The area A of a circle is r 2 . Find the instantaneous rate of change of
Question:
The area A of a circle is πr2. Find the instantaneous rate of change of area with respect r at r = 2 feet. What is the average rate of change from r = 2 to r = 3? What is the average rate of change from r = 2 to r = 2.5? From r = 2 to r = 2.1?
Step by Step Answer:
A2 lim r2 AA Ar AA Ar lim r2 lim r2 Ar ArA2 r2 r4K r2 li...View the full answer
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
-
1. Write the area A of a square as a function of its perimeter P? 2. Write the area A of a circle as a function of its circumference C?
-
The figure shows the percent of the U.S. population with diabetes (diagnosed and undiagnosed) for selected years from 2010 and projections to 2050. Assume this percent can be modeled by y = 6.97(0.5x...
-
The median income f (x), in thousands of dollars, is a function of the age of workers ages 20-62, x, and can be modeled by f (x) = 0.000864x3 - 0.128x2 + 6.61x - 62.6 (a) Find the instantaneous rate...
-
Penelope Pundit, an economics reporter, states that the European Union (EU) is increasing its productivity very rapidly in all industries. She claims that this productivity advance is so rapid that...
-
Create the ADD SOFTWARE EXPERT display on paper, using a word processor, or by modifying the Access form. Test the ADD SOFTWARE EXPERT display, using the drop-down lists and observing the status bar...
-
Fraser Baker opened Baker?s Accounting Service in Winnipeg on September 1, 2021. On September 30, the balance sheet showed Cash $5,700; Accounts Receivable $2,100; Supplies $350; Equipment $7,600;...
-
True or False: Multiple roots can exist when using IRR and MIRR methods.
-
Activity-based costing The job costing system at Smith's Custom Framing has five indirect cost pools (purchasing, material handling, machine maintenance, product inspection, and packaging). The...
-
Show that the function is a solution to y(x) = = Ce + Czex d y dy 2y = 0 dx dx for any choice of the constants C1 and C2. Then, determine C1 and C2 so that the initial conditions y(0) = 2 and dxx (0)...
-
You have been employed as a consultant to Golf R Us, Inc. The company has been having problems with account receivables and they want to use various dunning methods to better their receivables. But...
-
In physics, it is shown that the height s of a ball thrown straight up with an initial speed of 96 ft sec from a rooftop 112 feet high is s = s(t) = -16 t 2 + 96t + 112 where t is the elapsed time...
-
The following data represent the revenue R (in dollars) received from selling x wristwatches at Wilks Watch Shop (a) Find the average rate of change of revenue from x = 25 to x = 130 wristwatches....
-
Consider a region of space in which the energy density stored in the magnetic field (Eq. 21.35) is equal to the energy density in the electric field (Eq. 18.48). What is the ratio B/E? Express your...
-
How does the use of allusions to literary predecessors and canonical texts contribute to the development of literary traditions and genres, creating a dialogic relationship between past and present...
-
a. Project A costs $8,000 and will generate annual after-tax net cash inflows of $3,250 for 5 years. What is the payback period for this investment under the assumption that the cash inflows occur...
-
The Shape interface provides public getColor and setColor methods. The colors are defined in a public enum, in the Shape class, whose values include TRANSPARENT, BLACK, RED, ORANGE, YELLOW, GREEN,...
-
A wood crate sits in the back of a pickup truck. The coefficients of friction between the crate and the pickup truck are =0.61 and x=0.37. The pickup truck starts moving up a 11 slope. What is the...
-
On January 1, 2016, the Winderl Mining Co. paid $50 million for a copper mine owned by the state of Wyoming. To obtain the mine, Winderl agreed to restore the land to a suitable condition for other...
-
Crafted Furniture Ltd incurred the following actual costs during the year just ended: Direct material used...................................$412,500 Direct...
-
Transform the while loop from the previous exercise into an equivalent for loop (make sure it produces the same output).
-
In Problems 115124, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 3(x- (x + 1)/2 x 1 2 (x + 1)/2 + x.
-
In Problems 107118, find the value of each expression if x = 2 and y = 1. x + y 2 2
-
In Problems 79126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 4 14x 8x4 -
-
The December 3 1 , 2 0 2 4 , unadjusted trial balance for Demon Deacons Corporation is presented below. \ table [ [ Accounts , Debit,Credit ] , [ Cash , $ 8 , 0 0 0 , ] , [ Accounts Receivable, 1 3 ,...
-
During 2 0 2 3 , Manfred, who is 6 0 years old and unmarried, provided all of the support of his elderly mother. His mother was a resident of a home for the aged for the entire year and had no...
-
You have a friend who knows that you are studying Psychology in university. In a conversation you mention that you are doing a course on the History and Philosophy of Psychology. The friend tells you...
Study smarter with the SolutionInn App