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A tunnel has height, h, (in metres) given by h=14-x^2 where x is the horizontal distance from the centre of the tunnel. Find the cross sectional area of the tunnel. Also find the maximum height of a truck passing through the tunnel that is 4m wide.

Firstly, solve 0=14-x^2 to find the horisontal distance to the edges of the tunnel. x1=sqrt(14), x2= -sqrt(14). Integrate h=14-x^2 between x1 and x2 28*sqrt(14) -(2(sqrt(14)^3))/3. This is the required area ...
JG
Answered by James G. • Maths tutor
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How does the 3D dash and wedge notation work?

To make life easier we often treat molecules as flat - for example we draw methane on a page as a carbon with 4 hydrogens bonded to it at perfect 90 degree angles. This isn't really the case. Electron-electr...
DM
Answered by Dario M. • Chemistry tutor
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Express 3(x^2) - 12x + 5 in the form a(x - b)^2 - c.

Starting with a(x - b)^2 - c, if we expand the bracket we get: a(x^2 - 2xb + b^2) -c Since we need to end up with the coefficient on x^2 being 3 and in the expression above x^2 is only multiplied by a, this ...
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Answered by Lucy H. • Maths tutor
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What does ELISA measure?

ELISA, an acronym for enzyme linken immunoabsorbant assay, is a means of measuring the amount of a specific antibody in serum through treating a 96 well plate with antigens that stick well to the plastic wal...
KM
Answered by Kyle M. • Biology tutor
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What is historiography and how can it be used in an exam essay?

Historiography is history as written by academics who are experts in the areas they have studied, and so their commentary and interpretations are regarded as reliable and credible. Though not explicitly necc...
CR
Answered by Chloe R. • History tutor
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