Question

H varies directly to the cube of c.
When H = 40, C = 2.
(a) Express H in terms of c.

Answer 1

H in terms of c is H = 5c³.

Explanation:

Given that:

H = 40 and c = 2

H varies directly to the cube of c.

Which means that,

H ∝ c³

Let,

k be the proportionality constant.

H = kc³

Putting H=40 and c=2

`40=k(2)^3\\40=k(8)\\40=8k\\8k=40`

Dividing both sides by 8,

`(8k)/(8)=(40)/(8)\\k=5`

Now,

H in terms of c.

H = 5c³

Hence,

H in terms of c is H = 5c³.