Find a mathematical model representing the statement.(Determine the constant of proportionality. )
F is jointly proportional to r and the third power of s. $( F = 24750 \text { when } r = 18 \text { and } s = 5 . )$
A) $F = \frac { 11 r } { s ^ { 3 } }$
B) $F = \frac { r s ^ { 3 } } { 11 }$
C) $F = 11 r s ^ { 3 }$
D) $F = \frac { 11 } { r s ^ { 3 } }$
E) $F = \frac { 11 s ^ { 3 } } { r }$

Question

Find a mathematical model representing the statement.(Determine the constant of proportionality. ) ​
F is jointly proportional to r and the third power of s. $( F = 24750 \text { when } r = 18 \text { and } s = 5 . )$ ​
A) $F = \frac { 11 r } { s ^ { 3 } }$
B) $F = \frac { r s ^ { 3 } } { 11 }$
C) $F = 11 r s ^ { 3 }$
D) $F = \frac { 11 } { r s ^ { 3 } }$
E) $F = \frac { 11 s ^ { 3 } } { r }$

Quizplus · Accepted Answer

Given $F = k r s^3$ and $F = 24750$ when $r = 18$ and $s = 5$, substituting these values gives $24750 = k \cdot 18 \cdot 5^3$. Solving for $k$ gives $k = 11$, so the model is $F = 11 r s^3$.

Find a Mathematical Model Representing the Statement (F=24750 when r=18 and s=5.)( F = 24750 \text { when } r = 18 \text { and } s = 5 . )(F=24750 when r=18 and s=5.)

Find a Mathematical Model Representing the Statement $( F = 24750 \text { when } r = 18 \text { and } s = 5 . )$