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Solve x^2=4(x-3)^2

expand the brackets to obtain x^2=4(x^2-6x+9)expand the brackets to obtain x^2=4x^2-24x+36rearrange to obtain 0=3x^2-24x+36factorise to obtain 0=(3x-6)(x-6)solve for x=6 or x=2
EE
Answered by Edwin E. • Maths tutor
3669 Views

Sketch the curve with the equation y=x^2 +4x+4, labelling the points where it crosses or touches the axes.

The curve is a quadratic equation because it has a x^2 - as it is positive it will be a u shaped parabola. The equation can be factorised by thinking of two numbers which add to make 4 (the b value) and mult...
SS
Answered by Sophia S. • Maths tutor
4484 Views

What is the difference between quotient rule, product rule and chain rule, and when to use them in differentiation?

Chain rule: when we have a function on its own raised to a certain power . eg: f(x)=(2x+3) 3 --> f'(x)=3*2(2x+3) 2 Product rule: when we have 2 functions or more multiplied by each other. eg: f(x)=g(x)*h(...
RA
Answered by Ren A. • Maths tutor
7875 Views

Integrate Sin(x)Cos(x)dx.

Integral(Sin[x]Cos[x]dx) can be calculated. The method is to recognise that the trigonometric identity of 2Sin[x]Cos[x]=Sin[2x] can be applied. This would transform the integral into Integral(0.5Sin[2x]) whi...
DD
Answered by Daniel D. • Maths tutor
5243 Views

Solve the differential equation : dy/dx - x^3 -5x = 0

First rearrange the equation dy/dx = x 3 + 5x Then move the dx to the RHS of the equation dy = ( x 3 + 5x)dxThen integrate both sides, with respect to y on the LHS and with respect to x on the RHS (don't for...
OM
Answered by Olivia M. • Maths tutor
4958 Views