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A street lamp is 5 m tall. A person 2 m tall walks away from the lamp at a speed of 1.2 m/s. Let \(x\) be the distance of the person from the base of the lamp, and \(s\) the length of their shadow.
Show that \(\tfrac{5}{x+s} = \tfrac{2}{s}\).
Find the rate at which the length of the shadow is increasing when the person is 4 m away from the lamp.
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