A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The
Question:
A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet) of the outer ripple is given by r(t) = 0.6t, where t is the time in seconds after the pebble strikes the water. The area of the circle is given by the function A(r) = πr². Find and interpret (A º r) (t).
Step by Step Answer:
Aort Art 406t 0...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
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
A sample containing an alkali sulfate is dried, weighed and dissolved in dilute HCl. Barium chloride solution is added in excess to precipitate barium sulfate, and the precipitate is digested in the...
-
Googles ease of use and superior search results have propelled the search engine to its num- ber one status, ousting the early dominance of competitors such as WebCrawler and Infos- eek. Even later...
-
Different theories about early childhood inform approaches to children's learning and development. Early childhood educators draw upon a range of perspectives in their work ..." (EYLF p.12)....
-
Orange growers know that the larger an orange the higher the price it will bring. But as the number of oranges on a tree increases, the fruit tends to be smaller. Heres a table of that relationship....
-
When is a Form 8K issued by a company? What specific information does a Form 8K convey?
-
Consider the following observations: a. Fit the nonlinear regression model \[ y=\theta_{1} e^{\theta_{2} x}+\varepsilon \] to these data. Discuss how you obtained the starting values. b. Test for...
-
Spring Company's cost structure is dominated by variable costs with a contribution margin ratio of .20 and fixed costs of $60,000. Every dollar of sales contributes 20 cents toward fixed costs and...
-
What is equilibrium price and quantity for the market below? Calculate the amount of consumer and producer surplus at equilibrium. P 120 S 80 60 66 20 20 40 50 60 D Q
-
For what values of k does the graph of y = 4kx pass through the point? (a) (1, 1) (b) (2, 4) (c) (0, 0) (d) (3, 3)
-
For what values of k does the graph of y = kx pass through the point? (a) (1, 4) (b) (-2, 1) (c) (0, 0) (d) (-1, -1)
-
Draw the structure of the predominant form of pyridoxal-5-phosphate at pH 7.00.
-
Give the contents and length of the array for ResizingArrayStackOfStrings with this input: \[\text { it was - the best - of times - - - it was - the - - }\]
-
Give traces of insertion sort and mergesort in the style of the traces in the text, for the input it was the best of times it was.
-
Develop an implementation Sequentia7SearchST of the symbol-table API that maintains a linked list of nodes containing keys and values, keeping them in arbitrary order. Test your implementation with...
-
Write a stack client Parentheses that reads a string of parentheses, square brackets, and curly braces from standard input and uses a stack to determine whether they are properly balanced. For...
-
How much time does it take to call functions such as Math. \(\sin ()\), Math. \(\log ()\), and Math.sqrt()?
-
Simplify 84/-16 by hand.
-
What is your opinion of advertising awards, such as the Cannes Lions, that are based solely on creativity? If you were a marketer looking for an agency, would you take these creative awards into...
-
A batter hits a baseball 3 ft above the ground toward the center field fence, which is 10 ft high and 400 ft from home plate. The ball leaves the bat with speed 115 ft/s at an angle 508 above the...
-
A medieval city has the shape of a square and is protected by walls with length 500 m and height 15 m. You are the commander of an attacking army and the closest you can get to the wall is 100 m....
-
A medieval city has the shape of a square and is protected by walls with length 500 m and height 15 m. You are the commander of an attacking army and the closest you can get to the wall is 100 m....
-
Make an Excel worksheet to calculate SSxx SSyy and SSxy (Leave no cells blank be certain to enter "O" wherever required. Negative values should be indicated by a minus sign. Round your answers to 2...
-
Inventory Turnover and days' sales in inventory Kracker Corp., Foodstuff, Inc., and Winston Stores, Inc. are three grocery chains in the United States. Inventory management is an important aspect of...
-
Conduct Internet research on General Electric (GE) and update allegations and lawsuits against the company. Discuss the ethical issues of the cases?
Study smarter with the SolutionInn App