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Kit B.
Recent Georgetown Graduate
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French
TutorMe
Question:

What is the error in the following sentence? J'ai pris un cours de français au lycée.

Kit B.
Answer:

The expression "prendre un cours" (to 'take' a course) is an anglicism. The appropriate verb here would be suivre. The sentence now becomes: J'ai suivi un cours de français au lycée.

Calculus
TutorMe
Question:

Find the derivative with respect to x of the following expression: $$(x^{2}+3)/[(2x-3)(x+2)]$$

Kit B.
Answer:

This problem will actually be made easier by multiplying our the denominator to get: $$(x^{2}+3)/(2x^{2}+x-6)$$ We can now rewrite the expression as: $$(x^{2}+3)(2x^{2}+x-6)^{-1}$$ Using the product rule (and the chain rule), we find the derivative is equal to: $$-(x^{2}+3)(2x^{2}+x-6)^{-2}(4x+1)+2x(2x^{2}+x-6)^{-1}$$

Physics
TutorMe
Question:

You accidentally bump a 1kg wooden box at the edge of a 1m long table. It slides across the table and after 2s falls off the other side. Is the table made of wood?

Kit B.
Answer:

Our eventual goal is to find the coefficient of kinetic friction for this problem, and see if it is in the range of what one might expect for wood sliding on wood. To do this, we must first consider the kinetic energy of the box. It traverses 1m over a time of 2s, meaning its average speed was 0.5m/s. If we take the lower limit of speed when the box falls over to be 0m/s, this means the maximum initial speed was 1m/s, and the corresponding maximum initial energy was 0.5J. This 0.5J corresponds to the maximum amount of energy dissipated by the table as the box slid. Using the Work-Kinetic Energy Theorem and the definition of work, we can see that the greatest possible force of friction acting on the box was 0.5N. Plugging this number into the definition of kinetic frictional force, we can see that the maximum coefficient of kinetic friction would be about 0.05. This is much too small for a wood-wood interaction, and so the table must be made of something else!

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