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Calc Problem [Related Rates]
Problem
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A spotlight on the ground shines on a wall 12m away. If a man 2m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4m from the building?
What I did
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I used related triangles to say:
x/2 = 12/y
xy=24
Taking the derivitive of both sides, I get:
x(dy)+y(dx)=0
Substituting:
3(1.6)+8(dx)=0
*The 8 comes from him being 4m from the wall, which is 12m from the light
4.8+8(dx)=0
8dx=4.8
dx = .6
I know this is wrong, can someone figure this out please? Thanks.
__________________
- Artsemis
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1.) Never tell everything you know
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