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Why is it that the sum of all natural numbers up to n is 1/2(n)(n+1)?

First let's consider the case of even numbers. Suppose n is even, then it must be double some other number, so we have: n = 2k Where k is another natural number. We want to find out what: 1 + 2 + ... + (n - ...
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Answered by Ibrahim M. • Maths tutor
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Bob buys a car for £120 after it is reduced by 20% in the sale. What was the original price of the car?

£120 is the price of the car after it has been reduced by 20%. This means that £120 is equal to 80% of the original price.2 ways to work this out:1) £120 = 80 % £ ? =100%therefore: £? = (120 x 100)/8012000/8...
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Answered by Mary P. • Maths tutor
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How can I solve reverse percentage questions?

A bag in a sale is reduced by 20%. It now costs £40. What was the original price? Solution 1: Using ratios and basic percentagesA good way to solve this problem is by thinking about what percentage is left a...
MB
Answered by Madeleine B. • Maths tutor
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Expand (2x-1)(x+3)

Method 1: Foil method (each term of the first bracket are multiplied by each term of the second bracket, and hence the product have 4 terms before simplifying)(2x-1)(x+3) = 2x x + 2x 3 - 1 x -1 3 =2x 2 + 6x ...
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Answered by Cherish N. • Maths tutor
14585 Views

Find dy/dx in terms of t for the curve defined by the parametric equations: x = (t-1)^3, y = 3t - 8/t^2, where t≠0

The first step is to recognise that, by the chain rule, dy/dx = dy/dt * dt/dx. dy/dt and dt/dx can both be found by differentiating the functions given in the question, to give dy/dt and dx/dt. dt/dx is the ...
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Answered by Alex C. • Maths tutor
22074 Views