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Ignoring air resistance and assuming gravity to equal 9.81. If a ball of mass 1kg is dropped from a height of 100m, calculate it's final velocity before it hits the ground.

G = 9.81u = 0s = 100v 2 = u 2 + 2asv 2 = 2 * 100 * 9.81v = root( 2 * 100 * 9.81) = 44.29ms -1 This question can be made into a 3 part question suitable for advanced A level students B) Determine or show grap...
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Integrate with respect to x [x^2]

Integrate(x 2 )When we integrate we use the formula x n+1 /n+1So therefore as in this case n=2So taking this all into account, the integral of x 2 = x 3 /3
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∫ 4/x^2+ 5x − 14 dx

For this problem we want to look to split it into logical steps We first identify that it is an integration problem without limits therefore there will be a constant of integration +C present The denominator...
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Find the turning points on the curve with the equation y=x^4-12x^2

y = x^4 - 12x^2 dy/dx = 4x^3 - 24x The turning points are where dy/dx = 0 4x^3 - 24x =0 x(4x^2 - 24) = 0 Therefore one of the turning points is at x = 0 4x^2 - 24 = 0 4x^2 = 24 x^2 = 6 x = +/- √6 Substitute ...
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Show that arctan(x)+e^x+x^3=0 has a unique solution.

Since either sketching the function f(x)=arctan(x)+e x +x 3 or evaluating the precise/approximated solutions of the equation would be impossible with A-level techniques, we have to come up with an "alte...
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