Top answers

Solve the inequality x(x+2)>8 for x.

x(x+2)>8 if and only if x^2+2x-8>0 if and only if (x+4)(x-2)>0. There are three cases: x<-4, -4 In the first case x+4<0 and x-2<0, so their product is positive: (x+4)(x-2)>0. Next x+4&gt...
JT
Answered by Joshua T. • Maths tutor
4734 Views

The quadratic equation 2x^2+8x+1=0 has roots a and b. Write down the value of a+b and ab and a^2+b^2.

Since the quadratic has roots a and b, this means it can be fatored as 2(x-a)(x-b)=0. Expanding this out we get 2x^2-2(a+b)x+2ab=0 and matching the coefficients for the terms x^1 and x^0 we get a+b=-4 and ab...
JT
Answered by Joshua T. • Maths tutor
5378 Views

Why is the derivative of 2^x not x*2^(x-1)?

That technique for calculating derivatives only works for polynomial terms, that is terms of the form x^n, where n is some number. Here though our variable x is in the exponent, and so the term is not polyno...
JG
Answered by Josh G. • Maths tutor
3978 Views

Change of subject question. Make 'a' the subject of the formula v = u + at.

Rule: An equation must be balanced. Therefore, in order to keep the equation balances, what you do to one side you must do to the other side. Change of subject questions require you to isolate the required l...
SW
Answered by Sherin W. • Maths tutor
25163 Views

Given that y = (( 4x + 1 )^3)sin(2x), find dy/dx.

This is an example of the chain rule. The chain rule is the following: if y = uv, then dy/dx = udv/dx + vdu/dx So in this case, u = ( 4x + 1)^3, v = sin(2x) du/dx = (3)(4)( 4x + 1 )^2, dv/dx = 2cos(2x) dy/dx...
DS
Answered by Danielle S. • Maths tutor
5555 Views