The volume of a cube is increasing at a constant rate of 824 cubic centimeters per minute. at the instant when the volume of the cube is 683683 cubic centimeters, what is the rate of change of the surface area of the cube? round your answer to three decimal places (if necessary).

DA/dt  = 75.27 cm²

Step-by-step explanation:

Cube Volume    =   V(c)   =  683  cm³

DV(c) /dt    =  824 cm³

V(c,x) = x³    

Then

DV(c,x)/ dt   =  3x² Dx/dt

( DV(c,x)/ dt )/ 3x²  =  Dx/dt       (1)

Now  as  V(c,x) = x³    when    V(c,x)  =  683 cm³     x = ∛683

x  =  8.806     ( from excel)

And by subtitution of this value in equation (1)

Dx/dt   =  ( DV(c,x)/ dt )/ 3x²   ⇒  Dx/dt  =  824 / 3*x²

  Dx/dt   = 824 /3*77.55

Dx/dt   =  824/232,64

Dx/dt   = 3,542

Then we got  Dx/dt  where x is cube edge. The area of the face is x² then

the rate of change of the suface area is  

DA/dt  = ( Dx/dt )²*6         ( 6 faces of a cube)

DA/dt  = (3.542)²*6

DA/dt  = 75.27 cm²

the answer is a

step-by-step explanation:

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: