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A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y = ax 2 about the y-axis. If the dish is to have a 18-ft diameter and a maximum depth of 4 ft, find the value of a and the surface of area of the dish.

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A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y ax 2 about the yaxis If the dish is to have a 18f class=

Respuesta :

Parabola passes through the points (9,4) and (-9,4).

[tex]y=ax^2 \\4=a(-9)^2 \\ \\a= \frac{4}{81} \\ \\y=\frac{4}{81} x^2 [/tex]

The surface area of a paraboloid, not inculding its base

[tex]SA = \frac{\pi}{6}\frac{r}{h^2}[{(r^2 + 4h^2)}^{\frac{3}{2}} - r^3][/tex]

[tex]r=9,h=4 \\SA = \frac{\pi}{6}\frac{9}{4^2}[{(9^2 + 4\times4^2)}^{\frac{3}{2}} - 9^3]\approx 299.54[/tex]


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