Find the variation equation for the variation statement.
-$y$ varies inversely as the square of $x ; y = 3$ when $x = 6$
A) $y = \frac { x } { 108 }$
B) $y = \frac { x ^ { 2 } } { 108 }$
C) $y = \frac { 108 } { x }$
D) $y = \frac { 108 } { x ^ { 2 } }$

Question

Quizplus · Accepted Answer

The variation equation for an inverse square relationship is $y = \frac{k}{x^2}$, where $k$ is the constant of variation. Given $y = 3$ when $x = 6$, we find $k$ by substituting these values: $3 = \frac{k}{6^2}$, leading to $k = 3 \times 36 = 108$. Thus, the equation is $y = \frac{108}{x^2}$.

Find the Variation Equation for the Variation Statement yyy Varies Inversely as the Square Of

Find the Variation Equation for the Variation Statement $y$ Varies Inversely as the Square Of