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Integral of 1/(x^3 + 2x^2 -x - 2)

Factorise denominator using the factor theorem giving - 1/(x+1)(x+2)(x-1) Use partial fractions to turn this into an easier form to integrate giving - 1/3(x+2) + 1/6(x-1) - 1/2(x+1) using integral 1/x = ln(x...
MO
Answered by Mojowo O. • Maths tutor
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A curve has the equation 2x^2 + xy - y^2 +18 = 0. (1) Find the coordinates of the points where the tangent to the curve is parallel to the x-axis.

Firstly notice that the coordinates of the points where the tangent to the curve is parallel to the x-axis are precisely the points where the rate of change of y with respect to x is not changing. That is, w...
OL
Answered by Oliver L. • Maths tutor
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For Maths 11+. An Island on a map is measured to be 4cm across. The scale of the map is 4cm to 500m. How long is the island in km?

The island is 2km. If the scale is 1cm:500m we need to multiply both left and right sides by 4 to get to the 4cm that was measured. This gets us 4cm: 2000m . We now need to convert 2000m to km which gives us...
DT
Answered by David T. • Maths tutor
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Expand and simplify (x+6)(x+4)

Answer: x 2 +10x+24 Method: A handy way of knowing how to expand brackets involves the pneumonic FOIL: - F stands for First, so we multiply the first term in the first bracket by the first term in the second...
EM
Answered by Emma M. • Maths tutor
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How do I multiply or divide fractions without a calculator?

For multiplication: Firstly, write out the sum you are trying to do, for example 3/4 X 1/8 Then, times the top numbers by each other and the bottom numbers by each other 3 x 1 = 3, 4 x 8 = 24 Then, rewrite t...
WM
Answered by William M. • Maths tutor
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