Length of a tightrope The figure illustrates the apparatusfor a tightrope walker. Two poles are set 50 feet apart,but the point of attachment P for the rope is yet to bedetermined.(a) Express the length L of the rope as a function of the dis-tance x from P to the ground.(b) If the total walk is to be 75 feet, determine the distancefrom P to the ground.Exercise 76RopeL50'-

Given: To Find: a To express the length L of the rope as a function of the distance x from P to the…

Answered: Length of a tightrope The figure…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.4: Definition Of Function

Problem 76E

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Similar questions

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?
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
Distance A plane flying at an altitude of 7 miles above a radar antenna passes directly over the radar antenna (see figure). Let d be the ground distance from the antenna to the point directly under the plane and let x be the angle of elevation to the plane from the antenna. ( d is positive as the plane approaches the antenna.) Write d as a function of x and graph the function over the interval 0x.
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.)
Airplane Trajectory An airplane is flying at a speed of 350 mi/h at an altitude of one mile. The plane passes directly above a radar station at time t=0 . (a) Express the Distance s (in miles) between the plane and the radar station as a function of horizontal distance d (in miles) that the plane has flown. (b)Express d as a function of the time t (in hours) that the plane has flown. (c) Use Composition to express s as a function of t .

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