MATH SOLVE

2 months ago

Q:
# The equation of a circle is (x+4)2+(y−5)2=121.1.) What is the center and radius of the circle? center: (−4, 5); radius: 11 center: (−4, 5); radius: 121 center: (−4, −5); radius: 121 center: (4, −5); radius: 112.) One of the lamp posts at a bank has a motion detector on it, and the equation (x+15)2+(y−12)2=25 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? 5 ft 10 ft 50 ft 125 ft3.) Jenni plots her house and yard on a computer. She determines that the circle that defines the part of the front yard that gets watered by the sprinkler is (x−9)2+(y+11)2=16.What is the diameter, in meters, of the circular area that gets watered by the sprinkler? 4 m 8 m 16 m 32 m

Accepted Solution

A:

Part 1) The equation of a circle is (x+4)²+(y−5)²=121.

What is the center and radius of the circle?

we know that

the equation of a circle is of the form

(x-h)²+(y-k)²=r²

in the problem

(x+4)²+(y−5)²=121.------> (x+4)²+(y−5)²=11²

the center (h,k) is the point (-4,5) and the radius is 11

Part 2) we have that

(x+15)²+(y−12)²=25-------> (x+15)²+(y−12)²=5²

we know that

the greatest distance, in feet, a person could be from the lamp and be detected is the radius

the radius is equal to 5 ft

the answer Part 2) is 5 ft

Part 3) we have that

(x−9)²+(y+11)²=16--------> (x−9)²+(y+11)²=4²

the radius is equal to 4 m

so the diameter is ------> 4*2-----> 8 m

the answer Part 3) is

8 m

What is the center and radius of the circle?

we know that

the equation of a circle is of the form

(x-h)²+(y-k)²=r²

in the problem

(x+4)²+(y−5)²=121.------> (x+4)²+(y−5)²=11²

the center (h,k) is the point (-4,5) and the radius is 11

Part 2) we have that

(x+15)²+(y−12)²=25-------> (x+15)²+(y−12)²=5²

we know that

the greatest distance, in feet, a person could be from the lamp and be detected is the radius

the radius is equal to 5 ft

the answer Part 2) is 5 ft

Part 3) we have that

(x−9)²+(y+11)²=16--------> (x−9)²+(y+11)²=4²

the radius is equal to 4 m

so the diameter is ------> 4*2-----> 8 m

the answer Part 3) is

8 m