geno3141

That's a good calculator problem; fortunately this site has a good calculator --------

If you assume that the earth is approximately a sphere:

The formula for the surface area of a sphere is:  Area  =  4·π·r²

Find the radius of the earth by dividing its diameter by 2 and enter that value into the formula. 

Compound interest formula:      A  = P(1 + r/n)^(n·t)

A = final amount             P = initial amount = 7650.00          r = rate (as a decimal) = 0.05 

         t = number of years = 9          n = number of time compounded per year = 4

--->   A  = 7650(1 + 0.05/4)^(4·9)

Enter that into the calulator to get the final amount.

I believe that you need to re-do #6 and #9.

For ease of typing, I will replace "f(x)" with "y":

To find the inverse of  y = 1/3x + 2:

There are two steps:

Step #1:  interchange x and y:                x  =  1/3y + 2

Step #2:  solve this equation for y:

               -- multiply each term by 3:     3x  =  y + 6

               -- subtract 6 from both sides:  3x - 6  =  y 

So the inverse of             f(x) = 1/3x + 2

is                      f-inverse(x)  = 3x - 6

No. 

Reason:  Division works because it can be checked by doing multiplication:

              For instance 6 ÷ 2 = 3, because 3 x 2 = 6.

To have  -2 ÷ 0 = some number means that some number x 0 = 2;

                           but there is no number that multiplied by 0 will give you 2.

f(x) = (1/6)x³ - (1/2)x² + (13/3)x - 3

y - 4 = (3/4)y

You can get rid of all fractions by multiplying each term by 4:

4y - 16  =  3y

Subtract 4y from both sides:

    -16  =  -y

Multiply both sides by -1:

     16  =  y

First, find the reciprocal of the number that represents the tangent.

Then, find the inverse tangent of that answer.

For example:  If you want to find the inverse cotangent of 0.7500.

First, find the reciprocal of 0.7500:  1/0.7500  =  1.33333

Then, find the inverse tangent of 1.3333  --->   53.13°

905  =  (4/3)·π·r³

Multiply both sides by 3:   2715  =  4·π·r³

Divide both sides by 4:    678.75 =  π·r³ 

Divide both sides by π:    216.05  ≈ r³

Find the cube root:                  r  ≈  6.00