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b. f(x) = -3 cos [4 (x -+ 2

b. f(x) = -3 cos [4 (x -+ 2

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Module G-Assimilate and Apply Арogee YPerigee 1. As a spacecraft orbits the earth, it is said to be at its apogee when it is farthest above the earth's surface and at its perigee when it is closest to the earth's surface. The graph below models the satellite's approximate distance in kilometers from the surface of the earth at time t minutes. km a. At what times is the satellite at its apogee? How far from the earth's surface is it at this time? 960 840 720 b. At what times is the satellite at its perigee? How far from the earth's surface is it at this time? 600 480 C. State the period and amplitude of the function 360 240 d. Write a cosine function that models the situation. 120 e. Write a sine function that models the situation. times (minutes) 30 60 90 120 150 180 2. Mark Twain sat on the deck of a river steamboat. As the paddlewheel turned, he noticed a dead fish caught on one of the paddles. AS the wheel turned, the distance, d, that the fish was from the water's surface was a sinusoidal function of time. When his stopwatch read 4 seconds, the fish was at its highest, 16 feet above the water's surface. It took another 10 seconds before the fish reached that height again. The diameter of the wheel was 18 feet. a. Sketch a graph. b. Write an equation. Show work to support your answer. c. How far above the surface was the point when Mark's stopwatch read: 17 seconds. Show work to support your answer 3. For each function, give the domain, range, period, amplitude, max, min, and midline. Then sketch a well-labeled graph. a. f(x) = -10 sin * – 6 10 b. f(x) = -3 cos [4 (x -)+: Draw a careful graph of each function and describe its properties in detail. a. y = 2 tan nx b. y = 6 csc() +3 Ci Y = sin1x 4.
Transcribed Image Text:Module G-Assimilate and Apply Арogee YPerigee 1. As a spacecraft orbits the earth, it is said to be at its apogee when it is farthest above the earth's surface and at its perigee when it is closest to the earth's surface. The graph below models the satellite's approximate distance in kilometers from the surface of the earth at time t minutes. km a. At what times is the satellite at its apogee? How far from the earth's surface is it at this time? 960 840 720 b. At what times is the satellite at its perigee? How far from the earth's surface is it at this time? 600 480 C. State the period and amplitude of the function 360 240 d. Write a cosine function that models the situation. 120 e. Write a sine function that models the situation. times (minutes) 30 60 90 120 150 180 2. Mark Twain sat on the deck of a river steamboat. As the paddlewheel turned, he noticed a dead fish caught on one of the paddles. AS the wheel turned, the distance, d, that the fish was from the water's surface was a sinusoidal function of time. When his stopwatch read 4 seconds, the fish was at its highest, 16 feet above the water's surface. It took another 10 seconds before the fish reached that height again. The diameter of the wheel was 18 feet. a. Sketch a graph. b. Write an equation. Show work to support your answer. c. How far above the surface was the point when Mark's stopwatch read: 17 seconds. Show work to support your answer 3. For each function, give the domain, range, period, amplitude, max, min, and midline. Then sketch a well-labeled graph. a. f(x) = -10 sin * – 6 10 b. f(x) = -3 cos [4 (x -)+: Draw a careful graph of each function and describe its properties in detail. a. y = 2 tan nx b. y = 6 csc() +3 Ci Y = sin1x 4.
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