72

3 !

11 minutes 11 seconds to !

1. x^2              y^2

+ = 1

736^2        1467^2

2. 2PQ = <-16,2>  magnitude =sqrt(260)

3.The center is (0,0)

The vertices are at (0,±25)

The foci are at (0, ±20)

Step-by-step explanation:

1.  Equation for an ellipse

x^2/a^2+ y^2/b^2 = 1

a is the distance from  the center to the  ellipse

a = the radius of the moon  plus the shorter distance of the satellites orbit

a = 567+ 169

   =736

b =the radius of the moon  plus the longer distance of the satellites orbit

b = 567+ 900

b =1467

x^2              y^2

+ = 1

736^2        1467^2

2.  P( -5,5)  Q (-13,6)

PQ = Q-P

    = (-13--5, 6-5)

    = (-13+5,1)

   = (-8,1)

2 PQ = 2* (-8,1)

           = (-16,2)

magnitude = sqrt((-16)^2 +2^2)

                   = sqrt(256+4)

                    =sqrt(260)

3.  x^2/225 + y^2/625 = 1

is of the form (x-h)^2/a^2 + (y-k)^2/b^2 =1

where (h,k) is the center

The center is (0,0)

The vertices are at (±b,0)  since b>a

sqrt(b^2) = sqrt(625) = 25

The vertices are at (0,±25)

The foci are at (0, ±c)

where b^2= a^2 +c^2

         625^2 = 225+c^2

Subtract 225 from each side

         400 = c^2

sqrt(c^2) = sqrt(400)

c = 20

The foci are at (0, ±20)

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

a=24; b=12

step-by-step explanation:

a/b=2: 1

a=2b

36/(1+2)=12

b=12

a=24