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We know that dy/dx = (dy/dt) * (dt/dx). Differentiating each of the equations with respect to t gives. dy/dt = sec(t) tan(t) and dx/dt = sec²(t). Since dt/dx = 1 / (dx/dt) we have that dt...

There are three methods to solve these types of silmultaneous equation questions, substitutution, elimination and matrices. In this example we use substitution and elimination.Elimination example.Eq1). 7x...

x²+8x +15 = 0
(x+4)²-16 +15=0
(x+4)²-1=0
(x+4)= (+/-)1

x = -3 or -5

The easiest way to do this is to first work out the area of the whole circle. To work out the area of a circle, the equation is area = πr² , w...

Start by using the formula d = sqrt((x₂-x₁)²+(y₂-y₁)²)Therefore, substituting in our coordinates from P and Q:Length PQ = sqrt((-8-4)^...