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Calculus/calculus-optimization

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Expert: - 3/31/2010


Question
Painters are painting the second floor exterior wall of a building that adjoins a busy sidewalk. a cooridor 2m wide and 3m high is built to protect pedestrians. what is the length of the shortest ladder that will reach from the ground over the corridor to the wall of the building?

Answer
Let the amount on the floor from the corridor be x
and the amount above the corridor be y.

This means that y/2 = 3/x, so y = 6/x.

The length of the ladder is √(y²+2²) + √(3²+x²).

Put in y=6/x, and note that y²=36/x²

Take the derivative of  √(4 + 36/x²) + √(9 + x²).

Note that the derivative of √f(x) is f'(x)/(2√f(x)).

Once this has been done, set it equal to 0.

Calculus

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

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