The cost of fuel in running an engineis proportional to the square of the speed in km/hour I.e rs 48/hour when speed is 16km/hour, other cost is 300/hour find most economical speed ??
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Step-by-step explanation:
Also 48=k16
2
by given condition ∴k=3/16.
∴ Cost of fuel per hour =
16
3
v
2
.
Other charges per hour are 300.
∴ Charges per hour are
16
3
v
2
+300.
∴ Total expenses for the journey
E=(
16
3
v
2
+300)
v
S
or E=S(
16
3
v+
v
300
)
dv
dE
=S(
16
3
−
v
2
300
)=0
∴v
2
=1600orv=40
dv
2
d
2
E
=S(
v
3
600
)=+ive for v=40
and hence E is minimum.
Hence the most economical speed is 40 m.p.h.
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