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Make a the subject of the following equation, p=(3a+5)/(4-a)

In this question I would initially aim to get an a on both sides of the equation. My first step would be to multiply both sides by (4-a) to do this. After this point I would expand out the brackets on the le...
MO
Answered by Martin O. • Maths tutor
8281 Views

Derive from the standard quadratic equation, the form of the quadratic solution

ax 2 +bx+c=0 : basic quadratic equation a(x 2 + bx/a) + c=0 a((x+b/2a) 2 - b 2 /4a 2 ) + c=0 (retain equation with only one x variable; compensate for b term squared out with term - b 2 /4a 2, ) a(x+b/2a) 2 ...
JD
Answered by Jaiveer D. • Maths tutor
6806 Views

Factorise and solve: x^2 - 8x = -15

Step 1 : The first step is to rewrite the equation in the form a x 2 + b x + c = 0. So in this case, we achieve this by adding 15 to both sides: x 2 - 8x + 15 = -15 + 15 x 2 - 8x + 15 = 0 Step 2: Now we need...
MJ
Answered by Maisie J. • Maths tutor
7863 Views

Write tan(3x) in terms of tan(x). Hence show that the roots of t^3 - 3t^2 - 3t + 1 = 0 are tan(pi/12), tan(5pi/12) and tan(3pi/4)

The first part is relatively simple. If we write tan(3x) as tan(2x+x) we can use addition formulae to give: tan(2x+x)= (tan(2x)+tan(x))/(1-tan(2x)tan(x)) tan(2x) = 2tan(x)/(1-tan^2(x)) Substituing this in an...
DG
Answered by Daniel G. • Maths tutor
53892 Views

differentiate y = (4-x)^2

This is a basic example of a very important result: the chain rule. The difficulty of this sort of example is that we have a "function of a function". That is, we have the function '4-x' and then w...
BB
Answered by Ben B. • Maths tutor
8740 Views