The volume formula for a sphere is:

V = 4/3 * π * r³

We're given that the volume is 288π cubic centimeters:

288π = 4/3 * π * r³

Divide both sides by 4/3π:

216 = r³

Now, take the cube root of both sides:

r = 6

So, the radius of the sphere is 6 centimeters.

To find k(2), we first calculate h(2):

h(2) = (2 * 2 - 5)(2 + 3)(2 - 4) = (-1)(5)(-2) = 10

After translating h(x) down by 3 units, we find k(x):

k(2) = h(2) - 3 = 10 - 3 = 7

The value of k(2) is 7.

Since 3^x = 81, we can express the right side of the equation as a power of 3: 81 = 3^4.
So, we have 3^x = 3^4, which means x = 4.

First, let's find the total age of all 6 students:

Total age = average age * number of students = 20 * 6 = 120.

Since the oldest student is 25 years old, we subtract this age from the total age:

Total age of the other 5 students = 120 - 25 = 95 years.

Now, we find the average age of the other 5 students:

Average age = total age / number of students = 95 / 5 = 19 years.

To find the number of newspapers with a missing page, we divide the total number of newspapers by the frequency at which newspapers have missing pages:

40 / 5 = 8 newspapers

So, 8 newspapers in the stack have a missing page.