A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at the focus. If the dish is 96 feet across at its opening and 8 feet deep at its center, where should the receiver be placed?

72 feet

Step-by-step explanation:

We have that the vertex at the origin in an upward concave is:

y = a * x ^ 2, we solve for a:

a = y / (x ^ 2)

Thus:

The points from the origin (0,0) are (-48, 8) and (48, 8), we replace:

a = 8 / (48 ^ 2) = 1/288

Therefore the equation would be:

y = (1/288) * x ^ 2

288 * y = x ^ 2

Now, be distance above the vertex to put the receiver, which would be the focus, we have:

4 * p = 288

we replace:

4 * p = 288

p = 288/4

p = 72

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!