Alan

I guess you are trying to find the values of r in the equation A = P*(1+r*t) where all the other terms are known.

A = 5227.5

P = 5100

t = 3 months = 0.25 years

5227.5 = 5110*(1 + r*0.25)   where r will be in units of "per year".

Divide both sides by 5110

5227.5/5110 = 1 + r*0.25

Subtract 1 from both sides.

5227.5/5110 - 1 = r*0.25

Divide both sides by 0.25

(5227.5/5110 - 1)/0.25 = r

$${\mathtt{r}} = {\frac{\left({\frac{{\mathtt{5\,227.5}}}{{\mathtt{5\,110}}}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{{\mathtt{0.25}}}} \Rightarrow {\mathtt{r}} = {\mathtt{0.091\: \!976\: \!516\: \!634\: \!050\: \!9}}$$

So r ≈ 0.092 per year (or 0.092*12 ≈1.1 per month) 

sin(angle) is opposite/hypotenuse, so as long as you know the angle and the hypotenuse you can find the opposite from opposite = hypotenuse*sin(angle).

You might have drawn 1.  Red/White  2. Red sideA/Red sideB 3. Red sideB/Red sideA  

There are two out of three possibilities that the other side is red, so the probability that the other side is also red is 2/3.

9% as a fraction is 0.09, so you multiply $1000 by 0.09 to get $90.

If x = 64^2/3 then x³ = 64² so x is a number which, when cubed is the same as 64 squared.  That is, 64^2/3 is a number which when cubed is the same as 64².

$${{\mathtt{16}}}^{{\mathtt{3}}} = {\mathtt{4\,096}}$$

$${{\mathtt{64}}}^{{\mathtt{2}}} = {\mathtt{4\,096}}$$

So 16 is 64^2/3 because 16³ is the same as 64².

Here are my solutions:

Yes, there has to be a third component; but it is zero!

So p = −2i − 3j + 0k and q =4i +7j + 0k.  It measn p and q are both in the i,j plane; and their cross-product will be in the k direction. 

You're welcome.

I used u and v as general vectors.  a and b are your specific vectors.  That is they are specific examples of u and v.  But if you prefer to think of it as turning a and b into u and v ok!  Whatever works for you!

In fact, why don't you rewrite my u and v in terms of a and b (including their components - so u1 becomes a1 etc.)?