Question

If m varies directly as v² and m =3, when v=2, calculate the value of m when v=9

Answer 1

m=243/4 when v=9.

Explanation:

We know that when y varies directly with x², the formula of direct proportion is

• y=kx²

where 'k' is the constant of variation.

so

As m varies directly with v², and m=3 when v=2

m=kv²

k=m/v²

= 3/(2)²

=3/4

Hence, k=3/4

so when v=9 then the expression becomes

m=kv²

substituting v=9 and k=3/4

m= 3/4(9)²

=3/4 × 81

=243/4

Therefore, m=243/4 when v=9.