important...
-
If the standard deviation of SBP under the assumption in Problem 5.72 remained the same (15 mm Hg), and the distribution of SBP remained normal, then what would be the expected proportion of...
-
Break-Even Sales and Sales to Realize Income from Operations For the current year ending October 31, Yentling Company expects fixed costs of $537,600, a unit variable cost of $50, and a unit selling...
-
You buy a stock for $35 per share. One year later you receive a dividend of $3.50 per share and sell the stock for $30 per share. What is your total rate of return on this investment? What is your...
-
Filippucci Company used a budgeted indirect-cost rate for its manufacturing operations, the amount allocated ($200,000) is different from the actual amount incurred ($225,000). Ending balances in the...
Study smarter with the SolutionInn App