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Solve the simultaneous equations: y-2x-4=0, 4x^2+y^2+20x=0

Re-arrange y-2x-4=0 to y=2x+4Substitute y=2x+4 into 4x^2+y^2+20x=0 to get 4x^2+(2x+4)^2+20x=0Expand the brackets to get 4x^2+(4x^2+16x+16)+20x=0Simplify to get 8x^2+36x+16=0Divide by 4 to get 2x^2+9x+4=0Fact...
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Answered by Andrew H. • Maths tutor
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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
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Answered by Edwin E. • Maths tutor
3528 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...
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Answered by Sophia S. • Maths tutor
4285 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(...
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Answered by Ren A. • Maths tutor
7642 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...
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Answered by Daniel D. • Maths tutor
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