Which polar equation correctly identifies the curve on the polar axis below?

What basic trigonometric identity would you use to verify that csc x sec x cot x = csc^(2)x

Each morning papa notes the birds feeding on his bird feeder. so far this month he has see. 59 blue jays, 68 black crows, 12 red robin's and 1 cardinal. what is the probability of a blue jay being the next bird papa sees

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?