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3 years ago

9

Three-fifths (3/5) of a foot of rain was collected in two-thirds (2/3) of a day. At that rate, how much rain would be collected

in one day?

1 answer:

pickupchik [31]3 years ago

5 0

Nine-tenths (9/10) of a foot of rain would be collected in one day.

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Which of the following is a polynomial A.x^2+2 B.(x^8-2)/(x^-2+3) C. 7x^7-2x^-4+3 D.x^x-1

EastWind [94]

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B.(x⁸-2)/(x⁻²+3) rational function
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Answer:

what is this

Step-by-step explanation:

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<img src="https://tex.z-dn.net/?f=5%28sin%28t%29%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%2Bycos%28t%29%29%29%3Dcos%28t%29%20%20%28sin%28

Nataliya [291]

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

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

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3 years ago

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AlekseyPX

First I chose two points on the line that fall on 2 intervals or 2 lines. Then if found the slope of the two points. Using the slope and one of the points I pugged the numbers into an equation to solve for b. Once I found b I wrote an equation using b and the slope.
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steps:
(250,200)(300,100)
100-200/300-150
-100/150 or -2/3
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100=-200+b
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Step-by-step explanation:

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