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Thank you! 

HAHAHA!!!!........ it doesn't necessarily have to be.....but....I found that it "worked"......besides ....the problem just specified that it was a function of the cosine.....so this is legit

I think I've got this one, no needfor help! Thank you though :) 

4*4*4=64 

64^(1/3)

y =  4 sin [ ( pi/ 4)x  - pi/2 ]  - 3 

Look at the graph here : https://www.desmos.com/calculator/qrjaot4u81

The rate of change will be positive  from  2 < x < 4  and then on every interval given by

(  8x , 8x + 4)

where x is a natural number

The rate of change will be negative  from  4 < x < 8    and then on every interval  given by

( 8x + 4, 8x + 8) 

where x is a natural number

The rate of change will be 0   at every  4x      where x is a natural number

Why is it negative?

The minumum  height is 1 m off the floor

The max height will be  2.5 m off the floor

Here's one possibility

y = 1.75  - .75cos  [ ( pi/2 ) * t  ]

Here's the graph : https://www.desmos.com/calculator/52h81nrcjc

At t = 0   h  = 1

At t = 2   h  = 2.5

At t = 4   h =  1

At t = 6   h  =  2.5

At t = 8   h = 1

Thank you what I was looking for was to find the error in my checking of the equation you just wrote. Though I have now figured that out but thank you for your resonse. A stands for the amount dilated horzintoally and b stand for the amount dilated vertically. 

Can someone please close this forum/check that it has been answer?

I don't know what your  " a "  and  " b "  stand for, but it looks like you want the equation of a circle with its center at  (1, 4)  that passes through  (1, 13) .

the radius of the circle  =  the distance between the center and a point on the circle

the radius of the circle  =  the distance between  (1, 4)  and  (1, 13)

Notice how the (1, 4)  and  (1, 13)  both have the same  x  coordinate.

So the distance between the two points is just  13 - 4 .

the radius of the circle  =  13 - 4   =   9

So we know that  r = 9  ,  h = 1 ,  and  k = 4 .

Plugging these values directly into the standard form of a circle.....

(x - h)² + (y - k)²  =  r²

(x - 1)² + (y - 4)²  =  9²

I believe I figured it out if you use (x-1)² + (y-4)² = 9 and plug in 1 for x and 13 for y you will get 3 = 3.

As the x part of the equation equals zero then 13-4 equals 9 sqeared. So you end up with 9² = 9. Then just square root them and you get 3 equals 3. 

Meet Global Warming.....

I live in Lousisana....we have a severe drought with no rain in sight......apparently....this Winter will be much warmer and drier than usual, too.....

Remember that to find the x coordinate of the midpoint  we add the x coordinates of the two endpoints and divide by 2 and do the same for the y coordinates to find the y coordinate of the midpoint

So...we have that

[ Ax + Bx ] / 2     = x coordinate of the midpoint

So.......

Ax + Bx  =   2 * x coordinate of the midpoint

Ax  =   2 * x coordinate of the midpoint  - Bx

Similarly

[Ay + By ] / 2  =  y coordinate of the midpoint

Ay + By   =  2 * y coordinate of the midpoint

Ay  =   2 * y coordinate of the midpoint -  By

Note that the first couple  each shake 10 hands

The next couple each shake 8 hands

The next each shake shake 6 hands....etc.

So   2 * (10 + 8 + 6 + 4 + 2)  =  60 handshakes  

I am not squaring the right side of my equatin as It is already squared. I don't  need to put three squared unlike the left side where I need to do some steps before squaring. The right side is already solved. If you rerfer to the parent function x² + y² = r2 you'll see that r is squared. Sorry for the confusion.

Same to you!

I'm no expert at this, but notice that you have:

 x^2 + y^2 = r^2  as the "parent function", then further down you have this:

(x-1)^2 + (y-4)^2 = 9   Notice that you are squaring the LHS. Shouldn't you then square the RHS as well? So, when checking it you have this:

(1-1)^2 + (y-4)^2 = 9, but if you squared 9^2 on RHS, then you will have:

y =-5       and       y = 13, which is what you want.

You go to image then push "or upload". Then expand the window and push "chose file". Then chose an image and you will be good to go!

(If any of the steps don't work for you, just ask me for help)

  Does this help?

This answer of: x = -(log(7/3))/(log(3))  is the same as:

1 - log(base3), 7 = -0.771243749, which the correct value of x, but not: 1 - log(base7), 3 =0.43542496, which is NOT correct value of x.

Thanks!

d/3 = -81   cross multiply

d = -81 x 3

d =-243

There were 60 handshakes.

I greatly appreciate your answer, but the answer must be in the form a - log(b, 3). 

Where a and b are natural whole Numbers. 

I’ve found that a = 1 and b = 7 by trial and error. 

Solve for x :
7 3^(x + 1) = 3^(1 - x) + 2

Multiply both sides by 3^(x - 1):
7 3^(2 x) = 2 3^(x - 1) + 1

Subtract 2 3^(x - 1) + 1 from both sides:
-1 - 2 3^(x - 1) + 7 3^(2 x) = 0

The left hand side factors into a product with three terms:
1/3 (7 3^x - 3) (3^(x + 1) + 1) = 0

Multiply both sides by 3:
(7 3^x - 3) (3^(x + 1) + 1) = 0

Split into two equations:
7 3^x - 3 = 0 or 3^(x + 1) + 1 = 0

Add 3 to both sides:
7 3^x = 3 or 3^(x + 1) + 1 = 0

Divide both sides by 7:
3^x = 3/7 or 3^(x + 1) + 1 = 0

Take the logarithm base 3 of both sides:
x = -(log(7/3))/(log(3)) or 3^(x + 1) + 1 = 0

Subtract 1 from both sides:
x = -(log(7/3))/(log(3)) or 3^(x + 1) = -1

3^(x + 1) = -1 has no solution since for all z element R, 3^z>0 and -1<0:
x = -(log(7/3))/(log(3))

I am glad you understand now! One unique thing about divisibility tests is that there are absolutely no exceptions to any of the rules listed.