Variation Equation

Question

If y varies directly as x and inversely as m squared and r squared, and y = 5/3 when x = 1, m = 2 and r = 3 find y when x = 3, m = 1 and r = 8

Answer 1

If y varies directly as x and inversely as m squared and r squared, then y has the form:

 

y = kx / (m²r²) where k = a constant

 

Get k from the given information:

 

5/3 = k(1) / (2²3²) = k/36

 

k = 36(5/3) = 60

 

Then

 

y = 60x / (m²r²)

 

Now substitute x = 3, m = 1, and r = 8

 

y = 60(3) / (1²8²) = 180/64 = 45/16