Henry

10. A curve has equation y=x^2+x.

Find the values of k for which the line y=kx−4 is a tangent to the curve.

So far, i subbed y=kx-4 into the original equation to get:

kx-4=x^2+x which simplifies to:

x^2+(1-k)x +4=0

I don't know what to do next, i looked at the mark scheme and it says there is only 1 real root, so we can use b^2-4ac= 0, but how do i know there's only 1 real root? and how do i know i need to use the discriminant?

Thanks in advance :)

A circle with centre C has equation x^2+y^2−8x−2y−3=0.

ii. Find the values of k for which the line y= k is a tangent to the circle, giving your answers in simplified surd form.

I've worked out the alternative equation - (x-4)^2 + (y-1)^2 = 20 but cannot work out part ii above, i looked at the mark scheme and it said about using the discriminant (b^2-4ac) to work it out and the answer was 1± √20 but i have no clue how to do it. 10 points for a good explanation quickly, as i have my exam on monday! Thanks in advance!

The masses, x kg, of 50 bags of flour were measured and the results were summarised as follows.

n= 50

Σ(x−1.5) = 1.4

Σ(x−1.5)^2= 0.05

Calculate the mean and standard deviation of the masses of these bags of flour.

I've worked out Σ(x−1.5) = 1.4

Σx = (1.4/50) + 1.5

But i cannot work out how to figure out the Σx^2 and then the standard deviation using this Σ(x−1.5)^2= 0.05.

Thanks :)