Search over 10,000 free study notes

There are two stages to this problem: substituting x into the original equation and then expanding out the answer and simplify it. So, with the first stage, we replace every old 'x' with the new form in t...

Firstly, rearrange the equation to group the 'x' terms together, and the 'y' terms together.x^2 + 6x + y^2 -8y = 24'Complete the square' on each of the x and y groups:(x + 3)^2 - 9 + (y - 4)^2 - 16 = 24Re...

Integration can be conceptually understood in 2 different ways. firstly it is the reverse process of differentiation (Indefinite integration). Secondly it is used to work out the area under a curve (Defin...

y = arcsin(x) implies sin(y) = x
Differentiating with respect to x gives: cos(y)*dy/dx = 1So: dy/dx = 1/cos(y)
Noting that cos(y) = sqrt(1 - sin^2(y)): dy/dx = 1/sqrt(1 - sin^2...

method: complete the squares for (x^2 - 2x ) and ( y^2 + 14y ) using the formula (b/2)^2 (where the general equation is ax^2 + bx) so that the equation becomes ax^2 + bx ...