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Solve the differential equation dy/dx=(y^(1/2))*sin(x/2) to find y in terms of x.

Here, we must first rearrange our equation so all x terms are on one side and all y terms are on the other. Multiplying both sides by dx and diving both by y^(1/2) gives us y^(-1/2)dy = sin(x/2)dx, which is ...
AJ
Answered by Alex J. Maths tutor
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Expand and simplify (x+4)(x-5).

For this, we use the FOIL method of expanding brackets; start by multiplying the FIRST terms of each bracket together to get x x=x^2. Next multiply the OUTSIDE elements, ie the first element in the first bra...
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Answered by Alex J. Maths tutor
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Find the first differential with respect to x of y=tan(x)

To answer, we must be familiar with several trigonometric identities and expressions; first notice that tan(x)=sin(x)/cos(x). Now our function is a quotient of two functions of x that we can easily different...
AJ
Answered by Alex J. Maths tutor
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Explain how climate change threatens extreme environments. (6 marks)

Climate change can be described as a context hazard due to its worldwide impact. However, the effects that climate change has upon extreme environments poses a severe threat. Temperature fluctuations for exa...
IW
Answered by Imogen W. Geography tutor
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Discuss how goal setting is used in the long-term psychological preparation for sports performance.

As a discuss question the examiner will not be looking for the learner to simply focus on the positives of the technique. In addition the question states that the answer should be in the context of a long-te...
LW
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