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Describe homoeostasis using temperature control as an example.

Homeostasis is the maintenance of a constant internal environment. The body tends to use a series of negative feedback loops to allow this. Using temperature as an example, the body likes to maintain a core ...
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Answered by Priya S. • Biology tutor
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How do I structure a paragraph for an exam essay?

The ability to structure paragraphs is a quality that many students worry they do not possess. Fortunately, this is an easy and effective skill to master: once you crack the formula, your essays will appear ...
FD
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How do I construct a proof by induction?

There are typically 4 steps: proving the base case, making an assumption, making the inductive step and finally concluding the proof. The base case consists of proving that a statement is true for n = 1, the...
AF
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Using the definitions of hyperbolic functions in terms of exponentials show that sech^2(x) = 1-tanh^2(x)

tanh(x) = ((e x -e -x )/2)/((e x +e -x )/2) 1 - tanh 2 (x) = 1-((e x -e -x )/(e x +e -x )) 2 = ((e 2x +e -2x +2)-(e 2x +e -2x -2))/(e x +e -x ) 2 = (2e x .2e -x )/(e x +e -x ) 2 = 4/(e x +e -x ) 2 = sech 2 x
CB
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Core 3: Find all the solutions of 2cos(2x) = 1-2sin(x) in the interval 0<x<360

2cos(2x) = 1-2sin(x) 2(1-2sin 2 (x)) = 1-2sin(x) -- by our trigonometric functions 2-4sin 2 (x) = 1-2sin(x) 4sin 2 (x)-2sin(x)-1=0 -- rearrange sin(x) = (2±(4-4(4)(-1)) 0.5 )/8 -- quadratic formula x = 54 &a...
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Answered by Chris B. • Maths tutor
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