a video camera at ground level is taping the release and rise of a water balloon. the camera is located 500m away from the release point. as the balloon rises, the camera operator observes that when the angle of elevation between the camera and the balloon is pi/4 radians, the angle of elevation is increasing at a rate of 0.2 rad/sec. how fast is the balloon rising at this time?

step-by-step explanation:

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85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

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step-by-step explanation:

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step-by-step explanation: