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Express 5cosx - 3sinx in the form Rcos(x+a).

Find the area bounded by the curve x^2-2x+3 between the limits x=0 and x=1 and the horizontal axis.

Points A and B have coordinates (–2, 1) and (3, 4) respectively. Find the equation of the perpendicular bisector of AB and show that it may be written as 5x +3 y = 10.

Figure 1 shows a sector AOB of a circle with centre O and radius r cm. The angle AOB is θ radians. The area of the sector AOB is 11 cm2 Given that the perimeter of the sector is 4 times the length of the arc AB, find the exact value of r.

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