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Find the centre and radius of the circle with equation: x^2 + y^2 -4x +8y = 5, and determine whether the point (7,-4) lies on the circle.

First we complete the square on the equation of the circle to obtain: (x-2)^2 -4 + (y+4)^2 -16 = 5. Re arrange : (x-2)^2 + (y+4)^2 = 25 General equation of a circle: (x-a)^2 + (y-b)^2 = r^2, with centre ...

Answered by Alec S. • Maths tutor

5997 Views

How to express one quantity as a percentage of another?

There are several ways to do this which make it particularly interesting. I would advise trying to avoid doing it by eye, this leaves you open to many clumsy mistakes. My preferred method is using equival...

Answered by Sebastian P. • Maths tutor

2496 Views

Find the exact solutions, in their simplest form, to the equations : a) 2ln(2x + 1)-4=0 b)7^(x)e^(4x)=e^5

a) 2ln(2x + 1)-4=0

-> ln(2x + 1)-2=0

-> ln(2x + 1)=2

-> (2x + 1)=e²

-> 2x = e²-1

-> x = (e²-1)/2

b) 7^x

Answered by Elizabeth L. • Maths tutor

4402 Views

3(x-2) - 2(x-2)

First expand each set of brackets:

(3x - 6) - (2x - 4)

Then simplify:

3x - 6 - 2x - (-4) = x - 2

Answered by Beenita S. • Maths tutor

2861 Views

How do I find the equation of the tangent to y = e^(x^2) at the point x = 4?

This question can be broken up into two main parts, one you're probably familiar with from C1 + C2 and one which is newer. The first part relates to differentiating a compound function (where a function i...

Answered by Sam H. • Maths tutor

8866 Views