The volume V of a cube with sides of length x inches is changing with respect to time t (in seconds). When the sides of the cube are 10 in. long and increasing at the rate of 0.5 in/sec, how fast is the volume of the cube increasing?

dV/dt = 3×10^2 × 0.5 = 150 in^3/sec

the volume of the cube is increasing at 150in^3/sec

Step-by-step explanation:

Volume V = length l^3

V = x^3

Differentiating both sides;

dV/dt = 3x^2 dv/dt

Given;

x = 10 in

dx/dt = 0.5 in/sec

dV/dt = 3×10^2 × 0.5 = 150 in^3/sec

the volume of the cube is increasing at 150in^3/sec

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

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