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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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Briefly explain the common types of erosion that shape a river from source to mouth

The first is Hydraulic Action. This is the force of the river against the banks causing air to be trapped in cracks and crevices. The pressure then weakens the banks and gradually wears it away. Secondly, Ab...
JB
Answered by Joe B. • Geography 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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An engineering student found that the Youngs modulus of an alloy was 2.8 x 10^11 Pa. The 1.5m wire of the allow increased in length by 0.24% during an experiment. Calculate the stress on the wire.

The Youngs modulus of a material is = Stress / Strain. Therefore, the stress of an object is the strain multiplied by the Youngs modulus. We know that strain is the change in length (or extension) divided by...
DT
Answered by David T. • Physics tutor
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