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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
21041 Views

Explain the formation of two landforms associated with convergent tectonic plate boundaries

Possible answersAn ocean trench - created when a continental plate meets and oceanic plate, and the latter is subducted due to it being denser. As the oceanic plate is forced into the mantle, a deep under...

SW
Answered by Scott W. Geography tutor
2693 Views

Starting with mRNa in the cytoplasm, describe how translation leads to the production of a polypeptide ( without including transcription or slicing)

Once the mRNA is in the cytoplasm the smaller ribosomal subunit will connect to it. It will then slide in the 5' to 3' until it reaches the initialization codon ( AUG), once this happens the TRNA that ca...

Answered by Biology tutor
11741 Views

Should I include an inspirational quote as the first line of my personal statement?

I would personally refrain from using 'inspirational quotes' within personal statements, they are most probably used by many university applicants and may lead to a negative first impression from the read...

TD
1687 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
2081 Views

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