Question

RADIO TELESCOPES The cross section of a large radio telescope is a parabola. The equation that describes the cross section is y=275x2−43x−323, where y is the depth of the dish in meters at a point x meters from the center of the dish. If y=0 represents the top of the dish, what is the width of the dish? Solve by graphing. A) The width of the dish is 10 meters.

B) The width of the dish is 15 meters.
C) The width of the dish is 5 meters.
D) The width of the dish is 20 meters.

Answer 1

The width of the dish is determined as 10√41 meters (Option A).

How to calculate the width of the dish?

The width of the dish is calculated by applying the following formula as shown below;

y = 2/75x² - 4/3x - 32/3

0 = 2/75x² - 4/3x - 32/3

multiply through by 75

0 = 2x² - 100x - 800

0 = x² - 50x - 400

The solution of the quadratic equation above can be solved using formula method and graphical method.

Using formula method, we have;

a = 1, b = -50, c = -400

so the value of x becomes;

x = 25 ± 5√41

x = 25 + 5√41 or 25 - 5√41

The width of the dish is calculated as;

w = 25 + 5√41 - ( 25 - 5√41 )

w = 25 + 5√41 - 25 + 5√41

w = 10√41 meters