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Consider f(x)=a/(x-1)^2-1. For which a>1 is the triangle formed by (0,0) and the intersections of f(x) with the positive x- and y-axis isosceles?

We'll first compute these intersections by setting x=0 and y=0 consecutively. This gives y=a-1 and a/(x-1)^2-1=0. Hence we find (x-1)^2=a, so x=1+-sqrt(a). As we have a>1 and we want the intersection with...
WV
Answered by Ward V. • Maths tutor
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What is the largest positive integer that always divides n^5-n^3 for n a natural number.

First we note we can factorise the n^3 out of the expression, giving n^3(n^2-1). Secondly, we can see that the second term is a difference of two squares, allowing is to factorise the total to n^3(n-1)(n+1)....
WV
Answered by Ward V. • STEP tutor
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How can you find the coefficients of a monic quadratic when you know only one non-real root?

We know that non-real roots appear in complex conjugate pairs. Hence when we know one root, we know both of them. Then, as we can factorise a quadratic in it's linear factors, we know our quadratic is a cons...
WV
Answered by Ward V. • Maths tutor
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How can 'Natural Moral Law' be critiqued as an ethical theory?

‘Natural Moral Law’ was perhaps most famously developed by St. Thomas Aquinas, in his theological guide ‘Summa Theologica’. Aquinas’ ‘Natural Moral Law’ is an absolutist and deontological ethical approach – ...
EM
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At what time did Jane Austen write?

During the Victorian period in English Literary Scene.
AP
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