Aparabolic microphone used on the sidelines of a professional football game uses a reflective dish 24 in. wide and 6 in. deep. how far from the bottom of the dish should the microphone be placed

The answer is a 6 inches away

Answer : 6 in

A parabolic microphone used on the sidelines of a professional football game uses a reflective dish 24 in. wide and 6 in. deep

Parabolic microphone is in the form of vertical parabola

Vertex at the origin so vertex is (0,0)

24 inch wide so its 12 inches  on the right and 12 inches on the left

So coordinate on parabola are (6,12)  and (6,-12)

for vertical parabola we use equation y^2 = 4ax

WE use any one of the point and find out 'a'

Lets plug in (6,12)

144= 24a

Divide both sides by 24

a= 6

So microphone is 6 inches away

(1,4) is on graph of f(x)

f(1) = 4

so 1/4 f(x)

1/4 f(1)

1/4. ×4

1

so point for function 1/4. f(x) is (1,1)

(2,20) means that the 2 is 2 hours and 20 is 20$. so there both 20$ for 2 hours only the same price. like it says. so, the dunk tank and the bounce house are the same price (20$) for the same amount of time (2 hours).

hope i