Question

the ratio of the square of a number to the reciprocal of its cube is 243/16807.
what is the number?​

Answer 1

Answer:

Step-by-step explanation:

243=3^5

16807=7^5

Answer 2

The ratio of the square of a number to the reciprocal of its cube is 243/16807. Then the number is 3/7

Solution:

Let the number be $\frac{x}{y}$

Find the square of number

$square\ of\ number = \frac{x^2}{y^2}$

Reciprocal of cube is:

$Reciprocal\ of\ cube = \frac{y^3}{x^3}$

The ratio of the square of a number to the reciprocal of its cube is 243/16807

Therefore,

$\frac{\text{square of number}}{\text{reciprocal of cube}} = \frac{243}{16807}\\\\\frac{\frac{x^2}{y^2}}{\frac{y^3}{x^3}} = \frac{243}{16807}\\\\\frac{x^2}{y^2} \times \frac{x^3}{y^3} = \frac{243}{16807}\\\\\frac{x^5}{y^5} = \frac{243}{16807}\\\\\frac{x^5}{y^5} = \frac{3^5}{7^5}\\\\Powers\ are\ same,\ therefore\\\\\frac{x}{y} = \frac{3}{7}$

Thus the number is 3/7

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