Find a mathematical model representing the statement.(Determine the constant of proportionality.)
P varies directly as x and inversely as the square of y.(P = $\frac { 3 } { 2 }$ when x = 25 and y = 10.)

A) $P = \frac { x y ^ { 2 } } { 6 }$
B) $P = \frac { 6 x } { y }$
C) $P = \frac { 6 x } { y ^ { 2 } }$
D) $P = \frac { 6 y ^ { 2 } } { x }$
E) $P = 6 x y ^ { 2 }$

Question

Find a mathematical model representing the statement.(Determine the constant of proportionality.)  
P varies directly as x and inversely as the square of y.(P = $\frac { 3 } { 2 }$ when x = 25 and y = 10.)
 
A) $P = \frac { x y ^ { 2 } } { 6 }$
B) $P = \frac { 6 x } { y }$
C) $P = \frac { 6 x } { y ^ { 2 } }$
D) $P = \frac { 6 y ^ { 2 } } { x }$
E) $P = 6 x y ^ { 2 }$

Quizplus · Accepted Answer

The statement "P varies directly as x and inversely as the square of y" translates to $P = k\frac{x}{y^2}$, where $k$ is the constant of proportionality. To find $k$, use the given values $P = \frac{3}{2}$, $x = 25$, and $y = 10$. Substituting these into the equation gives $\frac{3}{2} = k\frac{25}{10^2}$, solving for $k$ gives $k = 6$. Thus, the correct model is $P = \frac{6x}{y^2}$.

Find a Mathematical Model Representing the Statement 32\frac { 3 } { 2 }23​

Find a Mathematical Model Representing the Statement $\frac { 3 } { 2 }$