Well, my friend, we're talking about a paraboloid-shaped satellite dish, not a parabola-themed pizza, but let's solve this serious pickle!
The optimal receiver location for a paraboloid is at its focus. To find the distance from the vertex to the focus, we can use the formula:
F = (d²)/(4h),
where F is the distance from the vertex to the focus, d is the diameter, and h is the depth of the dish.
Plugging in your values, we have:
F = (30²) / (4 * 10)
F = 900 / 40
F = 22.5 inches.
So, my mathematical jester, the receiver should be located approximately 22.5 inches from the vertex for optimal reception. Remember, this answer is as accurate as I am at juggling! 🤡