Mathematics: How do you solve this? as you can see, i already found the but i need to know how to solve.

Assuming the particle s position is given bythen the distance traveled over the interval is...

How do you solve this? as you can see, i already

Ответ:

sadmomsclub

18.01.2022

Mathematics

From what I am seeing, a "short" is a 1, and a "long" is an x.

So, you look at the side lengths.

The longer side length has two "longs" and three "shorts", so that is 2x + 3.

The shorter one has one "long" and one "short", which is x + 1.

Because those two are multiplied to create an area, the side lengths are multiplied. That gives us the answer you circled.

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Ответ:

loudermilkb117

26.02.2021

Mathematics

Assuming the particle's position is given by

$\begin{cases}x(t)=3-\sin2t\\y(t)=3-\cos2t\\0\le t\le4\end{cases}$

then the distance traveled over the interval is

$\displaystyle\int_{t=0}^{t=4}\sqrt{\left(\dfrac{\mathrm dx(t)}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy(t)}{\mathrm dt}\right)^2}\,\mathrm dt$
$=\displaystyle\int_0^4\sqrt{(-2\cos2t)^2+(2\sin2t)^2}\,\mathrm dt$
$=\displaystyle\int_0^4\sqrt{4\cos^22t+4\sin^22t}\,\mathrm dt$
$=\displaystyle2\int_0^4\mathrm dt$
=2(4-0)=8

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How do you solve this? as you can see, i already found the but i need to know how to solve.

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