Question 1167899
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Please answer this question, I tried but I don't understand it.

Suppose a designer of a 10 ft. parabolic solar cooker wants to place the cooking pot 5 ft. above the vertex. 
For reference, the first considers a parabolic string with a base 10 ft. and a focus at 5 ft. from the vertex. 
How deep is the parabolic solar cooker?

Thank you for your help!
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In this problem, you are given the size 10 ft of the opening of the parabolic solar cooker,
and the distance 5 ft from the vertex to the focus of the paraboloid (same as the place for cooking).


They want you find the depth of the parabolic mirror.



   &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U> S O L U T I O N </U>


<pre>
To solve such problems,  use an equation of the parabolic cross-section (which is a parabola)
in the form

    y = {{{(1/(4p))*x^2}}}.    (1)


In this form, 'p' is the focal distance, i.e. the distance of 5 ft from the vertex 
to the cooking place;  x is half of the opening, i.e. 10/2 = 5 ft;  y is the depth of the paraboloid.


So, we substitute  p = 5 ft  and  x = 5 ft  into equation (1), and we get

    y = {{{(1/(4*5))*5^2}}} = {{{25/20}}} = {{{5/4}}} ft = 1{{{1/4}}} ft.


At this point, the problem is completely solved.


<U>ANSWER</U>.  The depth of the paraboloid is 1{{{1/4}}} ft.
</pre>

Solved.