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A bus departs from Lancaster at 10.57a.m. The bus arrives at Manchester at 12:13p.m. How many minutes does the bus spend on its journey from Lancaster to Manchester?

76 minutes.
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Answered by Aadil V. • Maths tutor
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Differentiate x^x

(x^x)(ln(x)+1)
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Answered by Aadil V. • Maths tutor
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Using substitution, integrate x(2 + x))^1/2 where u^2 = 2 + x

u 2 = 2 + xx = u 2 - 2dx/du = 2u ʃ x(2 + x)) 1/2 dx= ʃ xu dx= ʃ u(u 2 - 2) dx= ʃ 2u 2 (u 2 - 2) du= ʃ 2u 4 - 4u 2 du= [2/5u 5 - 4/3u 3 + C]= 2/5 (2 + x) 5/2 - 4/3 (2 + x) 3/2 + C
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Answered by Sonali P. • Maths tutor
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Please explain (said question) surrounding a proof of 2 equal angles

I would firstly ask them how much they knew about trigonometry, and then guide them through the SoHCaHToA theory. I would use diagrams for this. I would then ask them to spot any ways they could work out any...
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Answered by Kate P. • Maths tutor
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The volume, V, of water in a tank at time t seconds is given by V = 1/3*t^6 - 2*t^4 + 3*t^2, for t=>0. (i) Find dV/dt

The differential of a function is is rate of range of that function. Therefore to find dV/dt, we are finding the rate of change of the volume per unit time.Recall, in order to differentiate a term, e.g. x a ...
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Answered by Samuel W. • Maths tutor
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