Question

Please need help in this 2 math questions

20. Q varies inversely as the square of p, and Q = 36 when p = 7. Find Q when p = 6.

A. Q = 6

B. Q = 42

C. Q = 176
D. Q = 49
12. Complete the property of exponents. (ab)n = _______

A. an + bn

B. anbn

C. abn

D. an – bn

Answer 1

20. OPTION D.

12. OPTION B.

Explanation:

20. An inverse variaton equation has this form:

`y=(k)/(x)`

Where "k" is the constant of variation.

If Q varies inversely as the square of p, then the equation is:

`Q=(k)/(p^2)`

Knowing that
`Q = 36` when
`p = 7`, you can solve for "k" and caculate its value:

`k=Qp^2\\k=(36)(7^2)\\k=1,764`

Then, to find the value of "Q" when
`p = 6`, substitute the known values into
`Q=(k)/(p^2)`:

`Q=(1,764)/(6^2)\\\\Q=49`

12. Given
`(ab)^n`, you get:

`(ab)^n=(a^1b^1)^n=a^((1*n))b^((1*n))=a^nb^n`

Then:

`(ab)^n=a^nb^n`

This matches with the option B.