CPhill

(3/4)  /  (7/8)     invert the second fraction and multiply

(3/4) * (8/7) =

24/28 =

6/7

Don't worry.....we get "F's"  in math all the time....LOL!!!!!

x:  8,  7,  10,  6,  2

y:15,14, 17,13,  9

The slope between any two points is   [ 13 - 9] / [ 6 - 2] =  4 /4 = 1

Using the first point we can write the equation of the line as follows:

y - 15 = 1 (x - 8)

y - 15 =  x - 8

y = x + 7

-x/2+20<4   subtract 20 from each side

-x/2 < -16      multiply both sides by 2

-x < -32        multiply through by -1 and reverse the inequality sign

x > 32

1. Solve x = 6/3 for x. Does the set of rational numbers include whole numbers ? Why or why not?

x = 6/3

x = 2

The set of rational numbers includes whole numbers because any whole number can be written as a/b....Example......10 can be written as 30/3

2. Solve y = -12/4 for y. Does the set of rational numbers include integers? Why or why not?

y = -12/4

y = -3

The set of rational numbers includes the integers.......for the same reason as above, any integer can be written in a/b form

x:   2,  4,   7,    10,  20

y:   2,  3,   4.5    6,   11

The slope between any two points  is constant  and equals 1/2.....for instance, the slope between the first two points =

[ 3 -2 ] / [ 4 - 2]  =  1/2

Using this and one of the points - I'll use the first one - we can write the equation of a line thusly

y - 2  = (1/2)(x - 2)

y  = (1/2)x - 1 + 2

y = (1/2)x + 1

x:   3,   6,   8,  10,  22

y:  13,31, 43, 55,127

The slope between any two points =   [31 - 13] / [ 6 - 3]  =  18/3  = 6

In similar fashion to the first problem, we have

y - 13 = 6 ( x - 3)

y - 13 = 6x - 18

y = 6x - 5

A) Given that y=(x^2 +7)^(1/2) find dy/dx

Let   x^2 + 7  = m

And we can write

dy/dx =  dy/dm * dm/dx

So we have

y = m^(1/2)          taking the derivative of this = 

dy/dm  =  (1/2)m^(-1/2)

And 

dm/dx =  2x

So...puting this all together, we have

dy/dx =  dy/dm * dm/dx =   (1/2)m^(-1/2) * 2x     =   (1/2)(x^2 + 7)^(-1/2) * 2x =    x * (x^2 + 7)^(-1/2)

Example ....if we wanted to evaluate :

log₂ 8   

Key in :

log(8, 2)      and hit "enter"

Can't do any more with this.....it's fully simplified....

Yep.........it's rational

Example →    .66666.......   =   2/3