Respuesta :
Answer:
The correct answer to the following question will be "V = 15 mph".
Step-by-step explanation:
According to the question,
C(V) ∝ V³
then,
C(V) = KV³
When, C = 100 and V = 10
then, [tex]100=K(10)^3[/tex]
⇒ [tex]K=\frac{1}{10}[/tex]
∴ [tex][C(V)=\frac{V^3}{10} ][/tex]
As we know,
Total cost per hour,
C₁ [tex]= \frac{V^3}{10}+675[/tex]
Cost per mile = [tex]\frac{C}{V}[/tex]
Now,
C₂ = [tex]\frac{\frac{V^3}{10}+675 }{V}[/tex]
⇒ = [tex]\frac{V^2}{10}+\frac{675}{V}[/tex]
Then we'll need to discover their derivative as well as set that to zero (0) to minimize it.
[tex]{C{2}}^{1},[/tex]
⇒ [tex]\\ \frac{2V}{10} -\frac{675}{V^2}=0[/tex]
⇒ [tex]\frac{V}{5} =\frac{675}{V^2}[/tex]
On applying cross-multiplication, we get
⇒ [tex]V^3=3375[/tex]
⇒ [tex]V = 15[/tex]
So that the cost is minimum at "V = 15 mph".
