Please help me with this question

Step-by-step explanation:

Haven't seen a related rates problem in a while! These are fun!  Not too bad when you keep your stuff organized.  First, label what you've been given.  If the radius is decreasing, then we have

We are told to find when r = 9.

Now we have to find the derivative of the volume of a sphere using implicit differentiation.  The derivative is

It looks like we have everything we need to solve for the unknown.  The derivative is even already set up to solve for the change in volume.  All we have to do now is plug in the values.

This does give us a negative number, -203.575 to be exact, but if you answer it without the negative, you say that the volume is decreasing at the rate of 203.575 cm/min cubed

the answer is 15% decrease

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.