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Answer :
Final answer:
To find the width of the parabolic antenna, we use the equation that describes a parabola and solve for the unknown values. The width of the antenna is found to be 0 centimeters.
Explanation:
To find the width of the parabolic antenna, we need to understand that a parabolic shape can be described using the equation y = ax^2. In this case, the distance from the receiver (focal point) to the bottom of the antenna is given as 8 centimeters. The depth of the antenna is given as 72 centimeters. Since the vertex of a parabola is at the origin (0,0), we can find the value of 'a' by substituting the known point (8, 72) into the equation:
72 = a(8)^2
Solving this equation, we find that a = 1.125. Now, to find the width of the antenna, we need to calculate the x-coordinate of the point where the parabolic curve intersects the x-axis (y = 0). Setting y = 0 in the equation, we get:
0 = 1.125x^2
Simplifying, we find that x = 0. Therefore, the width of the antenna is 0 centimeters.
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