An inverted pyramid is being filled with water at a constant rate of 70 cubic centimeters per second. the pyramid, at the top, has the shape of a square with sides of length 7 cm, and the height is 10 cm. find the rate at which the water level is rising when the water level is 4 cm.

Rate of change in height of the water level is 2.91 cm per second.

Step-by-step explanation:

Height of the inverted pyramid = 10 cm

Length of the square base = 7 cm

If water is filled up to the level of h cm then the volume of water up to height h will be

V =

V =

It is given that rate of water is filling with 70 cubic centimeters per second.

From two similar triangles in the figure attached,

By replacing the value of h,

V =

V =

V =

Now we integrate the equation with respect to time 't'

70 =

For h = 7 cm

Therefore, rate of change in height of the water level is 2.91 cm per second.

chad should not have included the values (1, 2) and (3, 6) because that would mean he only had half a healing card.

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).