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n is an integer greater than 1. Prove algebraically that n^2-2-(n-2)^2 is always an even number

We want to show that this gives an even number, so we need to get it into a form that it is 2 multiplied by some positive integer. We start by expanding the (n-2) 2 out, remember that (n-2) 2 =(n-2)(n-2). Th...
JC
Answered by Jacob C. • Maths tutor
27329 Views

Assess the arguments in favour of an elected House of Lords

The main arguments in favour of an elected House of Lords are that this would enhance democratic legitimcy in the House of Lords , widen the basis for represention and this could increase checks on governmen...
ED
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Find the length of the hypotenuse of a right-angled triangle using i) Pythagoras Theorem ii) Trigonometry. The triangle has sides of lengths 3cm and 4cm and an acute angle of 30 degrees.

Part i Pythagoras Theorem states a 2 = b 2 + c 2 , where a is the hypotenuse.Using this the lengths can be substituted into the equation as b and c, a 2 = 3 2 + 4 2 a 2 = 25a = sqrt(25) = 5cm Part ii Trigono...
ZS
Answered by Zaakir S. • Maths tutor
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How to form the imperfect subjunctive

For me, the easiest way of forming the imperfect subjunctive in Spanish is to firstly start with the 3rd person plural form of the preterite. Once you have this, drop the -ron ending of the verb. This base c...
ED
Answered by Emma D. • Spanish tutor
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Differentiate y = x^2 - 2x-3 + e^3x + 2ln(x)

The above function has several components with different rules on how to differentiate each of them. For each:(1) y = x 2 dy/dx = 2x This follows the general rule of differentiating polynomials: y = x n , dy...
JH
Answered by Jim H. • Maths tutor
4242 Views