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Use the substitution u=3+(x+4)^1/2 to find the integral of 1/(3+(x+4)^1/2) dx between 0 and 5.

We will call the integral I, so I = integral of 1/(3+(x+4)^1/2) dx between 0 and 5. First substitute u=3+(x+4)^1/2 into the equation to get I = integral of 1/u dx between 0 and 5 Next ...

Answered by Calum B. • Maths tutor

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Find the centre and radius of the circle with equation: x^2 + y^2 -4x +8y = 5, and determine whether the point (7,-4) lies on the circle.

First we complete the square on the equation of the circle to obtain: (x-2)^2 -4 + (y+4)^2 -16 = 5. Re arrange : (x-2)^2 + (y+4)^2 = 25 General equation of a circle: (x-a)^2 + (y-b)^2 = r^2, with centre ...

Answered by Alec S. • Maths tutor

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How to express one quantity as a percentage of another?

There are several ways to do this which make it particularly interesting. I would advise trying to avoid doing it by eye, this leaves you open to many clumsy mistakes. My preferred method is using equival...

Answered by Sebastian P. • Maths tutor

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