Consider the parametric equations below. x=√√t, y=3-t (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. y y 2 -2 -4 -6 -8 10 x 1 2 3 4 5 2 2 x -5 -4 -3 -1 1 2 3 4 5 -2 -2 -4H -6 -8 10 (b) Eliminate the parameter to find a Cartesian equation of the curve. 2 x -5 -4 -3 1 -2 A -4 -6 -8 -6 -8 -10 -10 for x ≥ 0 x

Find a set of parametric equations to represent the graph of y=x2+2, using each parameter. a. t=x b. t=2x

Test y2=6x for symmetry with respect to both axes and the origin.

The figure shows the parametric equations and the path for a ball thrown from a height of 5 ft, with an initial speed of 100 ft/s and at an angle of 45° with the horizontal. y (feet) x= (50/2)t y= 5+(50/2)t– 16?? 80 60 40 20 - x (feet) 100 200 300 (a) Compute the x- and y-coordinates of the ball when t = 2, 3, and 4 seconds. (Round the answers to one decimal place.) t = 2 (х, у) (x, y) = ( t = 3 t = 4 (х, у) = (b) How long is the ball in flight? (Round the answer to two decimal places.) sec What is the total horizontal distance traveled by the ball before it lands? (Round to the nearest foot.) ft