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2 years ago

Plzzz help me understand this!! Thank very much in advance!!

Mathematics

1 answer:

saul85 [17]2 years ago

5 0

First write both vectors in terms of their horizontal and vertical components.

G = (40.3 m)(cos(-35.0º) x + sin(-35.0º) y)

G = (33.0 x - 23.1 y) m

(where x and y are the unit vectors that point in the positive horizontal and vertical directions, respectively)

H = (63.3 m)(cos 270º x + sin 270º y)

H = (-63.3 y) m

Then the vector sum is

G + H = (33.0 x - 86.4 y) m

which has a magnitude of

|| G + H || = √[33.0^2 + (-86.4)^2] = 92.5 m

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N76 [4]

$\displaystyle\int\sin^3t\cos^3t\,\mathrm dt$

One thing you could do is to expand either a factor of $\sin^2t$ or $\cos^2t$ , then expand the integrand. I'll do the first.

You have

$\sin^2t=1-\cos^2t$

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$\displaystyle\int\sin t(1-\cos^2t)\cos^3t\,\mathrm dt$

Substitute $u=\cos t$ , so that $\mathrm du=-\sin t\,\mathrm dt$ . This makes it so that the integral above can be rewritten in terms of $u$ as

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Back-substitute to get the antiderivative back in terms of $t$ :

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2 years ago

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