One of the lamp posts at a shopping center has a motion detector on it, and the equation (x+16)2+(y−13)2=36 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?

(x+16)²+(y−13)²=36

The given equation is of a circle.

comparing it with general equation, radius r =6

so the lam post can detect upto 6 feet .

 6 feet is the greatest distance that a person could be from the lamp and be detected.

Step-by-step explanation:

Since we have given that

The equation is :

It is the equation of circle in which center is (h,k) i.e. (-16,13)

The general equation of circle is given by

Here, the radius 'r' is given by

Here, the greatest distance a person could be from the lamp and be detected is represented by radius i.e. r = 6 feet.

Hence, 6 feet is the greatest distance that a person could be from the lamp and be detected.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet