CPhill

The tranverse axis contains the two foci and two vertices

Thus.....this hyperbola  intersects the x axis

So....the form will be

(x - h)^2            (y  - k)^2

_______  -       ________   =       1

    a^2                    b^2

(h, k)  =  (-3, 2)

2a  = 12            2b  = 8

a  =  6                 b  = 4

So we have

(x  + 3)^2         ( y - 2 )^2

________  -   _________    =      1

    36                   16

First one......

a^2  =  45

a  = √45

a  =  3√5   

2a   =  length of  major axis  =   6√5

b^2  =  27

b  =√27

b =  3√3

2b  =  length of minor axis  = 6√3

Good job, Jenny   !!!

If we had a square  with a diagonal  =  4√2 units.....the side of the square  =  4 units

Then the area  of the square  =  side^2  =  4^2  =  16 units^2

So.....the area of this isosceles triangle will be  1/2  of this

Call the number of pages  he has read, R

Call the number of pages he hasn't read, 193 - R

So...we have that

R  =  3 + (1/4)(193 - R)       simplify

R  = 3 + 193/4  -  (1/4)R      add  (1/4)R  to both sides

(5/4)R  =  3 + 193/4          multiply through by  4

5R  =  12  +  193

5R  =  205       divide both sides by  5

R  =  41 = pages he has read

So ....  he hasn't  read  (193 - 41)   =  152  pages

Proof :

(1/4)  of the pages he hasn't read  = 152/4   = 38 pages

And 3 more than this  = 41  = pages he has read .....

Assuming exponetial growth.....the function  is

y  = 800 (1.032)^x

Here's the graph  :  https://www.desmos.com/calculator/w6fslnsljd

The y intercept  = (0, 800)

When  x =  35,  y  ≈  2409

Let N be the number  and we have that

.92 N  =  29             divide both sides by .92

N  =  29 / .92  =   29 / (92/100)   =    29 * 100  /92  =   29 *  25 / 23  =    725  / 23

LOL!!!.......

I don't see one, EP......

The smaller area  is the  difference between the area of a sector  of 1/6 of the circle  less the area of a equilateral triangle with a side of 6.....this is given by

[(1/6) pi * 6^2   -  (1/2)6^2 * √3/2  ]    (1)

So....the   larger area  =

Area  of circle  - (1) 

So

pi*6^2  -   [(1/6) pi * 6^2   -  (1/2)6^2 * √3/2  ]  =

(5/6) pi * 6^2  + 9√3   =

[30pi + 9√3] units^2

I get 20....

112     202      314     404   516   606   718   808  

134     224      336     426   538   628

156     246      358     448

178     268