Variations of equations

Question

Suppose r varies directly as the square of m, and inversely as s. If r=15 when m=9 and s=9, find r when m=45 and s=9

Answer 1

The idea here is that we need to find the proportionality constant first. The following is given to us-

 

R ~ M^2/S

 

Read ~ as "is proportional to"

 

We need to remove that ~ sign to an = sign. 

In order to do that, we introduce "K", as proportionality constant.

 

We can say

 

R = K . (M^2/S)

 

Now plug in the first set of values for the variables (R=15, M=9, S = 9) and solve for K

 

K = 5/3

 

Now use this K value with the other set that is asked.

 

R = (5/3) ( 45^2/9)

 

R = 375

 

Hopefully you understood the idea. I am assuming that you are comfortable in solving for a variable from an equation. 

Answer 2

r(m,s) = km²/s

 

k = constant

 

15 = k(9²)/9 = 9k

 

k = 15/9 = 5/3

 

r(m,s) = (5/3)m²/s

 

r(45,9) = (5/3)(45²)/9 = ?