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Makovka662 [10]
3 years ago
13

Find the value of 9!/(9-2)!. a. 72 b. 36 c. 504 d. 63

Mathematics
2 answers:
emmasim [6.3K]3 years ago
6 0

Answer:

a. 72

Step-by-step explanation:

Factorial (!) means take that number and multiply by all the numbers below it to 1

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

(9-2)! = 7! = 7*6*5*4*3*2*1

9*8*7*6*5*4*3*2*1

------------------------------

7*6*5*4*3*2*1

Canceling common factors

9*8

------------------------------

1

72

joja [24]3 years ago
3 0

Answer:

a. 72

Step-by-step explanation:

9!/(9-2)!

= 9 x 8 x 7! / 7!

= 9 x 8

= 72

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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

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

so that the particular solution over the interval is

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