Question

If a varies directly as the cube root of B and if a equals to 3 when B equals to 64 find the formula connecting the variables hence find b when a equals to 15 / 4

Answer 1

a=k1
`\sqrt[3]{B}`

B=125

Explanation:

Given :

a=3

B=64

According to question

a ∝
`\sqrt[3]{B}`

therefore

a=k1
`\sqrt[3]{B}`........Eq(1)

K1=
`\frac{a}{\sqrt[3]{B} }`......Eq(2)

Putting the value of a and B we get in Eq(2) we get

`K1=(3)/(4)`

Putting the value of k1 in Eq(1)

`a=(3)/(4)√(B)` .......................Eq(3)

putting the value of a=15/4 IN Eq(3) we get

`(15)/(4)\ =(3)/(4) \sqrt[3]{B} \\\\\sqrt[3]{B}\ =\ 5\\Cubing\ both\ side\ we\ get\\B=125`