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3 years ago

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2. David and Josh both drove to their grandmother's birthday party. David drove 225 miles and made it in 3 hours. Josh drove 320

miles and made it in 4 hours. Who was driving the faster speed per hour, Josh or David? Please show all your calculations and write your answer in a complete sentence.

2 answers:

Mandarinka [93]3 years ago

7 0

Josh was driving faster

AnnyKZ [126]3 years ago

6 0

Answer:

Josh was driving faster

Step-by-step explanation:

Josh was going faster becuase 320 divided by 4 is 80

and 225 divided by 3 is 75.

In conclusion Josh was going faster by 5mph.

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$\displaystyle\int\frac{\sqrt{25-x^2}}x\,\mathrm dx$

Setting $x=5\sin\theta$ , you have $\mathrm dx=5\cos\theta\,\mathrm d\theta$ . Then the integral becomes

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Now, $\sqrt{x^2}=|x|$ in general. But since we want our substitution $x=5\sin\theta$ to be invertible, we are tacitly assuming that we're working over a restricted domain. In particular, this means $\theta=\sin^{-1}\dfrac x5$ , which implies that $\left|\dfrac x5\right|\le1$ , or equivalently that $|\theta|\le\dfrac\pi2$ . Over this domain, $\cos\theta\ge0$ , so $\sqrt{\cos^2\theta}=|\cos\theta|=\cos\theta$ .

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$\displaystyle5\int\sqrt{\cos^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$

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$\displaystyle5\left(\int\csc\theta\,\mathrm d\theta-\int\sin\theta\,\mathrm d\theta\right)$
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