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What is the significance of time in Hardy's "At Castle Boterel"?

This poem, consisting of seven stanzas each of five lines (a quintet), comes from Hardy's 1912-13 sequence of poems, which were written to commemorate the death of his first wife, Emma Gifford, in 1912. H...

Answered by Sam L. • English tutor

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Prove that the sum of two consecutive integers is always odd

And integer is a whole numberLet the integer = 2X meaning it is even and the next number is (2X+1) making it oddTherefore the sum of the two consecutive integers is2X + 2X + 1=4X+1As this cannot be factor...

Answered by Scott S. • Maths tutor

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Factorise 3x^3y^2-6x^2y+9xy

look for a common factor. See that 3 divides 3, -6 and 9. Then see that x and y divide the equation also. so write 3xy(x²y-2x+3) and this is your answer.

Answered by Amber S. • Maths tutor

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How is the theme of guilt explored throughout Ian McEwan's 'Atonement'?

Guilt is a very prevalent theme running throughout Atonement, primarily centered around the central protagonist to the novel, Bryony. Towards the end of the novel the reader learns that Bryony is the auth...

Answered by • English Literature tutor

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The point P has coordinates (3, 4) The point Q has coordinates (a, b) A line perpendicular to PQ is given by the equation 3x + 2y = 7 Find an expression for b in terms of a.

Draw a diagramRearrange the given equation into the form y = mx + cy = -3/2x+7/2Gradients of perpendicular lines - m1*m2=-1, so gradient of PQ = 2/3PQ : y=mx+c -> 4=(2/3)*3+cc=2, therefore PQ: y=2/3x+2...

Answered by Jack W. • Maths tutor

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