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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 ...

First let’s break this statement down. At the core of this sentence are two consecutive multiples of 5. How can we represent these using algebra? Let’s use 5a where “a” is an integer. A consecutive multip...