Two circles, one of radius 5 inches, the other of radius 2 inches, are tangent at point P. Two bugs start crawling at the same t
ime from point P, one crawling along the larger circle at $3\pi$ inches per minute, the other crawling along the smaller circle at $2.5\pi$ inches per minute. How many minutes is it before their next meeting at point P?
1 answer:
Answer:
40 minutes
Step-by-step explanation:
The circumference of the larger circle is ...
C = 2πr = 2π(5 in) = 10π in
The bug navigates the circumference at 3π in/min, so will take
time = distance/speed = (10π in)/(3π in/min) = 10/3 min
to travel once around.
__
The circumference of the smaller circle is ...
C = 2πr = 2π(2 in) = 4π in
The bug navigates this circumference at 2.5π in/min, so will take
(4π in)/(2.5π in/min) = 8/5 min
to travel once around.
__
The bugs will meet at a time that is the least common multiple of these times. Both can be expressed in 15ths of a minute as ...
{50/15, 24/15}
Then the LCM of these will be ...
(1/15)LCM(50, 24) = (1/15)(50×24)/GCD(50, 24) = 1200/30 = 40
It will be 40 minutes before the bugs next meet at point P.
___
A graphing calculator can make use of the mod function to show when the bugs meet at point P (total is displacement of the two bugs from P is zero). It shows the meeting occurs after 40 minutes.
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Step-by-step explanation:
Given:
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a.Calculate the probability that 3 ≤X≤ 5
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Solution:
- The CDF gives the probability of (X < x) for any value of x. So to compute the P ( 3 ≤X≤ 5 ) we will set the limits.
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Answer:
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Step-by-step explanation:
Given that,
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we have to check all the apply.
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Then,
This is Equation of the given case(1).
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