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spin [16.1K]
3 years ago
13

The side of a cube is increasing at a rate of 2 kilometers per hour. At a certain instant, the side is 1.5. What is the rate of

change of the volume of the cube at that instant (in cubic kilometers per hour)?
Mathematics
1 answer:
Arisa [49]3 years ago
3 0

Answer:

dV/dt = 13,5 [Km³/h]

Step-by-step explanation:

The volume f the cube is:

V = x³                 where x is a side of the cube, then tacking derivatives with respect to  time on both sides of the equation

dV/dt = 3*x² dx/dt

dx/dt = 2 km/h

at the time when the side x =  1,5 Km

dV/dt = 3* (1,5)²*2   [km³/h]

dV/dt = 13,5 [Km³/h]

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N order to write an expression like (5x + 4)3 in expanded form, it helps to look at (5x + 4) as just one number, n.
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