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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
23478 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
3478 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
12784 Views

After one molecule of oxygen has bound to Haemoglobin, it is easier for a second molecule of oxygen to bind. Explain Why?

Binding of the first molecule of oxygen changes the tertiary/quarternary structure of Haemoglobin - this can be referred to as a conformational shift. This change in structure then exposes another binding...

AM
Answered by Alice M. Biology tutor
4103 Views

What is the optical activity of the product formed when propanone is refluxed with HCN with KCN dissolved in ethanol and why?

The product formed (hydroxybutanitrile) is optically inactive because the nitrile nucleophile can attack the propane at its carbonyl bond which is trigonal planar about it. There is an equal chance of it ...

AY
Answered by Aditya Y. Chemistry tutor
2540 Views

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