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How do you rationalize the denominator of a fraction?

Questions which ask for you to rationalize the denominator usually includes an integer and a square root of a number (x+sqrt(y)).We can use the following formula to our advantage: (a+b)(a-b)=a^2-b^2. ...

Answered by Maths tutor
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Prove that 8 times any triangle number is always 1 less than a square number

A triangle number is a number such that it is the sum of n consecutive integers, starting from 0. Eg 1, 1+2, 1+2+3... are the first 3 triangle numbers. The formula for the nth triangle number is well-know...

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Co-ordinate Geometry A-level: The equation of a circle is x^2+y^2+6x-2y-10=0, find the centre and radius of the circle, the co-ordinates of point(s) where y=2x-3 meets the circle and hence state what we can deduce about the relationship between them.

We have that x2 + y2 + 6x - 2y - 10 = (x+3)2 + (y-1)2 - 20 = 0 (step was motivated by the equation of a general circle (x-a)2 + (y-b)2 = ...

Answered by Maths tutor
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What are some criticisms of Augustine's Soul-Deciding Theodicy?

Peter Vardy  claims that there is no way to justify dysteleology or excess suffering. Evil seems to be more definite than a mere ‘privation of good’ for example Child cruelty is not just the lack of Child...

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What are the differences between the psychological approaches and how to compare them?

The approaches differ in terms of views, how they were developed and how they are applied in modern psychology whether it be studies or treating patients. Since the actual content is typically easier to g...

Answered by Psychology tutor
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