If p and q vary inversely and p is 29 when q is 16, determine q when p is equal to 116.

q = 4

Step-by-step explanation:

given p and q vary inversely then the equation relating them is

p = ← k is the constant of variation

to find k use the condition p = 29 when q = 16 , then

29 = ( multiply both sides by 16 )

464 = k

p = ← equation of variation

when p = 116 , then

116 = ( multiply both sides by q )

116q = 464 ( divide both sides by 116 )

q = 4

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

u bout ugly as   a mf

step-by-step explanation: lol