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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
4274 Views

If a star with a radius of 600000km has a surface temperature of 6000K, calculate its luminosity

Use the formula Luminosity = (Surface temperature)^4Surface area Stefan's constantCalculate surface area with 4piradius^2Area=4.5210^18therefore luminosity= 4.5210^18 * (6000)^4...

Answered by Physics tutor
1617 Views

What happens at the junction between neurons?

Neurons are the basic cells in the nervous system. They are made up of a soma, axon, dendrites and synapse. The synapse is the end part of the neuron that is in charge of sending a message from one neuron...

SD
Answered by Sean D. Biology tutor
2900 Views

Why is cyclohexene able to react with bromine water, but Benzene isn't

Cyclohexene's structure is 6 carbons bonded in a ring, with a single double bond existing between carbons 1 and 6Benzene is also a 6 carbon ring, however it has a delocalised electron ring around the stru...

Answered by Chemistry tutor
15374 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
2682 Views

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