A parabolic microphone used on the sidelines of a professional football game uses a reflective dish 20 in. and 5 in. deep. How far from the bottom of the dish should the microphone be placed?
4 in.
4.6 in.
4.8 in.
5 in.
I'm really sorry this is the only answer I need could someone help?
Update guys, it's 5 :)
unit 6 lesson 5
B
A
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A
C
20 inches what? Diameter at 5 inches from vertex?
then vertex at (0,0)
focus at (a,0)
rim at (5,10)
y^2 = 4 a x
100 = 4 a(5) = 20 a
a = 5 inches from vertex
Conic Sections Test Part 1:
1: 2 sqrt 13
2: have to type this one sorry D:
3: center: (0,-3); r= sqrt 5
4: (x+3)^2 + (y-2)^2=9
5: (x-4)^2 + (y+3)^2=4
6: (x-3)^2 / 16 + (y-1)^2 / 4=1
7: (x+4)^2 / 9 + (y+1)^2 / 49=1,(-4-1±2 sqrt 10)
8: this one too :(
9: 152.00 million km
10: x^2 / 3 + (y+5)^2 / 12 =1
11: (y-3)^2= -2(x-1)
12: focus: (4,3); directrix: x=6
13: 5 in
14: this is a graph question use mathway to graph it :D
15: (y+3)^2 / 25 - (x-1)^2 / 15 =1
16: y= sqrt 7 / 4 x+4 and y= - sqrt 7 / 4 x+4 (not the one in parentheses)
i'm not sure if they'll change up numbers but i got 100% so gl :D!!
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To determine the distance from the bottom of the dish where the microphone should be placed, we need to consider the shape of the reflective dish and the properties of a parabola.
The reflective dish is in the shape of a parabola, which is a curve with certain characteristics. One of these characteristics is that any sound originating from a focus point of the parabola will reflect off the surface and converge at another point called the vertex, which is also the center of the dish.
In this case, the diameter of the dish is given as 20 inches, which means the distance from one side of the dish to the opposite side (across the center) is 20 inches. The depth of the dish is given as 5 inches.
Now, we can use the properties of a parabola to find the distance from the bottom of the dish where the microphone should be placed. Since the microphone needs to be at the focus point (where the sound originates), we need to find the distance from the vertex (the center of the dish) to the focus point.
To do this, we can use the formula for the distance from the vertex to the focus point, which is given by the equation:
f = (1/4) * (depth of the dish)
In this case, the depth of the dish is 5 inches, so:
f = (1/4) * 5 = 1.25 inches
Therefore, the microphone should be placed 1.25 inches from the bottom of the dish.
None of the given answer choices matches this result of 1.25 inches, so it seems that there might be an error in the options provided. If none of the options match the calculated result, it is best to consult the source of the question or seek clarification.