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Leno4ka [110]
3 years ago
10

Two cars start moving from the same point. One travels south at 16 mi/h and the other travels west at 12 mi/h. At what rate is t

he distance between the cars increasing three hours later?
Mathematics
1 answer:
alexandr402 [8]3 years ago
4 0

Answer:

20 miles per hour

Step-by-step explanation:

The distances traveled by each car are perpendicular, so we can find the distance between the cars using the Pythagoras' theorem between their distances traveled:

d^2 = d_1^2 + d_2^2

Where d is the distance between the cars, d1 is the distance traveled by the first car and d2 is the distance traveled by the second car.

The distance traveled is calculated by the speed times the time traveled, so we have:

d^2 = (16t)^2 + (12t)^2

d^2 = 256t^2 + 144t^2

d^2 = 400t^2

d = 20t

The rate that the distance is increasing can be found with the derivative of the distance in relation to the time:

dd/dt = 20\ mph

So the rate that the distance increases is always 20 miles per hour, and it's independent of the time.

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0.362

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When drawing randomly from the 1st and 2nd urn, 4 case scenarios may happen:

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- Red ball is drawn from the 1st urn with a probability of 9/10, blue ball is drawn from the 2nd urn with a probability of 5/6. The probability of this event to happen is (9/10)*(5/6) = 45/60 = 3/4 or 0.75. The probability that a ball drawn randomly from the third urn is blue given this scenario is (1 blue + 4 blue)/(8 red + 1 blue + 1 red + 4 blue) = 5/14

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- Blue ball is drawn from the 1st urn with a probability of 1/10, red ball is drawn from the 2st urn with a probability of 1/6. The probability of this event to happen is (1/10)*(1/6) = 1/60. The probability that a ball drawn randomly from the third urn is blue given this scenario is (5 blue)/(9 red + 5 blue) = 5/14.

Overall, the total probability that a ball drawn randomly from the third urn is blue is the sum of product of each scenario to happen with their respective given probability

P = 0.15(3/7) + 0.75(5/14) + (1/12)*(2/7) + (1/60)*(5/14) = 0.362

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