Answer:
33.16 mph
EXPLANATION:
F' = 22-0.02v^2/(22+0.02v^2)
set F'=0 and solve to get the square root of 1100, which is about 33.16 mph.
The other person's answer is wrong :(, trust me I've looked it up on several other places as well.
The speed that will maximize the flow rate on the road is "1.13 miles/hour".
According to the question,
→ [tex]F = \frac{v}{(22+0.02 \ v^2)}[/tex]
We need to take the directive of the function as well as equation it to zero, then
→ [tex]F = \frac{v}{22} +0.02 \ v^2[/tex]
→ [tex]F' = \frac{1}{22} +0.04 v[/tex]
When [tex]F' =0[/tex],
→ [tex]\frac{1}{22} +0.04 v =0[/tex]
→ [tex]0.04v = -0.0454[/tex]
→ [tex]v = -\frac{0.0454}{0.04}[/tex]
→ [tex]= -1.13[/tex]
Thus the above answer answer i.e., 1.13 miles/hour is correct.
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