geno3141

I plan to use the quadratic formula on this equation:   x² + 2bx + (a - b)  =  0  

using     a = 1     b = 2b     c = a - b  

For the equation to have only one real solution  b² - 4ac  must be zero.

Replacing:     (2b)² - 4(1)(a - b)  =  0

                             4b² - 4a + 4b  =  0

                                             -4a  =  -4b² - 4b

Diviing by -4:                           a  =  b² + b

I hope that the variables in the equation did not confuse you with the variables in the quadratic formula.

One of the compound interest formula is:  F  =  A(1 + x )^t

where  F  =  final amount

            A  =  initial amount

            x  =  interest rate, as a decimal

            t  =  number of years

For this problem, if the inital population = A, then the final population will be 0.96A (because it decreased by 4%).

So:                                                    0.96A  =  A(1 + x)¹²

Divide both sides by A:                       0.96  =  (1 + x)¹²

Find the 12^th root of 0.96:    0.9966039468  =  1 + x

Subtract 1:                                                x  =  -0.003396                  (the '-' indicates that it is decreasing)

Notice that the coefficient of d decreases:

    2n + 1,  2n,  2n - 1,  2n - 2,  ...   1

The way that the coefficient can become one if the coefficient is   '2n - '

so that  '2n -

If  'something' is '2n - 1'  then  2n - (2n- 1)  =  2n - 2n + 1  =  1. 

Try these:    [  'cubrt' means 'cube root'   and   'sqrt' means 'square root' ]

a  =  4·cubrt(2)  -  sqrt(8)·cubrt(2)

b  =  4·cubrt(2)

c  =  4·cubrt(2)  +  sqrt(8)·cubrt(2)

I don't know if this is the smallest value of b, but it works.

If the '12' side could be the hypotenuse, then there is another answer:

Let  a = 5  and  c = 12:     a² + b²  =  c²

                                       (5)² + b²  =  (12)²

                                         25 + b²  =  144

                                                  b²  =  119

                                                    b  =  sqrt(119)

Total number of people = 90

Women = 57

Men = 90 - 57 = 33

Men who do not like tea = 7

Men who like tea = 33 - 7 = 26

People who like tea = 73

People who do not like tea = 0=90 - 73 = 17

Women who do not like tea = 17 - 7 = 10

Women who like tea = 57 - 10 = 47

In the range  0.000 < x < 0.025  the value will be  -2 - (-2)  =  0.     --->     0,025 - 0.000  =  0.025

In the range  0.100 < x < 0.250  the value will be  -1 - (-1)  =  0      --->     0.250 - 0.100  =  0.150

The value won't be zero for all x in the range (0,1).

0.025 + 0.150  =  0.175

The full distance from 0.000 to 1.000  =  1.000

Probability  =  0.175 / 1.000  =  0.175

The problem is to find the two zeros of the function and then find the distance between them.

First:  multiply out the equation:  y  =  -0.25(x - 2)(x - 22)  =  -0.25(x² - 24x + 44)

Second: set this equation to zero and solve:   0.25(x² - 24x + 44)  =  0

              Divide both sides by 0.25:                           x² - 24x + 44  =  0

              Factor:                                                         (x - 2)(x - 22)  =  0

              Find the zeros:                                             x = 2  or  x = 22

Third:  find the distance between these two answers:                                            (your turn)

You can follow these steps:

1) Use the Pythagorean Theorem to find the straight-line distance from A to C.

2) Subtract the diameter of the circle from the answer of step 1.

3) Find the circumference of the circle.

4) Find one-half of the answer of step 3.

5) Add the result of step 4 to the result of step 2.