Spreading fire A fire has started in a dry open field and isspreading in the form of a circle. If the radius of this circleincreases at the rate of 6 ft/min, express the total fire area Aas a function of time t (in minutes).

Definition used- Area of a circle having radius r -…

Answered: Spreading fire A fire has started in a…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.7: Operations On Functions

Problem 45E

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Area of an oil spill Suppose an oil spill from a tanker is spreading in the shape of a circular ripple. If the function dt=3t represents the diameter of the spill in inches at time t minutes, express the area, A, of the oil spill as a function of time. Find the area of the oil spill after 2 hours. Round to one decimal place.
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).
Population Growth The projected population of the United States for the years 2025 through 2055 can be modeled by P=307.58e0.0052t, where P is the population (in millions) and t is the time (in years), with t=25 corresponding to 2025. (a) Use a graphing utility to graph the function for the years 2025 through 2055. (b) Use the table feature of the graphing utility to create a table of values for the same time period as in part (a). (c) According to the model, during what year will the population of the United States exceed 430 million?
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Average Speed: A commuter regularly drives 70 miles from home to work, and the amount of time required for the trip varies widely as a result of road and traffic conditions. The average speed for such a trip is a function of the time required. For example, if the trip takes 2 hours, then the average speed is 70/2 = 35 miles per hour. a. What is the average speed if the trip takes an hour and a half? b. Find a formula for the average speed as a function of the time required for the trip. You need to choose variable and function names. Be sure to state units. c. Make a graph of the average speed as a function of the time required. Includes trips from 1 hour to 3 hours in length. d. Is the graph concave up or concave down? Explain in practical terms what this means
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Fluid Flow The intake pipe of a 100-gallon tank has a flow rate of 10 gallons per minute, and two drainpipes have flow rates of 5 gallons per minute each. The figure shows the volume V of fluid in the tank as a function of time t. Determine whether the input pipe and each drainpipe are open or closed in specific subintervals of the 1 hour of time shown in the graph. (There are many correct answers.)

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Spreading fire A fire has started in a dry open field and is spreading in the form of a circle. If the radius of this circle increases at the rate of 6 ft/min, express the total fire area A as a function of time t (in minutes).