geno3141

(1/4)^1/2  =  sqrt(1/4)  =  1/2

So, the problem reduces to:  1/2  =  n/9

Multiply both sides by 9:    9(1/2)  =  n      --->     n = 4.5

1.1⁶  =  1.771561

1.1²  =  1.21

But I don't know where to go from here ...

Let  k  represent the number of kilograms over the weight limit.

First airline:       Fee  =  $20 + $22k

Second airline:  Fee  =  $32 + $19k

Since the fees were equal:                 $20 + $22k  =  $32 + $19k

Subtracting $19k from both sides:        $20 + $3k  =  $32

Subtracing $20 from both sides:                     $3k  =  $12

Dividing by 4:                                                      k  =  4      <--     the bag was 4 k overweight.

First airline:       Fee  =  $20 + $22k     --->     Fee  =  $20 + $22(4)  =  $20 +  $88  =  $108

Second airline:  Fee  =  $32 + $19k     --->     Fee  =  $32 + $19(4)  =  $32 +  $76  =  $108

                                                                      (x - 1)³ - 2(x -1)²  =  0

Factor out the common term (x - 1)²:         (x - 1)²[ (x - 1) - 2 ]  =  0

Simplify:                                                              (x - 1)²[ x - 3 ]  =  0

So, the roots are 1 (a double root) and 3.

Try:  7 x (6 - 5)³

First:  subtract the length of the towel bar from the width of the door:  70 1/3 - ( 24 1/4 )  =  46 1/12

Now to place this in the center of the door place half of this length on each side of the towel bar:

                      46 1/12  /  2  =  23 1/24

The bar should be placed  23 1/24 centimeters from each edge of the door.

A formula that can be used is:  AF·AF  =  AB·AC          or:          AF²  =  AB·AC

Because replacing 'x' witn '-x' in the equation (and simplifying) shows no change, it is an even function.

sqrt( (-x)² - 9 )  =  sqrt( x² - 9 )

For number 2:  Since the zeros occur at -2, 1, 3, and 4, the values are:  a = -2, b = 1, c = 3, and d = 4.

This will create the function:  y  =  A(x + 2)(x -1)(x - 3)(x - 4)

To find the value of A:  Since the value of y = 4 when x = 0, place these into the function:

      y  =  A(x + 2)(x -1)(x - 3)(x - 4)         --->         4  =  A(0 + 2)(0 -1)(0 - 3)(0 - 4) 

                                Simplifying              --->         4  =  A(2)(-1)(-3)(-4)

                                                                              4  =  A(-24)        

                             Dividing by -24          --->      -1/6  =  A

City A:  population = 5000(1.04)ⁿ

City B:  population = 8000(1.02)ⁿ

These will be equal when:  5000(1.04)ⁿ  =  8000(1.02)ⁿ

Find the log of both sides:      log( 5000(1.04)ⁿ )  =  log( 8000(1.02)ⁿ )

Rewriting:                      log( 5000 ) + log( 1.04ⁿ )  =  log( 8000 ) + log( 1.02ⁿ )

Rewriting:                   log( 5000 ) + n · log( 1.04 )  =  log( 8000 ) + n · log( 1.02 )

Rearranging:        n · log( 1.04 )  -  n · log( 1.02 )  =  log( 8000 ) - log( 5000 )

Factoring:                   n ( log( 1.04 ) - log( 1.02 ) )  =  log( 8000 ) - log( 5000 )

Dividing:               n  =  [ log( 8000 ) - log( 5000 ) ]  /  [  log( 1.04 ) - log( 1.02 ) ]

Using a calculator, n = 25.

Also:  5000(1.04)²⁵  =  13329

          8000(1.02)²⁵  =  13125