geno3141

0.9  =  9/10

First, find out how much you still owe after your down payment:

     773  -  88   =   685

Since you are going to make 5 equal payments, divide  685  by  5:

     685  ÷  5   =   137

Your monthly payment will be  $137.00.

Check:  does  5 x 137 + 88  =  773?  If so, we have the right answer; if not, we'll have to rework this...

I would begin by writing all the perfect squares of the numbers from 10 dpwm through 1:

10² = 100                                          Do this, so that you have some numbers to look at.

9² = 81                                              There may be some cases, that you need numbers larger than

8² = 64                                                      these, but they won't occur often

7² = 49               

6² = 36                                              You really don't need to write the 1² = 1.

5² = 25

4² = 16                                              The reason to start with the largest number first is that your eyes

3² = 9                                                will go from top down and it will be easier to solve the problems

2² = 4                                                if you go from largest to smallest.

1² = 1

Example:  √1152                 Of the perfect squares above, which is the largest one that divides into

                                           1152 evenly (without a remainder)?  It is 64  -->  1152 ÷ 64  =  18.

Now, write  √1152  =  √64 · √18

                                           Now look at 18; what is the largest perfect square that divides into 10?

                                           It's  9  because  18  =  9 · 2

You have:  √1152  =  √64 · √9 · √2

                                            Since  2  can't be divided by any perfect square, you're done after you

                                            simplify your answer.

√1152  =  √64 · √9 · √2  =  8 · 3· √2  =  24 √2

This is tough; write back if you can use more help (or different help!).

The amplitude is the distance from the lowest point (y-value) to the highest point (y-value).

The lowest y-value is -1, the highest y-value is +1.

The distance from -1 to +1 is  1 - -1  = 2.

The amplitude is  2.

7x + 4x + 4 + 9  =  3x + 3 +7x

Simplify each side:  7x + 4x  =  11x                 4 + 9  = 13                 3x + 7x  =  10x

11x + 13  =  10x + 3

Get all x's to one side, all the numbers to the other.

Get all the x's to one side, if you subtract  10x  from both sides all the  x's  will disappear from the right side:

11x + 13 - 10x  =  10x + 3 - 10x

x + 13  =  3

Subtract  13  from both sides:

x + 13 - 13  =  3 - 13

x  =  -10

Using the Pythagorean indentity:  sec²X - tan²X = 1     --->     sec²(4) - tan²(4) = 1

4tan(4) / sec(4)    =    [ 4·sin(4) / cos(4) ] / (1/cos(4)    =    [ 4·sin(4) / cos(4) ]  x  cos(4)

                           =    4sin(4)

So, this reduces to 1 + 4sin(4)

Assuming that you want to sort from smallest to largest:

Create two groups: one that is sorted, one that isn't.

Before you start, there are no items in the sorted part, all are in the unsorted part.

As you work, place the sorted numbers before the unsorted numbers.

Go through the unsorted list and find the smallest number. It is 20. Place this number in the sorted part (at the beginning) and leave the rest alone:

20, 70, 40, 90, 100

Keep doing this, always adding to the sorted part and reducing the unsorted part.

The second time through, go through the unsorted part (70, 40, 90, 100) and find the smallest number in this sublist and place it at the end of the sorted part.

You now have: 20, 40, 70, 90, 100    (the sorted part is 20, 40 and the unsorted part is 70, 90, 100 -- OK,                                                           it's sorted but you don't know that yet)

Do it again, starting with 70:             (the smallest number in the unsorted part is 70)

You get 20, 40, 70, 90, 100               (the sorted part is 20, 40, 70; the unsorted part is 90, 100)

Do it again, starting with 90:              (the smallest number in the unsorted part is 90)

You get 20, 40, 70, 90, 100                (the sorted part is 20, 40, 70, 90; the unsorted part is 100)

Since the unsorted part contains only one number, you are done.

In an equation like this:  y  =  acos(bx + c)

The value of a is the amplitude. For this problem the amplitude is 3.

The value of b determines the period using this equation:  Period = 2π/b  =  360°/b  

For this problem, the period of cos is 2π/1  =  2π  or 360°.

The value of c determines the horizontal shift.

To which question?

The formula:   y  =  -4.9t² + vt    can be used:

    y  =  height          v  =  initial velocity         t  =  time (in seconds)

    -4.9 m/sec²  reflects the acceleration due to gravity, - because it pulls downward

y  =  -4.9t² + 8t 

At  t = 0,  y = 0 and the ball begins to rise.

When  y = 0  again, the ball has fallen back down to earth.

If you can find the time when the ball again hits the ground, then at half that time, the ball will be at its maximum height. So we need to solve the equation:

    0  =  -4.9t² + 8t                    Factor this by factoriing out the t:

    0  =  t(-4.9t + 8)

So:  t = 0     and     -4.9t + 8 = 0

                              -4.9t = -8

                                    t = -8/-4.9              which is approximately  t = 1.633

Halfway between these two times, the ball will be at its maximum height  --->   t = 0.816

When  t = 0.816   --->  y = (-4.9)(0.816)² + 8(0.816)  ≈  3.3 m