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How do you integrate (sinx)^3 dx?

Firstly, we must use the special property of trig functions which means that (sinx)ⁿis the same as sinⁿx. Likewise, (cosx)ⁿ=cosⁿx, (tanx)ⁿ=tan^n...

Answered by Shanti S. • Maths tutor

6908 Views

Show that 2(1-cos(x)) = 3sin^2(x) can be written as 3cos^2(x)-2cos(x)-1=0.

Firstly let's expand out the staring equation getting rid of any brackets. This gives: 2-2cos(x)) = 3sin^2(x). Now we can spot that the sin^2(x) term is in the first equation but no the final one. So let'...

Answered by Rebekah S. • Maths tutor

3651 Views

A matchbox of height h and uniform density stands on its end on a table with coefficient of friction μ. For accelerating it horizontally, at acceleration a, whilst upright, at which height y should the acceleration be applied?

Since the matchbox is of uniform density, the centre of mass is at the centre. In order to accelerate it horizontally, it must have zero resultant moment about the centre of mass, else it will rotate and ...

Answered by Dakshesh D. • PAT tutor

1631 Views

Deduce the main organic product for the reaction of benzene with nitric acid in the prescence of sulfuric acid, and provide a complete mechanism for this reaction. (5 marks)

The answer to this question mostly involves drawing of chemical structures and mechanistic arrows.The organic product is nitrobenzene, which students would draw out as part of the mechanism, but must also...

Answered by Erin B. • Chemistry tutor

2773 Views

How do you structure the response to a question about the changes of a population due to natural selection

Individuals within a species show a wide range of genetic variation. Some individuals will have characteristics more suited for their environment, meaning they are more likely to survive and reproduce. Th...

Answered by Samantha B. • Biology tutor

2370 Views