Concept explainers
Rainfall Suppose that during a storm rain is falling at a rate of 1 inch per hour. The water coming from a circular roof with a radius of 20 feet is running down a downspout that can accommodate 400 gallons of water per hour. See the figure.
(a) Determine the number of cubic inches of water falling on the roof in 1 hour.
(b) One gallon equals about 231 cubic inches. Write a formula for a function g that computes the gallons of water landing on the roof in x hours.
(c) How many gallons of water land on the roof during a 2.5-hour rain storm?
(d) Will one downspout be sufficient to handle this type of rainfall? How many downspouts should there be?
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
College Algebra with Modeling & Visualization, Books a la Carte Edition plus MyLab Math with Pearson eText -- Access Card Package (6th Edition)
- Titanic At 2:00 p.m. on April 11, 1912, the Titanic left Cobh, Ireland, on her voyage to New York City. At 11:40 p.m. on April 14, the Titanic struck an iceberg and sank, having covered only about 2100 miles of the approximately 3400-mile trip. (a) What was the total duration of the voyage in hours? (b) What was the average speed in miles per hour? (c) Write a function relating the distance of the Titanic from New York City and the number of hours traveled. Find the domain and range of the function. (d) Graph the function in part (c).arrow_forwardThe height h of a projectile is a function of the time t it is in die air. The height in feet for t seconds is given by the function h(t)=-16t2+96t . What is the domain of die function? What does the domain mean in the context of die problem?arrow_forwardField Trip A class of fourth graders walks to a park on a field trip. The function y=f(t) graphed below gives their distance from school in ft t minutes after they left school. What is the average speed going to the park? How long was the class at the park? How far away is the park? Graph the function y=0.5f(t). How is the graph of the new function related to the graph of the original function? What is the average speed going to the new park? How far is the new park? Graph the function y=f(t10). How is the graph of the new function related to the graph of the original function? How does the field trip described by this function differ from the original trip?arrow_forward
- A ball is thrown in the air from the top of a building.Its height, in meters above ground, as a function of time, in seconds, is given by h(t)=4.9t2+24t+8. How long does it take to reach maximum height?arrow_forwardTax Owed According to the Oklahoma Income Tax Table for 2010, the income tax owed by an Oklahoma resident who is married and filing jointly with a taxable income above 100, 000 is 5070 plus 5.5 of the taxable income over 100, 000. a. Use a formula to express the tax owed as a function of the taxable income, assuming that the taxable income is above 100, 000. Be sure to explain the meaning of the letters you choose and the units. b. What is the tax on a taxable income of 108, 650? Round your answer to the nearest dollar. c. For what taxable income would the tax be 5686?arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning