A number to the 9th power divided by the same number to the 6th power equals 512. What is the

1 answer:

5 0

The answer is 5

explanation:
Let's call our number
a
. The statement written as a formula is
a
12
a
9
=
125
We can simplify the fraction, and we have
a
3
=
125
To solve for
a
, take the third root of both sides:
a
=
(
125
)
1
3
=
5

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Simplify cos^2 A/1+sin A

Stels [109]

Answer:

$\displaystyle \frac{\cos^2(A)}{1+\sin(A)}=1-\sin(A)$

Step-by-step explanation:

We want to simplify:

$\displaystyle \frac{\cos^2(A)}{1+\sin(A)}$

Recall the Pythagorean Identity:

$\sin^2(A)+\cos^2(A)=1$

So:

$\cos^2(A)=1-\sin^2(A)$

Substitute:

$\displaystyle =\frac{1-\sin^2(A)}{1+\sin(A)}$

Factor. We can use the difference of two squares pattern:

$\displaystyle =\frac{\left(1-\sin(A))(1+\sin(A))}{1+\sin(A)}$

Cancel. Hence:

$\displaystyle \frac{\cos^2(A)}{1+\sin(A)}=1-\sin(A)$

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atroni [7]

So, I came up with something like this. I didn't find the final equation algebraically, but simply "figured it out". And I'm not sure how much "correct" this solution is, but it seems to work.

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