An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing East.
The ant first turns 72$$^\circ$$ anticlockwise at P, and then does the following two steps in sequence exactly FIVE times before halting.
1. moves forward for 10 cm.
2. turns 144$$^\circ$$ clockwise
The pattern made by the trade left behind by the ant is
$$x:y:z = {1 \over 2}:{1 \over 3}:{1 \over 4}$$
What is the value of $${{x + z - y} \over y}$$ = ?
Both the numerator and the denominator of $${3 \over 4}$$ are increased by a positive $${15 \over 17}$$ integer, x, and those of _____ are decreased by the same integer. This operation results in the same value for both the fractions. What is the value of x?
Two straight lines pass through the origin (x0, y0) = (0, 0). One of them passes through the point (x1, y1) = (1, 3) and the other passes through the point (x2, y2) = (1, 2). What is the area enclosed between the straight lines in the interval [0, 1] on the x-axis?