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Since y is equal to both 5-x and to x+1, we know that 5-x is equal to x+1. We can write 5-x=x+1. Take 1 away from each side: 4-x=x. Then add x to each side: 4=2x. Divide both sides by 2: 2=x. Now we have ...

Finding 51% of 400 is the same as finding 50% of 400, and 1% of 400, and adding them together. Finding 50% of a number is the same as finding half of the number, since half of 100% is 50%. Half of 400 is ...

To solve this question, we need to use the chain rule, because the function is too complicated to solve simply by inspection. The chain rule says that dy/dx = dy/du × du/dx, where u is a function of x. In...

This question is asking to find the values for x, such that h(x) is strictly less than g(x). We can write this as 9^x + 9 < 103^x and solve for x as follows. 9^x + 9 < 103^x => 3^(2x) - ...

Straight away we notice that two trigonometric terms on the left hand side have 2x but there are no 2x on the right hand side therefore we realise that this question will require double angle formulae. If...