A foam box's length and width are increasing by 4 and 3 centimeters per minute, respectively, while its height is decreasing by 2 centimeters per minute. At the time when the box's length, width, and height are 1, 2, and 4, respectively, what is the rate of change of the length of the long diagonal of the box

Therefore the rate change of the diagonal of the foam box is  cm per minute.

Step-by-step explanation:

Let the length, width and height of the foam be l, w and h respectively.

The diagonal of the rectangle is  d=

Given that, A foam box's length and width are increasing by 4 and 3 cm per minute.

Its height is decreasing by 2 cm per minute.

That is

cm per min., cm per min and    cm per min[ since the height is decreasing]

∴d=

Differentiating with respect to t

Putting ,  ,  

Now

Therefore the rate change of the diagonal of the foam box is  cm per minute.

seems like d

step-by-step explanation:

idk

step-by-step explanation: