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The alkanes and the alkenes are examples of homologous series of compounds. Name 3 properties of a homologous series.

There are a range of answers you could give: Homologous series' are chemically similar or chemically the same or react in the same way. They contain the same functional group, the same general formula (e.g. ...
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Answered by Ursula D. • Chemistry tutor
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Explain why the equation tanx + cotx = 1 does not have real solutions.

First of all, we need to express tangent and cotangent in terms of sine and cosine using the identities: tanx = sinx / cosx and cotx = cosx / sinx. Substituting these expressions into the initial equation we...
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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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