CPhill

1)

y  =  (1/12)x^2   multiply both sides by 12

12y  = x^2

And we have the form

4py  =  x^2

4p  = 12

p  =3

The vertex  is  (0,0) ...the parabola turns upward   

The focus  is  ( 0, 0 + p )   =   (0, 3)

The directrix  is  y  =  -3

Third answer

If I can see this correctly..... believe that "d" is correct

BC  not a tangent because  ABC  =  (180 - 25 - 60 )  =  95° (not equal to 90 )

We have  12 equal sides  in the 4 triangles

Let s  =  the side of each

The total area is     4 (1/2)(s^2)√3/2   =  √3s^2

So....in a larger equilateral triangle.....each  side  will be  12s/3  =  4s   

So....the area of the largwer equilateral triangle  =  

(1/2) (4s)^2 √3/2  =  16s^2√3/4   =  4√3s^2

So....the desired ratio is     √3s^2  / [ 4√3  s^2 ]   =   1 / 4

3.

Multiply both sides by -8

-8x  =  y^2

We have the form

4px  =  y^2     ⇒     -8  = 4p  ⇒     p  =  -2

The vertex of this parabola  is  (0,0)

The focus  is  ( 0 + p , 0 )   =   ( 0 - 2, 0 )  =  (-2, 0)

The directrix  is  x  =  2

Last answer

4.  Vertex  (0, 0 )    Focus  = (2.5, 0)

This parabola opens to the right

The form is

4px  = y^2

p  = 2.5   so

4 (2.5)x  = y^2

10x  =  y^2   divide both sides by 10

x  = (1/10) y^2

7 ( n + 4)  =  5(n + 8)

7n + 28  = 5n + 40

2n  =  12

n  = 6

We have 

2/11  *  9/10   =       18 / 110   =   9 /55

The Intersecting Chord Theorem  says that the products of the respective chord segments are equal

2 * 15  =  5 * n

30  = 5 * n          divide both sides by 5

6m  =  n

Number of liters consumed  =  3000 / 100 * 6  =  30 * 6  =  180

Total cost  =  Liters onsumed * Price per liter  = 

180 * 1.20   =  $216

Cost per person    =  216 / 4  =  $54

You have given the probability, RP...."odds"  are a little different

Odds  =  # Favorable Outcomes  / # Unfavorable Outcomes  =

4 :  2    =

2 :  1

This makes sense....we are twice as likely to land in a shaded area as a non-shaded one!!!