The blueprints for a police station show that one of the lamp posts has a motion detector on it, and that the equation (x+14)2+(y−6)2=9 describes the boundary within which motion can be sensed. what is the greatest distance, in feet, a person could be from the lamp and be detected?

3 ft

6 ft

9 ft

81 ft

3 feet

Step-by-step explanation:

Given: The blueprints for a police station show that one of the lamp posts has a motion detector on it, and that the equation describes the boundary within which motion can be sensed. :

→ which is a equation of a CIRCLE.

When we compare it to the standard form of equation of circle i.e. , we get the radius of the circle = 3

Consider the lamp post as the center of the area covered by the detector.

Then the greatest distance a person could be from the lamp and be detected = Radius of the circular area

=3 feet.

y < -3

step-by-step explanation:

-3y - 2 > 7

-3y -2 + 2 > 7+2

-3y > 9

-3y/-3 < 9/-3   (change the inequality sign when multiplying or dividing by a negative number)

y < -3