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Differentiate the function y = (x^2)/(3x-1) with respect to x.

This requires use of the quotient rule: d/dx[f(x)/g(x)] = [g(x)f'(x) - g'(x)f(x)]/[g(x)^2]dy/dx = ([(3x-1)*2x] - 3x^2)/[(3x-1)^2],= (3x^2-2x)/[(3x-1)^2], =[x(3x-2)]/[(3x-1)^2]
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Answered by Ted S. • Maths tutor
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A curve has equation y = x^3 - 3x^2 -24x + 5, find the x co-ordinates of the two stationary points of the curve and hence determine whether they are maximum or minimum points.

y = x 3 - 3x 2 - 24x + 5, First, calculate the derivative of y and find its roots when y = 0:dy/dx = 3x 2 - 6x -24 = 0 -> x 2 - 2x - 8 = 0 -> (x+2)(x-4) = 0Therefore the coordinates of the stationary p...
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Answered by Ted S. • Maths tutor
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Sphere A (mass m), moving with speed 3v, collides with sphere B (mass 2m) which is moving in the opposite direction with speed v. The two spheres then combine, calculate the resulting velocity of the combined spheres.

Sphere A has mass m and velocity +3v so its initial momentum is 3mv. Sphere B has mass 2m and velocity -v so its initial momentum is -2mv. Therefore we can say:3mv - 2mv = M c v c , where M c and v c are the...
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Answered by Ted S. • Physics tutor
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Why is it important that the baryon and lepton numbers of an interaction are conserved?

Conservation Laws are useful because they establish fixed rules that physical interactions must follow, which helps physicists to better understand these processes. In particular, they provide a picture of w...
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Answered by Ted S. • Physics tutor
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Why am I not good at Spanish?

First of all you need to know that learning a language is not easy, so do not worry if sometimes you are struggling with it. It is important to practice as much as you can, to do the homework in the target l...
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