Volume of a Cube The volume V of a cube with sides of length x in. is changing with respect to time. At a certain instant of time, the sides

Question

Volume of a Cube The volume V of a cube with sides of length x in. is changing with respect to time. At a certain instant of time, the sides of the cube are 3 in. long and increasing at the rate of 0.2 in./s. How fast is the volume of the cube changing (in cu in/s) at that instant of time?

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Peyton 2 weeks 2021-10-01T06:15:32+00:00 1 Answer 0

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    2021-10-01T06:16:44+00:00

    Answer:

    DV(t)  = 5.4 in³/s

    Step-by-step explanation:

    Volume of cube of side x is   Vc  = x³

    If the sides are increasing  at a rate  0.2 in/sec and sides of a cube are 3 in.

    V(t) = x³

    Taking derivatives on both sides of the equation we get

    DV(t)  = 3*x² * dx/dt     (2)

    Plugging values in equation (2)  

    DV(t)  = 3* (3)²* 0,2    ⇒   DV(t)  = 5.4 in³/s

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45:7+7-4:2-5:5*4+35:2 =? ( )