5.) a 10-foot ladder is placed against a vertical wall such that the bottom of the ladder is sliding away from the wall at the rate of 3 feet per second. how far is the top of the ladder sliding down the wall when the bottom of the ladder is 6 feet away from the wall. use the pythagorean theorem to set up the equation.

If x is the distance the base of the ladder is from the wall, and y is the distance to top of the ladder is up the wall, then the Pythagorean theorem tells you

... x² + y² = 10²

Differentiating with respect to time, we have

... 2x·dx/dt + 2y·dy/dt = 0

... dy/dt = (-x/y)·dx/dt

We are given x = 6 ft and dx/dt = 3 ft/s. Using the first equation, we can find y as

... y = √(10² -6²) = 8

Then

... dy/dt =(-6/8)·(3 ft/s)

... dy/dt = -2.25 ft/s

The top of the ladder is sliding down the wall at -2.25 ft/s.

answer: the sun

explanation:

water cycle describes the evaporation of water from earth's surface, formation of clouds and precipitation water back onto the surface of earth. seventy percent of the earth is covered with water in the form of seas and oceans. the heat of the sun causes the evaporation of water from the surface of the ocean. the water vapors rise and condense to form water droplets. the collection of these water droplets form clouds which rain down again.

the evaporation of the oceans surface water as part of the water cycle is caused by the sun

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step-by-step explanation: