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Where do the graphs of y=3x-2 and y=x^2+4x-8 meet?

In order to find the points where these functions meet, we can equate them to get 3x-2 = x^2+4x-8 . Subtraction (3x-2) from both sides, we get x^2+x-6 =0 which we can factorise to get (x+3)(x-2)=0 Therefore ...
HS
Answered by Helen S. • Maths tutor
4126 Views

Given that z=sin(x)/cos(x), show that dz/dx = sec^2(x).

We have a "fraction" which we wish to differentiate, so we use the quotient rule with u=sin(x) and v=cos(x). This means that d/dx of u/v = (v du/dx - u dv/dx)/(v^2). We have u=sin(x) so du/dx= cos(...
GG
Answered by Gabriela G. • Maths tutor
5169 Views

Integrate y with respect to x, where y = cos(x)/[1+tan^2(x)]

y = cos(x)/sec 2 (x) = cos 3 (x) y = cos(x)(1-sin 2 (x)) = cos(x) - cos(x) sin 2 (x) -> sin(x) - sin 3 (x)/3 + c
DC
Answered by Daniel C. • Maths tutor
4162 Views

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 is ...
HK
Answered by Helena K. • Maths tutor
5208 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). So to d...
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Answered by Aidan D. • Maths tutor
3766 Views