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A street light is at the top of a 13.0 ft. tall pole. A man 6.3 ft tall walks away from the pole with a speed of 3.5 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 48 feet from the pole?

Respuesta :

Answer:

[tex]\dfrac{dL}{dt}=5.82 \ ft/s[/tex]

Explanation:

given,

street light height = 13 ft

man height = 6.3 ft

speed of the man = 3.5 ft/sec

[tex]\dfrac{H}{L} = \dfrac{h}{l}[/tex]

[tex]\dfrac{H}{L} = \dfrac{h}{L-x}[/tex]

[tex]\dfrac{L}{H} = \dfrac{L-x}{h}[/tex]

hL = H(L-x)

hL = HL-Hx

[tex]L = \dfrac{Hx}{H-h}[/tex]

[tex]L = \dfrac{13x}{13-6.3}[/tex]

L = 1.94 x

[tex]\dfrac{dL}{dt}=\dfrac{dL}{dx}\dfrac{dx}{dt}[/tex]

[tex]\dfrac{dL}{dt}=1.94\times 3[/tex]

[tex]\dfrac{dL}{dt}=5.82 \ ft/s[/tex]

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