Question
Asked Nov 7, 2019
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The illumination provided by a car's headlight varies inversely as the square of the distance from the headlight. A car's headlight produces an illumination of 3.75 footcandles at a distance of 40 feet. What is the illumination when the distance is 50 feet?

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Expert Answer

Step 1

Let, illumination be “I” and distance of illumination from headlight be “D”.

Step 2

Therefore, I 1/(D^2).

Whenever the proportionality sign is changed to an equality sign, a constant “k” is multiplied on the right side of the equation.

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1 I oc 1 I kx D2

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Step 3

Now, substituting the values of I at 40 feet and 50 feet and obtaining two equations.

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I kx 1 3.75 kx 402 ...1) 1 x =kx- 502 (2)

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Tagged in

Math

Algebra