Verify the identity. cotangent of x divided by quantity one plus cosecant of x equals quantity cosecant of x minus one divided by cotangent of x

Cody worked 42.5 hours per week in july. this is 12.25 hours more per week than he worked in june. how many hours did cody work per week in june?

Let f(x) = 1/x^2 (a) use the definition of the derivatve to find f'(x). (b) find the equation of the tangent line at x=2

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)