Question

if a varies jointly as b and the cube of c when a = 200 when b = 5 and c = 2. find a when b = 6 and c = 3?

Answer 1

If a varies jointly as b and the cube of c

For joint variation, y varies jointly as x  and z  we use equation

y = kxz, where k is the constant of proportionality

Given : a varies jointly as b and the cube of c

So equation becomes

$a = kbc^3$

a = 200 when b = 5 and c = 2. we use the given values and find out k

200 = k (5)(2)^3

$200 = k (5)(2)^3$

200= 40k (divide by 40 on both sides)

k = 5

find a when b = 6 and c = 3 , k = 5

$a = kbc^3$

$a = 5*6*(3)^3$

a = 810