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

Answer:

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

B=125

Step-by-step 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

$K1=\frac{3}{4}$

Putting the value of k1 in Eq(1)

$a=\frac{3}{4}\sqrt{B}$ .......................Eq(3)

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

$\frac{15}{4}\ =\frac{3}{4} \sqrt[3]{B} \\\\\sqrt[3]{B}\ =\ 5\\Cubing\ both\ side\ we\ get\\B=125$