A radio tower can transmit a signal 25 miles. Suppose you orient a coordinate plane with the tower at the origin. Which inequality represents all the points on the coordinate plane that would receive the signal? O² +3² ≤25 O² + y² ≤625 *********** ********* *********** O +3² ≥ 625 Submit Answer
A radio tower can transmit a signal 25 miles. Suppose you orient a coordinate plane with the tower at the origin. Which inequality represents all the points on the coordinate plane that would receive the signal? O² +3² ≤25 O² + y² ≤625 *********** ********* *********** O +3² ≥ 625 Submit Answer
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![### Understanding Radio Signal Coverage on a Coordinate Plane
A radio tower can transmit a signal 25 miles. Suppose you orient a coordinate plane with the tower at the origin. Which inequality represents all the points on the coordinate plane that would receive the signal?
- \( x^2 + y^2 < 25 \)
- \( x^2 + y^2 \geq 625 \)
- \( x^2 + y^2 \leq 625 \)
**Explanation:**
In the context of the coordinate plane, the equation of a circle with radius \( r \) centered at the origin \((0,0)\) is given by:
\[ x^2 + y^2 = r^2 \]
Since the radio tower has a transmission radius of 25 miles, the equation would be:
\[ x^2 + y^2 = 25^2 \]
\[ x^2 + y^2 = 625 \]
Therefore, the inequality representing all the points on the coordinate plane that would receive the signal (inside or on the circle) is:
\[ x^2 + y^2 \leq 625 \]
#### Important Notes:
- \( x^2 + y^2 < 25 \) represents points inside a circle with a radius of 5, which does not correlate to the given problem.
- \( x^2 + y^2 \geq 625 \) represents points outside and on the boundary of a circle with a radius of 25, opposite of what is needed.
Thus, the correct inequality is \( x^2 + y^2 \leq 625 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0890c2ce-3692-4718-a578-4f9466fde9bf%2F97404c6e-620b-413f-a0fd-1feea61a4489%2Fh6bspj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Radio Signal Coverage on a Coordinate Plane
A radio tower can transmit a signal 25 miles. Suppose you orient a coordinate plane with the tower at the origin. Which inequality represents all the points on the coordinate plane that would receive the signal?
- \( x^2 + y^2 < 25 \)
- \( x^2 + y^2 \geq 625 \)
- \( x^2 + y^2 \leq 625 \)
**Explanation:**
In the context of the coordinate plane, the equation of a circle with radius \( r \) centered at the origin \((0,0)\) is given by:
\[ x^2 + y^2 = r^2 \]
Since the radio tower has a transmission radius of 25 miles, the equation would be:
\[ x^2 + y^2 = 25^2 \]
\[ x^2 + y^2 = 625 \]
Therefore, the inequality representing all the points on the coordinate plane that would receive the signal (inside or on the circle) is:
\[ x^2 + y^2 \leq 625 \]
#### Important Notes:
- \( x^2 + y^2 < 25 \) represents points inside a circle with a radius of 5, which does not correlate to the given problem.
- \( x^2 + y^2 \geq 625 \) represents points outside and on the boundary of a circle with a radius of 25, opposite of what is needed.
Thus, the correct inequality is \( x^2 + y^2 \leq 625 \).
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