7.An ant is sitting on the rim of a bike wheel suspended 0.5ft in the air (thecircle shown below is meant to symbolize the bike wheel).RS0.5ftThe ant is initially at the point P on the wheel, but the wheel is spun at a constantspeed so that it moves around in circles counterclockwise, making 1 full revolutioneach minute. As a result, the ant's height as a function of time t (measured inminutes) can be modelled using an equation of the formh(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 valuesof 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 verticalAt what time(s) (in the first minute) is the ant's vertical velocity 0?(d)Does your answer make sense based on the picture?

Answered: 7. An ant is sitting on the rim of a…

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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A swimmer on a floating air mattress will follow the rise and fall of the waves in lake. When the person is on the top of the wave her feet are 0.5m above the average surface height of the lake. When she is in a trough her feet dig 0.5m into the water (-0.5m). The peaks of the waves are separated by two seconds. Create an equation of the sinusoidal function that models this movement assuming that she starts at the average surface height of the lake and heads upwards.
2) A 50 foot diameter Ferris wheel is constantly turning at four revolutions per hour. The bottom of the Ferris wheel is 10 feet of the ground. Graph the height of the Farris wheel as a function of time, f(t), if the starting time is when the Farris wheel is at the highest point. Be sure to state the angular frequency, period, amplitude, and midline of the function. Angular Frequency: Period: Amplitude: Midline: 2a)Write a possible formula for the cosine function f(t) represented by the information and graph from question 5.
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he paddle wheel on a riverboat is shown in the accompanying figure. 8 ft 6 ft Write an equation for the height s of a paddle relative to the water at time t. The radius of the paddle wheel is 8 feet, and the distance from the center of the paddle wheel to the water is 6 feet. Assume that the paddle wheel rotates at 5 revolutions per minute and that the paddle is at its highest point at t = 0. = S
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