Which of the following is the most appropriate unit to describe the rate at which water flows over niagara falls? .a) day per billion gallons, because the independent quantity is volume of water in billion gallons and dependent quantity is time in days. b) billion gallons per day, because the independent quantity is volume of water in billion gallons and dependent quantity is time in days. c) billion gallons per day, because the independent quantity is time in days and dependent quantity is volume of water in billion gallons. d) day per billion gallons, because the independent quantity is time in days and dependent quantity is volume of water in billion gallons.

C) Billion gallons per day, because the independent quantity is time in days and dependent quantity is volume of water in billion gallons.

Step-by-step explanation:

The rate of change for any function tells the change in dependent variable for every change in independent variable.

In option A and B , time is given to be dependent quantity but time is not dependent quantity, it is independent quantity and volume of water depends on it.

Thus the rate of at which water flows must be change in the volume of water for every change in the time.( which means D is also incorrect)

Therefore, C is the right answer.

The rate of at which water flows over Niagara Falls= Billions gallons per day.

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: