A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y=ax2 about the y-axis. If the dish is to have a 6-foot diameter and a maximum depth of 2 feet, find the value of a and the surface area (in square feet) of the dish.

Question

Physics

Shaun Shepard

28 June, 13:27

A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y=ax2 about the y-axis. If the dish is to have a 6-foot diameter and a maximum depth of 2 feet, find the value of a and the surface area (in square feet) of the dish.

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Answers (1)

Know the Answer?

Cael Davenport · Answer 1

Answer:a=2/25 ... 90.01ft²

Explanation:

y=ax²

2=a (5) ²

2=25a

a=2/25

Find a by x=5, y=2

y=2/25x²

∆y/∆x=4/25x

S=2π|x√1 + (4/25x) ² dx

2π|x√1+16/625x² dx

625/24π[ (1+16.25/25) ³/² - (1+0) ³/²

625/24π[41√41/125-1]

=90.01ft²