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anonymous

  • 5 years ago

Calculus 1: The illumination of an object by a light source is directly proportional to the strength of the sourcee and inversely proportional to the square of the distance from the source. if 2 light sources, one 3 times as strong as the other, are placed 10 ft apart, where should the object be placed on the line between the sources so as to receive the least illumination

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  1. nowhereman
    • 5 years ago
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    1. Choose a coordinate system on that line between the two sources. 2. Write down the light intensity as a function in these coordinates. You can take all proportionality constants as 1 because they don't influence extremal points. 3. Find the local and then global extrema of that function.

  2. anonymous
    • 5 years ago
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    How do I write down the light intensity as a function?

  3. nowhereman
    • 5 years ago
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    You have to write the distance in terms of your coordinate and add the intensities of the two lamps together.

  4. dumbcow
    • 5 years ago
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    to get you started we know our function needs to be in terms of distance because thats what they want as an answer. define variables I = illumination s=strength of lamp 1 d=distance from lamp 1 direct proportion means s goes up, I goes up inverse proportion means d^2 goes up, I goes down Lamp 1: I = s/d^2 Lamp 2: I = 3s/(10-d)^2 second lamp 3X as strong and total space between lamps is 10 so distance from lamp 2 is 10-d Total Illumination: like nowhereman said we have to add them together I = s/d^2 + 3s/(10-d)^2 Now the goal is to minimize illumination Differentiate with respect to d and set equal to 0 solve for d

  5. amistre64
    • 5 years ago
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    tag!!

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