Mathematics: Find the arc length of the curve on the given interval. (round your answer to three decimal places.) parametric equations interval x = 6t + 5, y = 7 − 7t −1 ≤ t ≤ 3

Find the arc length of the curve on the given

Ответ:

vanessafalcon1198

04.01.2022

$\displaystyle\int_{-1}^3\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt$

$x=6t+5\implies\dfrac{\mathrm dx}{\mathrm dt}=6$
$y=7-7t\implies\dfrac{\mathrm dy}{\mathrm dt}=-7$

$\displaystyle\int_{-1}^3\sqrt{36+49}\,\mathrm dt=\sqrt{85}(3-(-1))=4\sqrt{85}$

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Ответ:

aidanfbussiness

09.05.2020

Mathematics

3c - 11 5/8

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Find the arc length of the curve on the given interval. (round your answer to three decimal places.) parametric equations interval x = 6t + 5, y = 7 − 7t −1 ≤ t ≤ 3

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