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Discuss the use of doubling in the plays of Shakespeare.

Emma Smith states that Doubling is not just a 'practical necessity, but a representational technique that could also make connections and contrasts between distinct characters or worlds'. She explains it is ...
TJ
Answered by Tesni J. • English tutor
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Prove the identity: (sinx - tanx)(cosx - cotx) = (sinx - 1)(cosx - 1)

(sinx - tanx)(cosx - cotx)= (sinx - sinx/cosx)(cosx - cosx/sinx)= sinxcosx - (sinx + cosx) + 1= (sinx - 1)(cosx - 1)
CP
Answered by Charlie P. • Maths tutor
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For what values of k does the line y=kx-1 have two distinct points of intersection with the circle (x-2)^2+(y-3)^2=2?

sub y=kx-1 into circle equation, get (k^2+1)x^2-(8k+4)x+18=0for 2 distinct solutions need b^2-4ac>0, ie -8k^2+64k-56>0iff k^2-8k+7<0complete the square: intersections of equation in k satisfy(k-4)^2...
CB
Answered by Christopher B. • Maths tutor
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Discuss the depiction of the natural world in one of the poems written by Ted Hughes.

Ted Hughes' Thrushes delineates the natural world as a a brutal realm of savagery and survival. An analysis of Hughes' careful use of phonological patterning, selection of lexical items and symbolism illumin...
EM
Answered by Eamon M. • English tutor
3606 Views

Prove by induction that the nth triangle number is given by n(n+1)/2

base case: (1 x 2)/2 = 1 as required inductive step: assuming statement holds for n=k, the (k+1)th triangle number is given by k(k+1)/2 + (k+1) by definition=(k^2+3k+2)/2=(k+1)(k+2)/2=(k+1)((k+1)+1)/2result ...
CB
Answered by Christopher B. • Maths tutor
4029 Views