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7. An ant is sitting on the rim of a bike wheel suspended 0.5ft in the air (the circle shown below is meant to symbolize the bike wheel). R P 0.5ft The ant is initially at the point P on the wheel, but the wheel is spun at a constant speed so that it moves around in circles counterclockwise, making 1 full revolution each minute. As a result, the ant's height as a function of time t (measured in minutes) can be modelled using an equation of the form h(t) = A+ B sin(2nt) + C cos(2nt). (a) is at the points P, Q, R and S. Identify the times during the first minute of spinning at which the ant (b) the points Q, R and S. Then use this and your answer to (a) to find the values of A, B and C so that h(t) models the ant's height for all t. Given that the bike wheel has a radius of 1ft, identify the heights of (c) velocity). Find the rate of change of the ant's height (i.e. the ant's vertical (d) Does your answer make sense based on the picture? At what time(s) (in the first minute) is the ant's vertical velocity 0?

7. An ant is sitting on the rim of a bike wheel suspended 0.5ft in the air (the circle shown below is meant to symbolize the bike wheel). R P 0.5ft The ant is initially at the point P on the wheel, but the wheel is spun at a constant speed so that it moves around in circles counterclockwise, making 1 full revolution each minute. As a result, the ant's height as a function of time t (measured in minutes) can be modelled using an equation of the form h(t) = A+ B sin(2nt) + C cos(2nt). (a) is at the points P, Q, R and S. Identify the times during the first minute of spinning at which the ant (b) the points Q, R and S. Then use this and your answer to (a) to find the values of A, B and C so that h(t) models the ant's height for all t. Given that the bike wheel has a radius of 1ft, identify the heights of (c) velocity). Find the rate of change of the ant's height (i.e. the ant's vertical (d) Does your answer make sense based on the picture? At what time(s) (in the first minute) is the ant's vertical velocity 0?

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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7. An ant is sitting on the rim of a bike wheel suspended 0.5ft in the air (the circle shown below is meant to symbolize the bike wheel). R S 0.5ft The ant is initially at the point P on the wheel, but the wheel is spun at a constant speed so that it moves around in circles counterclockwise, making 1 full revolution each minute. As a result, the ant's height as a function of time t (measured in minutes) can be modelled using an equation of the form h(t) = A+ B sin(2nt) +C cos(27t). (a) is at the points P, Q, R and S. Identify the times during the first minute of spinning at which the ant (b) the points Q, R and S. Then use this and your answer to (a) to find the values of A, B and C so that h(t) models the ant's height for all t. Given that the bike wheel has a radius of 1ft, identify the heights of (c) velocity). Find the rate of change of the ant's height (i.e. the ant's vertical At what time(s) (in the first minute) is the ant's vertical velocity 0? (d) Does your answer make sense based on the picture?
Transcribed Image Text:7. An ant is sitting on the rim of a bike wheel suspended 0.5ft in the air (the circle shown below is meant to symbolize the bike wheel). R S 0.5ft The ant is initially at the point P on the wheel, but the wheel is spun at a constant speed so that it moves around in circles counterclockwise, making 1 full revolution each minute. As a result, the ant's height as a function of time t (measured in minutes) can be modelled using an equation of the form h(t) = A+ B sin(2nt) +C cos(27t). (a) is at the points P, Q, R and S. Identify the times during the first minute of spinning at which the ant (b) the points Q, R and S. Then use this and your answer to (a) to find the values of A, B and C so that h(t) models the ant's height for all t. Given that the bike wheel has a radius of 1ft, identify the heights of (c) velocity). Find the rate of change of the ant's height (i.e. the ant's vertical At what time(s) (in the first minute) is the ant's vertical velocity 0? (d) Does your answer make sense based on the picture?
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