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 largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.