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equation of a circle: (x - a)^2 + (y - b)^2 = r^2, where the circle has centre (a, b) and radius r.
Let's draw the diagram, where (x, y) is some point on the circle, which for ease we'll call P, and...

Use the method of substitution to answer this question.
Step 1: Rearrange one of the equations to find x or y.
y-x=3 y=x+3
Step 2: Substitute your y into the first equation
x^2<...

When we are presented with a quadratic equation in this form, and asked to expand, it is important to make sure that every term is used. For example, we would begin with the 'x' from the (x+1) bracket, an...

Use integration by parts, by setting u=x and cos(x)=dv/dx. The final result should be xsinx + cosx + c.

we must integrate (4cos⁴ x-4cos² x+1)^1/2 factorise first ((2cos²x-1)²)^1/2this becomes (2cos²x-1)which equals cos 2xthe integral...