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 4 in. long and increasing at the rate of 0.5 in./s. how fast is the volume of the cube changing (in cu in/s) at that instant of time?

24 in³ per sec.

Step-by-step explanation:

Since, the volume of a cube ,

Where,

x = side length,

Differentiating equation (1) w. r. t ( time ),

Here,

That is, volume of the cube is changing with the rate of 24 in³ per sec.

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

  the correct choice is marked

step-by-step explanation:

the first two graphs show multiple turning points. the last graphs matches the description in every detail.