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A semicircle has a diameter of 8cm, what it the area?

Area of a circle = pi × r 2 Area of semi-circle = 1/2(Area of circle) = 1/2(pi × r 2 ) Diameter = 2r r = 8÷2 = 4 Area of semi-circle = 1/2(pi × 4 2 )
AP
Answered by Annabelle P. • Maths tutor
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Evaluate the following integral: (x^4 - x^2 +2)/(x^2(x-1)) dx

This type of question appears over-complicated with limited options, but one must not fear! At first, the numerator seems to be of a higher degree than the denominator (x^4 compared to x^2), but from the fir...
NH
Answered by Nicholas H. • Maths tutor
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Differentiate the function f(x) = 3x^2/sin(2x)

Using the product rule, f=uv, df = (vu'-uv')/v^2. we first set u = 3x^2 and v = sin(2x). u' = 6x, v'=2cos(2x) Therefore, vu' = 6x sin(2x). uv' = 6x^2 cos(2x), v^2 = 4cos^2(2x) Therefore the differential is [...
KS
Answered by Kilian S. • Maths tutor
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Solve algebraically the simultaneous equations: x^2+y^2 = 25 and y-3x=13

To answer this question, we need to make y the subject of the second equation. We can do this through simple rearrangement: y-3x=13 so y=13+3x Now that we have y on its own, this means we can substitute for ...
JK
Answered by James K. • Maths tutor
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Differentiate the function f(x)=2xsin3x

Use the product rule: u'v + uv' u = 2x V= sin3x u'= 2 v'= 3cos3x = (2)(sin3x) + (2x)(3cos3x) = 2sin3x + 6xcos3x
TW
Answered by Thomas W. • Maths tutor
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