Because of its special reflective properties, a
parabola is an ideal shape for collecting
weak radio signals. The European Space
Agency has asked you to write an equation
for the parabolic dish of their new radio
telescope. It is parallel to the ground and
should have the following dimensions:
Width of dish: 60 m
Depth of dish: 10 m
Height above ground level (measured from
the bottom of the dish): 50 m
Horizontal distance from the bottom of the
dish to the control room (the origin): 100 m

Aking and his army will attempt to capture a fortress. the left and right flanks break off from the main group to attack the west and east guard towers. suppose the left flank has a 60% chance of success and the right flank has a 75% chance of success, independently of one another. if both flanks capture their respective targets, then the king has a 98% chance of successfully taking the fort. if, however, only the left flank captures its tower, the king has an 80% chance of success; if only the right flank succeeds, the king has a 50% chance. if both flanks fail, then the king's chance of capturing the fort drops to 20%. it turns out the king captures the fort. what is the probability that one, and only one, flank was successful (either the left, or the right, but not both)? (round your answer to 3 decimal places)