2. Let l be the line x² + y² − 4x + 2y +1 = 0 and drop a perpendicular from O to Q E l. (a) Explain why Q has co-ordinates (✓t, - ✓t) for some t = (0,1). (b) Show that the hyperbolic distance 8 = d(O,Q) of l from the origin is In 1+15. 2 (c) = (0,-1) is an omega-point for l. Compute the angle of parallelism μ = LQON Ω explicitly and check that cosh 8 = cscµ.

Find fe(x? + 3y)i + 3y³j) · dr where C consists of the three line segments from (2, 0, 0) to (2, 2, 0) to (0, 2,0) to (0, 2, 3). So((x² + 3y)i + 3y³j) · dr = 5/3

Two archers will simultaneously shoot once at a target. Let Xi , i = 1, 2, be marksman i's horizontal error, measured in meters. If the target's position is (a, b), and marksman i's shot ends up at (x, y), then Xi = (x - a). These errors are modeled by X1 ~ N(0, 0.5) and X2 ~ N(0, 1). What is the probability that both shots will be within 1 meter of the target, in the horizontal direction?