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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 ...

2x +3 + (4x-1)/2 = 10                  The divisor (2) is the biggest problem right now so we need to get it on its own...

(4x-1)/2 = 10-2x-3                       Equation has been rearranged!

We will call the integral I, so I = integral of 1/(3+(x+4)^1/2) dx between 0 and 5. First substitute u=3+(x+4)^1/2 into the equation to get I = integral of 1/u dx between 0 and 5 Next ...

First we complete the square on the equation of the circle to obtain: (x-2)^2 -4 + (y+4)^2 -16 = 5. Re arrange : (x-2)^2  + (y+4)^2 = 25 General equation of a circle: (x-a)^2 + (y-b)^2 = r^2, with centre ...

There are several ways to do this which make it particularly interesting. I would advise trying to avoid doing it by eye, this leaves you open to many clumsy mistakes. My preferred method is using equival...