Pregunta
A parabolic microphone used on the sidelines of a professional football game uses a reflective dish 16 in. wide
and 4 in . deep. How far from the bottom of the dish should the microphone be placed?
(1 point)
3 in .
3.2 in .
3.8 in .
4 in .
and 4 in . deep. How far from the bottom of the dish should the microphone be placed?
(1 point)
3 in .
3.2 in .
3.8 in .
4 in .
Ask by Owen Riley. in the United States
Jan 04,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The microphone should be placed 4 inches from the bottom of the dish.
Solución

¡Inicia sesión para desbloquear respuestas gratis!
Una plataforma de aprendizaje en la que confían millones de estudiantes y profesores reales.

Respondido por UpStudy AI y revisado por un tutor profesional
Como
Bonus Knowledge
To find out how far from the bottom of the dish to place the microphone, we can model the parabolic dish as a parabola in the standard form
, where
is the distance from the vertex (bottom of the dish) to the focus (where the microphone should be). Given that the dish is 16 inches wide, the parabola opens sideways and has a width of 16 inches. The depth of the dish (4 inches) helps us find the value of
.
Setting the vertex at the origin
and the overall width of the parabola as 16 inches, we sketch it from
to
at the width and at a height (depth) of 4 inches. At the edge, the parabola meets the line
when
.
Substituting these coordinates into the parabola equation gives:
This simplifies to:
From which it follows that:
Now since the focus (where the microphone should be placed) is located at
units above the vertex, we take the positive value of
as 16 inches (since we consider distances without sign). Therefore,
.
Thus, the microphone should be placed 4 inches away from the bottom of the dish, which leads us to select the option: 4 inches.

¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium