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First we have to use the product rule, remember that if we have h(x)=f(x)g(x) then h'(x)=f'(x)g(x)+f(x)g'(x).
So h'(x) = x^3D[(x+1)^5]+(x+1)^5D[x^3]
Completing the unfinished derivatives,
h'(x) = x^3[5(x+1)^4]+(x+1)^5[3x^2]
h'(x) = 5x^3(x+1)^4+3x^2(x+1)^5
remember that we do the (x+1)^5 in the standard way.see more
This is a 40 mark question so roughly an hour should be spent on it. I won't fully develop an answer here but would help a student through it in the following stages.
Advice; with these essay writing is key, I would place high importance on doing several open book essays in timed conditions to help you get into the flow of writing intro, middle/development, end.
Can you bring in anything from outside the syllabus? For example I can help with university level plate tectonic theory (so going beyond the view that plates meet at discrete boundaries, geochemical transistions and so on), including just a pinch of this will wow any examiner. Make sure not to overstrech however, you probably have enough learning on your plate!
They say a picture is worth a 1000 words and this is absolutely true, if I were marking this question I'd be looking for diagrams incl. the benioff zone, spreading ridges, transform faults ect.
On to the body of the question with a few bullet points.
>Explain plate tectonic theory, what is it? When did it arise?
>What is the distribution of earthquakes and volcanoes?
>Throughout the next two points be sure to pepper in a few case studies, you might explain for example why Iceland has numerous frequent but small earthquakes and Pakistan experiences occasional, extremely large magnitude quakes. For the volcanoe side, think, what is the difference between Mt Etna and Mauna Loa?
>Earthquake section; why does an earthquake occur? In what relation to a tectonic plate does it occur? Can we predict the type of earthquake based on the type of plate, where are the greatest and lowest magnitude earthquakes found? Are there any anomalies? Is there anything plate tectonic theory can't explain?
>Volcanoe section; as above but for volcanoes, additionally be sure to mention hot spots (I know far too much about these and would be happy to help up to the level required! http://www.mantleplumes.org/PPPs.html )
>How far have we come? Are these ideas developing? Contrast today to 60s when plate tectonic theory was just getting going.
>Conclude, what have you said? Bring everything together and state your opinion based on the evidence you have stated.
>Have a quick once over, anything you've missed out?see more
So electrons fall into the category of particles called lepton s with don't interact with the strong nuclear force, this means they can be used for diffraction without getting affected too much by the nuclei they are intended to measure. This is because neautrons and alpha particles are affected by the strong nuclear force.
A beam of moving electrons ahs a de Broglie wavelength which at high speeds is approximated by hc/E where h is the planck constant, c is the speed of light and E is the charge in coulombs. Remember that in a question you're likely to get the beam strength in MeV so you need to times by 1.6*10-19 to get to coulombs!
Once we have the wavelenght we can use the sin function to obtain the diameter through the equation sin(theta)= 1.22*wavelength/d where d is the diameter of the nucleus and theta is the angle of the straight through posistion to the first minimum. This bit is somewhat easier to explain with a diagram. The 1.22 may sound a little arbitrary but it does have it's basis in reasonably complex physics, https://www.quora.com/Where-does-this-%CE%B8-1-22-%CE%BB-D-come-from-Whats-its-derivationsee more