Please help, I am desperate!?! Will name Brainliest!! Suppose that a spotlight is used for lighting objects at many different distances and that the area A of the light circle produced is related to the distance x to the lighted object by A=0.1x^2.

a. If the spotlight produces 250 lumens of light energy, what function gives the intensity of the light I, (in lumens per square foot) as a function of the distance x in feet from the spotlight to its target?

b. Write and solve equations that match these questions about the light intensity from the spotlight.

i. What is the intensity of light on an object that is 20 feet from the spotlight source?

ii. How far from the spotlight is an object that recieves 100 lumens of light per square foot?

Intensity = 2500/x^2

6.25 lumem

5 Feets

Step-by-step explanation:

Given the following :

Area (A) = 0.1x^2

Intensity, Energy and Area are related by the formular :

Intensity = power / Area

A) If 250 lumens of light energy is produced :

Intensity (I) = 250 / 0.1x^2

Intensity = 2500/x^2

x = distance

B) USING THE EQUATION :

1) What is the intensity of light on an object that is 20 feet from the spotlight source?

x = 20

Intensity = 2500/x^2

Intensity = 2500/20^2

Intensity = 2500/400

Intensity = 6.25 lumen

11) How far from the spotlight is an object that recieves 100 lumens of light per square foot?

Intensity = 100

100 = 2500 / x^2

100x^2 = 2500

x^2 = 2500/ 100

x^2 = 25

x = 5 Feets

step-by-step explanation:

a child is 12 years old, and his father is 32 years older. in how many years will the age of the father be 2 times the age of the child?

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this needs to be the answer format, or else your answer is incomplete.

if the number of years is x, then the equation is

in __ years

where is the graph? need more info