CPhill

Thanks, Supermanaccz

He is correct.....

The correct choice  is  the third one

This is a hyperbola that intercepts the y axis

Here's the graph, NSS

https://www.desmos.com/calculator/bmuwoataoe

The center  is  (0,0)

Putting this into standard form by dividing both sides by 84  we have

y^2            x^2

___    -    _____     =     1

  7              28

The domain is all real numbers because the graph  extends to infinity in both directions along the x axis

The  range  is   y ≤ - √7   and  y  ≥ √7

The first answer is correct

Hmmm....maybe someone else knows how they got this......

We can find the first term a₁, thusly

a₁

____    =  Sum             .......so......

1 - (r)

  a₁

_______    =    25

1 - (-1/3)

  a₁

____   =  25           multiply both sides by 4/3

  4/3

a₁  =  25 (4/3)  =  100/3

So.....the second term is   (100/3) (-1/3)  =  -100 / 9

If the question is "how much greater"  we have  subtraction

9* 10^(-5)  - 3* (10)^(-6)  =  0.000087  m

If the question is "how many times greater"  we have  division

9 * 10^(-5)              3 * 10^6             3 * 10  =       30  times 

_________   =       _______     =

3 * 10^(-6)                   10^5

Here's the graph, NSS

https://www.desmos.com/calculator/udd3cenf8a

An ellipse has two lines of symmetry

So.....the correct answer  is  the second one

Let x  be th first number and y be the second

So  x + y  =  18   ⇒   y  =  18 - x

Call the function that we wish to maximize, M....so we have

M  =  xy^2

M = x (18 - x)^2

M =  x (x^2 - 36x + 324)

M = x^3 - 36x^2 + 324x

Take the derivative and set to 0

M'  = 3x^2 - 72x + 324  =  0     

x^2 - 24x + 108  =  0        factor

(x - 18) (x - 6)  =  0

Set each factor to  0  and solve for x  and we have that x  =  18  or x = 6

The second derivative will gives us a min and max for the function

Taking the second derivative. we have

6x - 72

Subbing 18  into this gives a positive....so.... this is a  minimum for the function

Subbing 6  into this gives a negative so this is a  max  for the function

So the max product  is  when x  = 6  and y  = 12  =    6 (18 -6)^2   =  6 * 12^2  =  864

The largest possible value for X  will be when the two integers are the same....this will occur when the first two integers are  > 9  but < 10

Rounding them up   produces  10 * 10  =  100

Rounding them down produces  9 * 9   =   81  =  X

Let the height of the prism = H  

Since the cone touches all four sides of the prism, the base must be square

So.....Let S be the side of the prism

So.....the volume of the prism is  S^2 *H  (1)

The radius of the cone  =  (1/2)S  and its height is H

So....its  volume  is   (1/3)*pi *(1/2 S)^2 * H   = (1/12)*pi*S^2*H  (2)

So.....the  ratio of (2)  to (1)  is

(1/12)* pi * S^2 * H                    pi

________________  =            ___

    S^2  * H                                12

A little tricky  !!!

I  to D   we go back 5

5 to 7   we go up 2

So   (x - 5, x + 2)  ⇒ "b"

10 left, 3 down   =  (x - 10, y - 3)  ⇒  "d"

We only need to look at one vertex and its after-image....look at C, C'

C =   (2, - 2)      C'  =  ( -2, -7)

So    (  x - 4,  y  - 5)  ⇒  "b"