35. A pilot can travel 400 miles with the win

Mathematics

1 answer:

fgiga [73]3 years ago

5 0

Answer:

The wind speed is 20 miles per hour.

Step-by-step explanation:

Speed = distance/time.

With the wind

230 + w = 400 / t where w is the speed of the wind.

Against the wind:

230 - w = 336/t

From the above equations:

t = 400/ (230 + w)

t = 336/ (230 - w) So:

400/ (230 + w) = 336/ (230 - w)

336(230 + w) = 400(230 - w)

77280 + 336w = 92000 - 400w

736w = 92000 - 77280 = 14720

w = 14720 / 736

w = 20.

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Assuming you mean

$5\sin t\dfrac{\mathrm dy}{\mathrm dt}+5y\cos t=\cos t\sin^2t$

This ODE is linear in $y$ , and you can already contract the left hand side as the derivative of a product:

$\dfrac{\mathrm d}{\mathrm dt}\left[5y\sin t\right]=\cos t\sin^2t$

Integrating both sides with respect to $t$ yields

$5y\sin t=\displaystyle\int\cos t\sin^2t\,\mathrm dt$
$5y\sin t=\dfrac13\sin^3t+C$
$y=\dfrac1{15}\sin^2t+C\csc t$

Given that $y\left(\dfrac\pi2\right)=9$ , we have

$9=\dfrac1{15}\sin^2\dfrac\pi2+C\csc\dfrac\pi2$
$9=\dfrac1{15}+C$
$C=\dfrac{134}{15}$

so that the particular solution over the interval is

$y=\dfrac1{15}\sin^2t+\dfrac{134}{15}\csc t$