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What do I do when quadratic equations aren't written in the standard format ax^2 + bx + c = 0 ?

This isn't a trick so much as a way to let you show you can think for yourself. You might be thrown off initially if a quadratic equation is in a format that you don't recognise, but usually all it takes ...

Answered by Helena K. Maths tutor
3937 Views

White paint costs £2.80 per litre. Blue paint costs £3.50 per litre. White paint and blue paint are mixed in the ratio 3 : 2 Work out the cost of 18 litres of the mixture.

To work out how many litres of white and blue paint is needed, use the ratio 3:2. To find the specifc ratio for 18 litres, of paint: 2+3=5, 18/5=3.6 so (3:2)3.6 becomes 10.8:7.2 (check 10.8+7.2=18). S...

Answered by Aidan D. Maths tutor
2773 Views

Using the equation cos(a+b) = cos(a)cos(b) - sin(a)sin(b) or otherwise, show that cos(2x) = 2cos^2(x) - 1.

First let a = b = x such that:          

          cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

becomes:

          cos(x + x) = cos(x)cos(x) - sin(x)sin(x)

Leading to:

     ...

Answered by Benjamin H. Maths tutor
3332 Views

A general function f(x) has the property f(-x)=-f(x). State a trigonometric function with this property and explain using the Maclaurin series expansion for this function why this property holds. Write down the integral in the limits -q to q of f(x) wrt x

Note that this property is the definition of an odd function, or draw a sketch of what this looks like in general about the horizontal axis. E.g. f(x)=sin(x) which has the expansion f(x)=x-((x^3)/3!)+((x^...

Answered by James H. Maths tutor
3554 Views

Rearrange to make x the subject of the equation: 4(3x+y) = 12-2y

To tackle this question, start by expanding the brackets:
12x + 4y = 12 - 2y
Making x the subject of the equation requires x to be on its own. 
So, in this example, we need to first get ...

Answered by Mana R. Maths tutor
5056 Views

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