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For a quadratic equation ax^2 +bx +c = 0 with equal roots we know the discriminant b^2-4ac must equal 0. From our equation we have a=1, b=4k and c=2(k+1) so using b^2-4ac = 0 we have (4k)^2 -412(...
That was always my biggest problem with my GCSE maths, I would get excited when I thought I knew what I was doing then slip up with silly mistakes. One of the best ways I found, after checking over at the...
Here, we must first rearrange our equation so all x terms are on one side and all y terms are on the other. Multiplying both sides by dx and diving both by y^(1/2) gives us y^(-1/2)dy = sin(x/2)dx, which ...
For this, we use the FOIL method of expanding brackets; start by multiplying the FIRST terms of each bracket together to get xx=x^2. Next multiply the OUTSIDE elements, ie the first element in the fir...
To answer, we must be familiar with several trigonometric identities and expressions; first notice that tan(x)=sin(x)/cos(x). Now our function is a quotient of two functions of x that we can easily differ...
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