Question

If y varies inversely as x cubed, and y = 12 when x = 5, find the value of y when x = 2.

Answer 1

187.5

Explanation:

`\sf {If \; y \; varies \; inversely \; as \; x^3\; represented \; by\; y\propto (1)/(x^3)} \\then\\y = (k)/(x^3)\; where\; k \;is\; a \;constant\\\\== > k = y\cdot x^3\\\\When y = 12, x = 5 \;means\\\\k = 12.\cdot 5^3 = 12 \cdot 125 = 1500\\\\\sfTherefore \;when\; x = 2\\y = (1500)/(2^3) = (1500)/(8) = 187.5\\\\\sf Answer:\;\; \boxed {\sf y = 187.5\; \sf when\; x = 2}`