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.

answer are

step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.