9709/May June/33/2016/Q2

The variables x and y satisfy the relation 3^y = 4^(2−x).

(i) By taking logarithms, show that the graph of y against x is a straight line. State the exact value of the gradient of this line. [3]

(ii) Calculate the exact x-coordinate of the point of intersection of this line with the line with equation y = 2x, simplifying your answer. [2]

Solutions:

Reference: PYQ - May/Jun 2016 Paper 33 Q2

9709/May June/2011/42/Q2

An object of mass 8 kg slides down a line of greatest slope of an inclined plane. Its initial speed at the top of the plane is 3ms−1 and its speed at the bottom of the plane is 8ms−1. The work done against the resistance to motion of the object is 120 J. Find the height of the top of the plane above the level of the bottom.

Solution:

Reference: PYQ - May/Jun 2011 Paper 42 Q2