TheMathsStudent

If X must be a whole number:
Can't remember if there is a faster way, but you need to find a multiple of 26 that when 1 is added to it is a multiple of 7.

If X can be anything, fractional too, then X=27/7 is one such X

Your question needs to be more specific, 8 what? Sheep? Monkeys? Pies? Revolutions? Radians? Degrees?

The word "sine" in maths usually refers to the trigonmetric sine function, which you will see everywhere when trying to find angles, have a look here for a starting point: http://en.wikipedia.org/wiki/Sine

If you multiply both sides by 28 and simplify you are done.

To convert into binary, you have to consider how the number can be decomposed into a sum of power of 2. You must start from the highest power of two lower than your number.

So take your number 6 in your first problem. $$2^3 = 8$$ And so we must start at $$2^2$$. We hence write 6 below:

$$6 = 1 \mbox{x} 2^2 + 1 \mbox{x} 2^1 + 0 \mbox{x} 2^0$$

You can read straight off this as 6 = 110 in binary

It may help you to notice that you can take 7 out as a factor. You may be able to factorise the smaller version! So look at this version below:

$$7(x^2 + 5x + 6)$$

$$(\frac{1}{3})^2 = \frac{1}{9}$$