Search over 10,000 free study notes

Solution: Let us consider the function f(k) = k² - k -12. Firstly, we want to find out the roots of this function. We calculate the discriminant: Δ = b² – 4ac = 49 hence we ...

a)    First we can rewrite y=arccos(x/2) as cosy = x/2 which allows us to use implicit differentiation to easily differentiate each side. Taking d/dx of each side gives u...

There is a total of 7! possible ways in which the seven children can be seated on the bench. The number of favourable arrangements when four boys are seated on one side and three girls on the other side i...

a,y=5xfinding the inverse: x=5y - dividing by 5 (1/5)x=y f^-1(x)=(1/5)x
b,5x(7²+1)=250

Firstly, (x - c) is a factor of a polynomial P(x) if and only if there exists a polynomial Q(x) such that P(x) = (x - c)Q(x), where c is a real or complex constant.
Therefore, we can write: P(x) = x...