CPhill

That's very nice, Melody  !!!!

x^2 + y^2  =  5625

This is a circle centered st the origin with a radius of 75  (miles)

a)  To find the x intercepts, let y  = 0  and we have

x^2  =  5625       take both roots

x  = +75     and x  = -75

So....the x intercepts are   (-75, 0) and (75, 0)

To find the y intercepts, let x  = 0   and we have

y^2  = 5625   take both roots

y  = +75   and y  = -75

So.....the y intercepts  are  (0, 75)  and (0, - 75) 

b)  In the form x^2 + y^2  = r^2

The radius   =  sqrt (r^2)  = sqrt (5625)  =  75

c)  =  The area  is  the area of a circle with a radius of 75....so we have

Area  = pi * r^2   =   pi (5625)   ≈  17671.45  sq miles

\(h(x)=f^{-1}(x)\)

\(h(2)=10 \)

\(h(1)=2 \)

\(f(f(10) \)   ???

The points  (2,10)  and ( 1,2)  are on the graph of h(x)

Since h(x)  is the same as  f^-1(x) ...then  the points  (10,2) and (2, 1)  are on the graph of f(x)

So   f(10)  = 2

And 

f(f(10)  =  f(2)    =     1

Vertex  ( -2, 5 )    focus  (-2, 6)

The parabola opens upward since the focus is above the vertex

p  =  the distance from the vertex to the focus  =  1

So  we have

4p(y - 5) = (x - ( -2))^2

4(1)(y - 5)  =  ( x + 2)^2

4 ( y - 5)  = ( x + 2) ^2        divide both sides by 4

y - 5 =  (1/4)(x + 2)^2       add 5 to both sides

y  = (1/4) (x + 2)^2   + 5

θ  ≈ 223.6  ....  so  .... θ/2    will lie in the 2nd quadrant

r  =  √[ 20^2 + 21^2 ]   =  √841  =  29

cos (θ)  =  -21/  29

cos (θ/2)  =   - √  [  (  1  + ( -21 / 29 ) ) / 2 ]

cos (θ/2)  =    -  √ [ (29 - 21) / (2*29) ]  = -  √ [ (8) / (2*29) ]   = - √ [ 4 /29) ] =

-   2 / √ 29

Thanks, hectictar....

Let me add that  these angles always sum to 90°

So..all you need to solve is this :

x +  41  =  90

Edit to correct an error.....there's no "pi"  in the final answer to the second part....sorry!!!

theta / 360

Area  =  theta/2  * r^2

In order, we have :

Inscribed Angle Theorem

Substitution

Division Property of Equality

Definition of Supplementary

Nothing wrong with "Research"....LOL!!!!