geno3141

(-1)² = 1

(-1)³ = -1

(-1)⁴ = 1

2(-1)^4-(-1)^3-42(-1)^2+16(-1)+160

= 2(1) - (-1) -42(1) +16(-1) + 160

= 2 + 1 - 16 + 160

= ...

3x - 7y  =  7     --->  multiply by 9  --->      27x - 63y  =  63

2x - 9y  =  7     --->  multiply by -7  -->    -14x + 63y  =  -49

               Add down the columns:    --->     13x           =  14

                                                                         x    =  14/13

3x - 7y  =  7     --->  multiply by 2  --->      6x - 14y  =  14

2x - 9y  =  7     --->  multiply by -3  -->     -6x + 27y  =  -21

               Add down the columns:    --->             13y  = -7

                                                                         y    =  -7/13

If the problem is  169.88 / (6.022 x 10²³)  then the answer is  28.21 x 10^-23  =  2.821 x 10^-22.

If the problem is  (169.88 / 6.022) x 10²³   then the answer is 28.21 x 10²³  =  2.821 x 10²⁴.

Since  tan(2x) = [2tan(x)] / [1 - tan²(x)]  

--->  cot(2x)  =  [1 - tan²(x)]  / [2tan(x)]

--->  cot(4x)  =  [1 - tan²(2x)]  / [2tan(2x)]

--->  4cot(4x)  =  2[1 - tan²(2x)]  / [tan(2x)]

                      =  2[ 1 - ( 2tan(x) / [1 - tan²(x)] )² ] / [ 2tan(x) / (1 - tan²(x) ) ]  

                      = 2 / [ 2tan(x) / ( 1 - tan²(x) ) ]   -   2( 2tan(x) / [1 - tan²(x)] )² /[ 2tan(x) / ( 1 - tan²(x) ) ]  

                       =  2 · ( 1 - tan²(x) ) / 2tan(x)  -  2( 2tan(x) / [1 - tan²(x)] )² · ( 1 - tan²(x) ) / ( 2tan(x) )

                      =  ( 1 - tan²(x) ) / tan(x) - 2( 2tan(x) / [1 - tan²(x)] )

                      = ( 1 - tan²(x) ) / tan(x) - ( 4tan(x) / [1 - tan²(x)] )

                      = 2cot(2x) - 2tan(2x)

----------------------------------------------------

Because:

2cot(2x)  =  [1 - tan²(x)]  / [tan(x)]

2tan(2x)  =  [4tan(x)] / [1 - tan²(x)]  

If two angles are supplementary, then their sum = 180°   --->   ∠A + ∠B  =  180°

∠A = 19·∠B          --->         substituting:                             19∠B + ∠B  =  180°

                                           simplifying:                                       20∠B  =  180°

                                           dividing:                                              ∠B  =  9° 

Since  ∠A = 19·∠B    --->  ∠A = 19·9°   --->  ∠A = 171°

percent of change  =  (amount of change) / (original amount) x 100

amount of change  =  83 - 56  =  27

original amount = 83

percent of change  =  27 / 83 x 100  =  32.53%  (approximately)

Area = length x width

length = 41 1/5 inches = 41.2 inches

width = 23 3/4 inches = 23.75 inches

Area  =  41.2 x 23.75  =  978.5 square inches

cos^-1(24) does not exist because the value of cos must be between -1 and 1, inclusively.

What is x approaching?

If you let n = 5:

a = 2n + 1  --->  a = 2(5) + 1  =  11

b = 2n² + 2n  --->  2(5)² + 2(5)  =  60

c = 2n² + 2n + 1  --->  2(5)² + 2(5) + 1  =  61

Now, verify that  11² + 60²  =  61²