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Factorise z^3+1 into a linear and quadratic factor. Let y=(1+i√3)/2. Show that y is a cube root of -1. Show that y^2=y-1. Find the value of (1-y)^6.

To factorise z 3 +1 into a linear and quadratic factor, it is best to try the factor theorem first. We set the equation to zero: z 3 +1=0.We need to find a value of z such that the above is true. By inspecti...
HL
Answered by Henry L. • Maths tutor
25051 Views

Make y the subject of (y/x)+(2y/(x+4))=3

We want to make y the subject of the equation and so we need to write it in the form y=f(x) where f(x) is a function in terms of x.When rearranging equations with fractions for a certain subject, factorising...
HL
Answered by Henry L. • Maths tutor
16816 Views

Solve the simultaneous equations 4x + 7y = 1 and 3x +10y = 15.

There are two main ways of solving this equation, substitution and elimination, here we go through the susbtitution method. This involves rearranging one of the equations to get one of the variables in terms...
LC
Answered by Luke C. • Maths tutor
17589 Views

Simplify (3x^2 - 15x)/(3x^2 - 13x -10)

Begin by considering the numerator and denominator separately, simplify both: 1) 3x^2 - 15x Here, a common factor of 3x can be removed to give 3x(x^2 -5). 2) 3x^2 - 13x -10 This involves using two brackets e...
GO
Answered by Gabriella O. • Maths tutor
9256 Views

Find dy/dx when y = x^2(cos(x)).

y = x 2 (cos(x)) therefore we will need to use the product rule, dy/dx = u dv/dx + v du/dx where u = x 2 and v = cos(x) du/dx = 2x and dv/dx = - sin(x), (don't forget the negative symbol when differentiating...
JS
Answered by Joseff S. • Maths tutor
33130 Views