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Michel E.
C++, Math & Physics Tutor
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French
TutorMe
Question:

What's the difference between the subject pronouns "On" and "Nous?" When would you use "On" instead of "Nous" and vice versa?

Michel E.
Answer:

Both subject pronouns "On" and "Nous" mean "We" or "Us" in English. However, we usually use "on" when we are speaking in a general sense or context. For example, it would make more sense to say, "En France, on parle francais," instead of "En France, nous parlons francais." This is because it is a fact that in France, the general population speaks French. If you used "Nous" it technically wouldn't be wrong, but "On" is more convenient in the context.

Writing
TutorMe
Question:

Which statement is correct and why? "Jon and Rosie decided to go to the gym, because they hadn't worked out in a long time." "Jon and Rosie decided to go to the gym because they hadn't worked out in a long time."

Michel E.
Answer:

The second statement would be the correct one. If you look at the first sentence, there is the placement of an unnecessary comma between "gym" and "because." A comma indicates a pause between the ending of an introductory word, phrase, or clause, and the beginning of the main part of the sentence. A comma also splits to independent clauses. Notice how the second half of the first statement is a fragment. Removing the comma would make the sentence whole.

Calculus
TutorMe
Question:

Can you use the IMVT (Intermediate Value Theorem) to prove that the equation x^3 = x + 3 is solvable?

Michel E.
Answer:

Let f(x)= x^3 -x - 3 and let m = 0, where f is continuous for all x-values (it is continuous because f is a polynomial). Note that f(0) = -3 and f(2) = 3 and m = 0 is in between f(0) and f(2), so choose the interval [0,2]. Thus, by IMVT, there is at least one x-value "c" on the closed interval 0<c<2, so that f(c) = m , i.e, c^3-c-3 = 0 and the equation is solvable.

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