Question

if (a/b)^2 = (16/9) ÷ (4/3) find the value of (b/a)^3​

Answer 1

Answer:

result is (sqrt(3))/2 it may help you

Answer 2

Answer:

$\displaystyle{\boxed{\red{\sf\:\left(\:\dfrac{b}{a}\:\right)^3\:=\:\dfrac{3\:\sqrt{3}}{8}}}}$

Step-by-step-explanation:

We have given that,

$\displaystyle{\sf\:\left(\:\dfrac{a}{b}\:\right)^2\:=\:\dfrac{16}{9}\:\div\:\dfrac{4}{3}}$

We have to find the value of

$\displaystyle{\sf\:\left(\:\dfrac{b}{a}\:\right)^3}$

Now,

$\displaystyle{\sf\:\left(\:\dfrac{a}{b}\:\right)^2\:=\:\dfrac{16}{9}\:\div\:\dfrac{4}{3}}$

$\displaystyle{\implies\sf\:\left(\:\dfrac{a}{b}\:\right)^2\:=\:\dfrac{4\:\times\:\cancel{4}}{3\:\times\:\cancel{3}}\:\times\:\dfrac{\cancel{3}}{\cancel{4}}}$

$\displaystyle{\implies\sf\:\left(\:\dfrac{a}{b}\:\right)^2\:=\:\dfrac{4}{3}}$

$\displaystyle{\implies\sf\:\dfrac{a^2}{b^2}\:=\:\dfrac{2^2}{(\:\sqrt{3}\:)^2}}$

$\displaystyle{\implies\boxed{\pink{\sf\:a\:=\:2}}\sf\:\quad\:\&\:\quad\:\boxed{\pink{\sf\:b\:=\:\sqrt{3}}}\:\quad\:\dots\:[\:By\:compairing\:]}$

Now,

$\displaystyle{\sf\:\left(\:\dfrac{b}{a}\:\right)^3}$

$\displaystyle{\implies\sf\:\left(\:\dfrac{\sqrt{3}}{2}\:\right)^3}$

$\displaystyle{\implies\sf\:\dfrac{(\:\sqrt{3}\:)^3}{(\:2\:)^3}\:\quad\:\dots\:\left[\:\left(\:\dfrac{a}{b}\:\right)^m\:=\:\dfrac{a^m}{b^m}\:\right]}$

$\displaystyle{\implies\sf\:\dfrac{\sqrt{3}\:\times\:\sqrt{3}\:\times\:\sqrt{3}}{2\:\times\:2\:\times\:2}}$

$\displaystyle{\implies\sf\:\dfrac{3\:\sqrt{3}}{8}}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:\left(\:\dfrac{b}{a}\:\right)^3\:=\:\dfrac{3\:\sqrt{3}}{8}}}}}$