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a) u is perpendicular to w, so u • w =0. This means that 23 + 3(-1) + (-1)*p = 0, so 6-3-p=0, hence p=3. b) The magnitude of v ...

a) f(x)=ln(x), so f'(x)=1/x. By MVT, f'(c) = (f(b)-f(a))/(b-a) = (ln b - ln a)/(b-a) = ln(b/a)/(b-a), where c lies between a and b.  Now, since 1/x is a decreasing function, and a < c < b, we get 1/...

The pKa is a way of measuring the strength of an acid in water solution. An acid, in this context, is a molecule that releases a proton (H+) when in water. The more readily this molecule releases a proton...

Intro:

-Background information on Geographical Italy

-Introduce other major players that will not be analysed in the essay (Mazzini, King Vittorio Emanuele)

-T...

A negative externality of consumption is when the consumption of a good or service results in negative effects to the third party. An example of this is smoking cigarettes. The consumption of a cigarette ...