A 15-meter-long rope is hanging vertically from a ceiling. A mouse is climbing up the rope at a constant rate of 2 meters per minute. How fast is the mouse moving when it is 9 meters from the floor?
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To find the rate at which the mouse is moving when it is 9 meters from the floor, we can use the concept of similar triangles.
Let's consider two triangles. The first triangle is formed by the entire 15-meter long rope, the distance from the floor to the ceiling, and the height from the floor to the mouse. The second triangle is formed by the 9-meter distance from the floor to the mouse and the height from the floor to the mouse.
Since the two triangles are similar, the ratio of their corresponding sides will be equal.
Let's let x be the rate at which the mouse is moving when it is 9 meters from the floor.
Using the similar triangles, we have:
(15 meters - 9 meters) / (15 meters) = x / 2 meters per minute
Simplifying, we have:
6 meters / 15 meters = x / 2 meters per minute
0.4 = x/2
x = 0.4 * 2
x = 0.8 meters per minute
Therefore, the mouse is moving at a rate of 0.8 meters per minute when it is 9 meters from the floor.
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