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Juan B.
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Spanish
TutorMe
Question:

Spanish speakers from Latin America frequently use words that, with the same spelling, can be used in different contexts due to they hold different meanings. How are they called and give me an example of one of them.

Juan B.
Answer:

Nice question. They are called polysemy words or "palabras polisemicas" in Spanish. These words have multiple meanings, normally related by contiguity of meaning within a semantic field. A common example of these words in Colombia is the word "pasta": You can use "pasta" to talk about: - Toothpaste: Se acabo la PASTA de dientes, y no quiero tener mal aliento / The TOOTHPASTE is finished, and I do not want to have bad breathe. - Food: ¿Que quieres comer hoy de cena ? Quiero PASTA con pollo / What do you want to have for dinner? I want chicken and PASTA. - Pill: Me duele la cabeza, necesito una PASTA. / I have headache. I need a PILL. - Money: Quiero un nuevo carro, pero necesito más PASTA/ I want a new car, but I need more MONEY.

Calculus
TutorMe
Question:

Vectors: m=(1,1); u= (1,2). Prove that vector h is orthogonal to the proj(m)(u), if vector h makes the following equation true: h + proj (m) (u) = u.

Juan B.
Answer:

First, proj(m)(u) = [(m.u)/(IImII^2)].m= [(1,1).(1,2)/(II1^2+1^2II)].(1,1)=[(1+2)/2].(1,1)=(1.5 , 1.5). Now solving for h: h= u- proj (m) (u)= (1 , 2)-(1.5 , 1.5)= (-0.5 , 0.5). Now, if h is orthogonal to proj(m)(u), then, their dot product is zero: h. proj(m)(u)= o. (-0.5 , 0.5).(1.5 , 1.5) = [(-0.5*1.5)+(0.5*1.5)]=-0.75 + 0.75 = 0. Therefore h is orthogonal to proj(m)(u).

Finance
TutorMe
Question:

How is it possible for an enterprise to have positive cash flows but still be heading to bankruptcy?

Juan B.
Answer:

Two examples might implicate unsustainable improvements in working capital if, for instance, the company is selling off inventory and delaying payables. The second one might involve lack of revenues going forward in the pipeline.

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