Answered: Please help with c

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter12: Multiplication Of Decimal Fractions

Section: Chapter Questions

Problem 5A: Determine the length of B.

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Please help with c

Expert Solution

Step 1 (Solution for part A)

First we will calculate $x^{'}$ (t) i.e x'(t)=2t-4 (Calculating the derivative)

y'(t)= $\frac{d y}{d t}$ =te^t-3 - 1 ( Already given in the question)

Now, speed = $\sqrt{(x' {(t))}^{2} + (y' {(t))}^{2}}$

We calculated x'(t)

In the question we have to find for t=3 seconds ,so replacing t by 3,we get

speed (at t = 3 seconds) = $\sqrt{(x' {(3))}^{2} + (y' {(3))}^{2}}$ = $\sqrt{(2 {(3) - 4)}^{2} + (3 {(e)}^{(3 - 3)})}$ ² =2.828 metres per second

Step 2 (Solution for part b)

Now x'(t) =2t-4 (Calculated in part a)

So distance would be equal to $\int_{0}^{4}$ $\sqrt{(x' {(t))}^{2} + (y' {(t))}^{2}}$ dt = $\int_{0}^{4} \sqrt{{(2 t - 4)}^{2} + {(t e^{t - 3} - 1)}^{2}} d t$ =11.587 metres

Reason behind using upper limit 4 and lower limit 0 is that we have to calculate between t=0 and t=4 (As mentioned in the question)

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9781337798310

Author:

Peterson, John.

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Cengage Learning,