Evaluate the following a) 4!= b) 0!= c) 2! + 3!= d) 3! x 4! e) 10! / 7!

Mathematics

1 answer:

IRISSAK [1]2 years ago

6 0

Answer:

See below for answers and explanations

Step-by-step explanation:

4! = 4*3*2*1 = 24

0! = 1

2! + 3! = 2*1 + 3*2*1 = 2 + 6 = 8

3! * 4! = 3*2*1 * 4*3*2*1 = 6 * 24 = 144

10! / 7! = 10*9*8*7*6*5*4*3*2*1 / 7*6*5*4*3*2*1 = 10*9*8 / 1 = 720

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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

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