Question

 y varies inversely as the cube root of x this statement can be expressed in the symbol as ..

option:-
A)
B)
C)
D)​

Answer 1

Answer:

option A will be the answer

Answer 2

Given,

y varies inversely as the cube root of x.

$\[\begin{array}{l}\left( a \right)y \propto \sqrt[3]{x}\\\left( b \right)x \propto \sqrt[3]{y}\\\left( c \right)x \propto \frac{1}{{\sqrt[3]{y}}}\\\left( d \right)y \propto \frac{1}{{\sqrt[3]{x}}}\end{array}\]$

Solution,

Know that if two variables are inversely proportional then increment of one responsible for decrement of other.

y varies inversely as the cube root of x.

$\[y = k\frac{1}{{{{\left( x \right)}^{\left( {\frac{1}{3}} \right)}}}}\]$

$\[y = k\frac{1}{{\sqrt[3]{x}}}\]$

$\[y \propto \frac{1}{{\sqrt[3]{x}}}\]$

The statement is expressed as $\[y \propto \frac{1}{{\sqrt[3]{x}}}\]$

Hence the correct option is (d), i.e. $\[y \propto \frac{1}{{\sqrt[3]{x}}}\]$