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If a particle of mass m is launched vertically upwards from the ground with velocity u m/s, how long will it take to return to the ground in terms of m, u and g?

Taking upwards to be positive, and using the 'suvat' equation s=ut+1/2at 2 we know that u=u, a=-g and s=0 when the particle returns to the ground. Then we solve for t: 0=ut-1/2gt 2 0=t(u-1/2gt) So the partic...
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Answered by Jackie V. • Maths tutor
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Use the substitution u=x^2-2 to find the integral of (6x^3+4x)/sqrt( x^2-2)

First use the substitution to find du/dx which is 2x. From this we now know that dx= du/2x (just re-arranging.) Substituting that into the integral we now get (6x 3 +4x)/ (sqrt (u) x 2x) du. Cancelling out t...
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Answered by Khalil S. • Maths tutor
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Let f(x)=x^3 - 2x^2 + 5. For which value(s) of x does f(x)=5?

Although it can be tempting to dive straight into such a question, its always useful in mathematics to take a step back and assess the question before scribbling down panicked answers. For instance, in this ...
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Answered by Jed G. • Maths tutor
4259 Views

Integrate lnx

This question often throws maths students off fairly easily as they are generally not taught the integral of lnx, and do not usually realise that integration by parts can be used for anything, as you can use...
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Answered by Owen M. • Maths tutor
3886 Views

Find the coordinates of the stationary point of the graph y = 3x^2 - 12x

Firstly, we need to differentiate the equation to find an equation for the gradient of the line.dy/dx = 6x-12We know the original graph was quadratic, and therefore only has one stationary point. This is whe...
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Answered by Jack M. • Maths tutor
7012 Views