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3 years ago

PLEASE HELPPPP IM SOOOOOOO CONFUSED ++YOU GET MANY POINTS++

Mathematics

1 answer:

Reil [10]3 years ago

6 0

Answer:

I DONT KNOW

Step-by-step explanation:

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Write a word pharse to representbthe numerical expression below. 4+(27-10)

Aleksandr-060686 [28]

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A girl's feet are negative 4 over 5 yards from the surface of a pool. A boy's feet are negative 2 over 5 yards from the surface

ANTONII [103]

There are many ways you can do this. To me, the easiest way is cross multiplying, but since the denominators are the same, there is no need to do that. Also, the fractions are negatives, the one closest to 0 is closer to the surface of the pool
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Answer: the boy's feet are closer to the surface of the pool

6 0

3 years ago

Read 2 more answers

Find the integral <br> ∫√(9+x)/(9-x)

densk [106]

I suppose you mean

$\displaystyle \int \frac{\sqrt{9+x}}{9-x} \, dx$

Substitute y = √(9 + x). Solving for x gives x = y² - 9, so that 9 - x = 18 - y², and we have differential dx = 2y dy. Replacing everything in the integral gives

$\displaystyle \int \frac{2y^2}{18 - y^2} \, dy$

Simplify the integrand by dividing:

$\dfrac{2y^2}{18 - y^2} = -2 + \dfrac{36}{18 - y^2}$

$\implies \displaystyle \int \left(\frac{36}{18-y^2} - 2\right) \, dy$

For the first term of this new integral, we have the partial fraction expansion

$\dfrac1{18 - y^2} = \dfrac1{\sqrt{72}} \left(\dfrac1{\sqrt{18}-y} + \dfrac1{\sqrt{18}+y}\right)$

$\implies \displaystyle \frac{36}{\sqrt{72}} \int \left(\frac1{\sqrt{18}-y} + \frac1{\sqrt{18}+y}\right) \, dy - 2 \int dy$

The rest is trivial:

$\displaystyle \sqrt{18} \int \left(\frac1{\sqrt{18}-y} + \frac1{\sqrt{18}+y}\right) \, dy - 2 \int dy$

$= \displaystyle \sqrt{18} \left(\ln\left|\sqrt{18}+y\right| - \ln\left|\sqrt{18}-y\right|\right) - 2y + C$

$= \displaystyle \sqrt{18} \ln\left|\frac{\sqrt{18}+y}{\sqrt{18}-y}\right| - 2y + C$

$= \boxed{\displaystyle \sqrt{18} \ln\left|\frac{\sqrt{18}+\sqrt{9+x}}{\sqrt{18}-\sqrt{9+x}}\right| - 2\sqrt{9+x} + C}$

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2 years ago