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 $F = 24750$, $r = 18$, and $s = 5$, we substitute these values into the general form $F = k r s^3$ to find the constant $k$. Solving $24750 = k \cdot 18 \cdot 5^3$, we find $k = 11$. Thus, 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 $( F = 24750 \text { when } r = 18 \text { and } s = 5 . )$