# calculus

A hemispherical dome has a diameter of 100m. A spotlight is placed on point B along the circumference on ground level. A balloon is released at point A on the center at a rate of 2m/s. how fast is the shadow of the balloon move on the roof when the balloon is 25m high?

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1. what does "on the center" mean? The center of the roof of the dome?

If the light is on the ground, and the balloon is rising from the top of the dome, it does not cast a shadow on the dome.

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