Answer:
6 knots
Step-by-step explanation:
Let the velocity be v knots
thus, the time required to traverse 500 M is given by 500 / v hours
Fuel consumption per hour is equal to 216 plus half the cube of the speed (v^3).
Let F denote the fuel consumption for the journey
= [500/v][216 + 0.5v^3]
= 500[216/v + 0.5v^2]
The derivative of F with respect to v is: dF/dv = 500[ - 216/v^2 + v]
The second derivative, d^2F/d^2v = 500[432/v^3 + 1], indicates positivity.
Setting dF/dv to zero helps find the minimum.
500[ -216/v^2 + v] = 0
or v = 216/v^2
or v^3 = 216
By solving, we arrive at v = [216]^(1/3) = 6 knots
Answer:
The correct choice is the third one.
Step-by-step explanation:
Answer:
Let the train's speed be denoted as x km/h.
Scenario 1:
Distance = 288 km
Speed = x km/h
Time = Distance divided by Speed
= 288/x hours
Scenario 2:
Distance = 288 km
Speed = (x + 4) km/h
Time = 288/(x + 4) hours
As 288/x is greater than 288/(x + 4)
288/x - 288/(x + 4) = 1
288[1/x - 1/(x + 4)] = 1
[x + 4 - x] / [x(x + 4)] = 1/288
[4 / (x^2 + 4x)] = 1/288
x² + 4x = 1152
x² + 4x - 1152 = 0
x² + 36x - 32x - 1152 = 0
x(x + 36) - 32(x + 36) = 0
(x + 36)(x - 32) = 0
x + 36 = 0, x - 32 = 0
x = -36, x = 32
x = -36 is not valid as speed cannot be negative.
Conclusively, the train's speed = 32 km/h
Answer:
28 hours required for 15 toy bears
Step-by-step explanation:
hope this assists
