geno3141

a + 1/a = √3    Multiply by a:

a² + 1 = √3a

a² - √3a + 1 = 0    Solve by quadratic formula:

a = [ √3 ± √(3 - 4) ] / 2

a = [ √3 ± i ] / 2

a^4 = (a²)²

a² =  [ √3 + i ]/ 2  x  [ √3 + i ]/2  =  [1 + √3i] / 2

a^4 =  [1 + √3] / 2 x  [1 + √3] / 2  =  [-1 + √3i] / 2

1/ a^4  =  1 / (  [-1 + √3i] / 2 )  =  2 / [-1 + √3i]  x  [-1 - √3i]  / [-1 - √3i]  = [-1 - √3] / 2

a^4 + 1 / a^4  =  [-1 + √3i] / 2 + [-1 - √3] / 2  =  -1

log(10000)

What is the last symbol right before the equal sign?

(-3x³y³)^5  =  (-3)^5 · (x³)^5 · (y³)^5

                  =  -243 · x^15 ·y^15

When you have an exponent to an exponent, multiply the exponents together.

ln(π) / [3ln(π)] + 2

The ln(π)'s cancel:

   1/3 + 2    =    2 1/3

To find the value of b, divide both sides by 17:

   7b ÷17  =  1/2 ÷ 17

          b  =  1/2 x 1/17

          b  =  1/34

There are three types of problems; all can be solved using this equation:  Part  =  Percentage x Total

In that formula, the percentage is to be written as a decimal.

First type:

You want to know the percentage:

     What percentage is 23 out of 86?

     Percentage = Part / Total x 100     --->     Percentage  =  23 / 86 x 100  =  26.7%  (approximately)

You know the total amount and the percentage and you want to find the part:

     How many are 35% of 219?      (35% as a decimal is .35)

     Part =  Percentage x Total     --->   Part  =  .35 x 219  =  76.65

You know the part and the percentage and you want to find the total:

     75 is 42% of how many?           (75% as a decimal is .75) 

    Total  =  Part / Percentage    --->     Total  =  75 / .42  =  178.6  (approximately)

Product goes on the top; sum goes on the bottom.

Does 8 divide evenly into 216; if it does, your answer is 8.

If it doesn't, try 4.

If 4 doesn't work, try 2.

You will also need to know the number of terms.

If you know the first term:  a

the last term:  l

and the number of terms:  n,

you can use these to find the common ration: r

by using this formula that finds the last ters:  l  =  a·r^(n-1).

Example:  The first term is 16 and the 10th term is 615.09375, what is the common ratio?

Solution:     615.09375  =  16·r^(10-1)

                 615.09375  =  16·r^(9)

Divide both sides by 16:

                 38.443359375  =  r^9

Take the ninth root of both sides ( use  r^(1/9) ):

                  38.443359375 ^ (1/9)  =  1.5  <----  Answer