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(i) Identify the ablative absolute and (ii) translate the sentence into good English: 'Urbe capta, hostes cives occiderunt.'

(i) Urbe (3rd declension feminine noun) capta (past participle passive in agreement with urbe). The ablative noun and participle are 'cut off' from the rest of the sentence - if we removed the phrase from th...
SM
Answered by Samuel M. • Latin tutor
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A stone is thrown horizontally at 5m/s from a platform 10m above ground. Find time till impact with ground.

Use SUVAT for constant vertical acceleration. Solve for t. S = -10U = 0V = -A = -gT = tS=UT+(AT^2)/2t = sqrt(20/g)
MH
Answered by Mathew H. • Physics tutor
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Convert 0.22222222... (recurring) into a fraction

x=0.22222222...10x= 2.222222...10x-x=9x=2x=2/9=0.2222222... x=2/9
RG
Answered by Rachel G. • Maths tutor
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Integrate tan(x) wrt x

Use substitutionlet u = cos(x)du = - sin(x)dxint(tan(x)) dx = int(sinx/cosx) dx = - int(1/u) du = - ln(u) + c= ln(secx) + c
MH
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Solve the equation log2(x + 3) + log2(x - 3) = 4

log2(x + 3) + log2(x - 3) = 4log2 [(x + 3)(x - 3)] = 4x^2 - 9 = 16x^2 = 25x = 5
Answered by • Maths tutor
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