Question The speed, V (km/h), of a car at time t (seconds) is given by. where 0 ≤t ≤ 150. 75 + 30sin (л(t-75) 150 V = f(t) 2- sin (π(t-75) 150 a) We want to know when the car will reach speed. Solve for the time t in terms of the speed V, and hence find the formula for the inverse function ƒ¯¹(t). b) Write down the domain of f¯¹(t). c) Plot f(t) from t = 0 to t = 150 and then plot f¯¹(t) on the same axes but only for the values of t in the domain of the inverse function found in (b).
Question The speed, V (km/h), of a car at time t (seconds) is given by. where 0 ≤t ≤ 150. 75 + 30sin (л(t-75) 150 V = f(t) 2- sin (π(t-75) 150 a) We want to know when the car will reach speed. Solve for the time t in terms of the speed V, and hence find the formula for the inverse function ƒ¯¹(t). b) Write down the domain of f¯¹(t). c) Plot f(t) from t = 0 to t = 150 and then plot f¯¹(t) on the same axes but only for the values of t in the domain of the inverse function found in (b).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question
The speed, V (km/h), of a car at time t (seconds) is given by.
where 0 ≤t ≤ 150.
75 + 30sin
(л(t-75)
150
V = f(t)
2- sin
(π(t-75)
150
a) We want to know when the car will reach speed. Solve for the time t in terms
of the speed V, and hence find the formula for the inverse function f¯¹(t).
b) Write down the domain of f¯¹(t).
c) Plot f(t) from t = 0 to t = 150 and then plot f¯¹(t) on the same axes but
only for the values of t in the domain of the inverse function found in (b).
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These are the last two parts of the same question.
Please need assistance to solve it.
Thank you.
Transcribed Image Text:d) Describe the geometric relationship that you can see when you consider both
f(t) and f-¹(t).
e) When will the speed of the car be equal to 60km/h?
Use the inverse function you found in part (a) to help you answer this.
Solution
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This is Parts b and c of the same question.
Please need assistance to find the solution.
Cheers.
Transcribed Image Text:b) Write down the domain of f¨¹(t).
c) Plot f(t) from t = 0 to t = 150 and then plot f-1(t) on the same axes but
only for the values of t in the domain of the inverse function found in (b).
Solution
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