A stone is dropped into a lake, creating a circular ripple that travels outward at a speed
Question:
(a) Express the radius of this circle as a function of the time (in seconds).
(b) If A is the area of this circle as a function of the radius, find A o r and interpret it.
Step by Step Answer:
a Using the relationship distance rate ...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 Calculus questions
-
A stone is dropped into a river from a bridge 43.9 m above the water. Another stone is thrown vertically down 1.00 s after the first is dropped. The stones strike the water at the same time. (a) What...
-
A vehicle is travelling along road at a speed of 60 kmh How many revolutions per second are the wheels of the vehicle doing if they are rolling without slipping Assume that the external radius of the...
-
A stone is dropped into a well. The splash is heard 3.00 s later. What is the depth of the well?
-
In April 1999, one of Capital Blue Cross' health-care insurance plans had been in the field for three years, but hadn't performed as well as expected. The ratio of premiums to claims payments wasn't...
-
On December 31, 2016, $300 of salaries has been accrued. (Salaries before accrued amount totalled $26,000.) The next payroll to be paid will be on February 3, 2017, for $6,000. Do the following: a....
-
For the in-line skate example described in Problem 10, design a production line to achieve an output rate of 90 per hour. TaskTime (sec.) 1...........20 2...........10 3...........30 4...........10...
-
Think about bosses, coaches, and teachers you have had. Under the headings Bad Boss and Good Boss, list the names of a few of these people. Now list a few adjectives that describe the people in each...
-
Beckett Corporation realized $800,000 of taxable income from the sales of its products in States A and B. Beckett's activities establish nexus for income tax purposes in both states. Beckett's sales,...
-
What information does the sales budget provide for forecasted financial statements? Multiple answers: Multiple answers are accepted for this question Select one or more answers and submit. For...
-
Sensitive care can help preterm infants recover, but they are less likely than full-term newborns to receive such care. Explain why.
-
Use the given graphs of f and to estimate the value of f (g(x)) for x = -5, -4, -3 ....5. Use these estimates to sketch a rough graph of f o g.
-
An airplane is flying at a speed 350 mi/hf at an altitude of one mile and passes directly over a radar station at time t = 0. (a) Express the horizontal distance (in miles) that the plane has flown...
-
Using the Conceptual Framework definition and recognition criteria, explain why each of the following items are liabilities.
-
Use the following information for questions 1 and 2. Caterpillar Financial Services Corp. (a subsidiary of Caterpillar) and Sterling Construction sign a lease agreement dated January 1, 2020, that...
-
Identifying Binomial Distributions. Determine whether the given procedure results in a binomial distribution or a distribution that can be treated as binomial (by applying the 5% guideline for...
-
Case 6: TOMS Shoes in 2016: An Ongoing Dedication to Social Responsibility, by Margaret A. Peteraf, Sean Zhand, and Meghan L. Cooney (page C-57) Read the case and then respond to the case questions...
-
Quatro Co. issues bonds dated January 1, 2019, with a par value of $740,000. The bonds' annual contract rate is 13%, and interest is paid semiannually on June 30 and December 31. The bonds mature in...
-
Wildcat Mining wants to know the appropriate discount rate to use in their capital budgeting decision making process. Based on the following data, what is the weighted average cost of capital the CFO...
-
The UK has always been unusual in having such a substantial occupational pensions sector. There is a similar system in the Netherlands and in the Republic of Ireland, but in most EU countries most...
-
Difference between truncate & delete
-
Suppose 0.086 mol of Br 2 is placed in a 1.26-L flask and heated to 1756 K, a temperature at which the halogen dissociates to atoms. If Br 2 is 3.7% dissociated at this temperature, calculate K c ....
-
Find f'(a). (a) f(x) = 3x2 - 4x + 1 (b) f(t) = 2t + 1/t + 3 (c) f(x) = 1 - 2x
-
(a) Find the slope of the tangent line to the parabola y = 4x - x2 at the point (1, 3) (i) Using Definition 1 (ii) Using Equation 2 (b) Find an equation of the tangent line in part (a). (c) Graph the...
-
Each limit represents the derivative of some function f at some number a. State such an f and in each case. (1 h)101 lim 2 32 x5 im cos( + h) + 1 lim
-
1. (A nice inharitage) Suppose $1 were invested in 1776 at 3.3% interest compounded yearly a) Approximatelly how much would that investment be worth today: $1,000, $10,000, $100,000, or $1,000,000?...
-
Why Should not the government subsidize home buyers who make less than $120K per year. please explain this statement
-
Entries for equity investments: 20%50% ownership On January 6, 20Y8, Bulldog Co. purchased 25% of the outstanding common stock of $159,000. Gator Co. paid total dividends of $20,700 to all...
Study smarter with the SolutionInn App