Find a mathematical model representing the statement.(Determine the constant of proportionality.)
Z varies jointly as x and y. $( z = 128 \text { when } x = 4 \text { and } y = 8 . )$
A) $z = \frac { 4 y } { x }$
B) $z = \frac { 4 } { x y }$
C) $z = \frac { x y } { 4 }$
D) $z = \frac { 4 x } { y }$
E) $z = 4 x y$

Question

Find a mathematical model representing the statement.(Determine the constant of proportionality.)  
Z varies jointly as x and y. $( z = 128 \text { when } x = 4 \text { and } y = 8 . )$  
A) $z = \frac { 4 y } { x }$
B) $z = \frac { 4 } { x y }$
C) $z = \frac { x y } { 4 }$
D) $z = \frac { 4 x } { y }$
E) $z = 4 x y$

Quizplus · Accepted Answer

The statement "Z varies jointly as x and y" means $z = kxy$, where $k$ is the constant of proportionality. Substituting $z = 128$, $x = 4$, and $y = 8$ into the equation gives $128 = k \cdot 4 \cdot 8$. Solving for $k$ gives $k = 4$, so the model is $z = 4xy$.

Find a Mathematical Model Representing the Statement (z=128 when x=4 and y=8.)( z = 128 \text { when } x = 4 \text { and } y = 8 . )(z=128 when x=4 and y=8.)

Find a Mathematical Model Representing the Statement $( z = 128 \text { when } x = 4 \text { and } y = 8 . )$