A company designed and sells an ultrasonic receiver, which detects sounds unable to be heard by the human ear. The receiver can detect mechanical and electrical sounds such as leaking gases, air, corona, and motor friction noises. It can also be used to hear bats, insects, and even beading water. The receiver is 1818 in. deep. The focus is 6 in.6 in. from the vertex. Find the diameter of the outside edge of the receiver.

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ajeigbeibraheem ajeigbeibraheem · Answer 1 · 2020-04-24T06:38:11+02:00

Answer:

the diameter of the outside edge of the receiver is [tex]8\sqrt{18} \ \ \ inches[/tex]

Explanation:

From the schematic free body diagram illustrating what the question is all about below;

Let represent A to be the vertex where the receiver is being placed

S to be the focus

BP to be equal to r (i.e radius of the outer edge)

BC to be 2 r (i.e the diameter)

Given that AS = 4 in and AP is 18 in

Let AP be x- axis and AY be y -axis

A=(0,0)

S=(4,0) = (0,0)

So that the equation of the parabolic path of the receiver will be:

[tex]y^2 =4 ax \\ \\ y^2 = 4*4*x \\ \\ y^2 = 16x[/tex]

B = (AP, BP)

B = (18, r)

B lies y² = 16 x

r² = 16 x

r² 16 × 18

[tex]r = \sqrt{16*18 } \\ \\ r = 4\sqrt{18}[/tex]

Diameter BC = 2r

[tex]2* 4\sqrt{18} \\ \\= 8\sqrt{18 } \ \ \ inches[/tex]