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Prove algebraically that n^3 +3n -1 is odd for all positive integers n

There are 2 possible cases.

First when n is even, then let n = 2k where k is a positive integer.
Substituting n = 2k gives us:
(2k)3 + 3(2k) -1
= 8k3 + 6k ...

Answered by Maths tutor
21926 Views

A restaurant can be hired out for children's parties, and the cost is shown by the formula "Cost = (£13.50 x number of children) + £23". What is the cost for 8 children?

Cost = (13.50 x number of children) + 23.Cost = (13.50 x 8) + 23.BIDMAS. Brackets first.Cost = 108 + 23 = £131.

TD
Answered by Thomas D. Maths tutor
2248 Views

Prove algebraically that n^3+3n^2+2n+1 is odd for all integers n

To show this we should consider when n is odd and when n is even,If n is odd then we can find an m such that n=2m+1. Substituting n=2m+1 and expanding gives 8m^3+12m^2+6m+1+12m^2+12m+3+4m+2+1=8m^3+24m^2+2...

AP
Answered by Alistair P. Maths tutor
4562 Views

Calculate the volume obtained when rotating the curve y=x^2 360 degrees around the x axis for 0<x<2

I haven't yet figured out how to write in proper mathematical notation on here, and my drawing pad is yet to arrive, so please forgive the formatFirst, the formula for the volume of revolution is V= pi *...

Answered by Maths tutor
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Renee buys 5 kg of sweets to sell. She pays £10 for the sweets. Renee puts all the sweets into bags. She puts 250 g of sweets into each bag. She sells each bag of sweets for 65p. Renee sells all the bags of sweets. Work out her percentage profit.

5kg bag of sweets split into bags of 250g. Convert 5kg to grams which equals 5000By dividing the weight of each bag you can figure out how many bags she can make are 20 bags as 5000/250 = 20. She sells ea...

CM
Answered by Connor M. Maths tutor
8335 Views

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