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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
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 \( x^2 + y^2 \leq 625 \).
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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