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s2008m [1.1K]
3 years ago
10

two wheels are rolled simultaneously. The radius of the smaller wheel is r feet and the radius of the larger wheel 2r feet. If b

oth wheels did a total of 4 rotations, how much further did the large wheel travel? PLEASE SHOW STEPS TYSM
Mathematics
1 answer:
Nuetrik [128]3 years ago
6 0
The circumference of a circle is C=2πR, where R is the radius of the circle and π≈3.14.

So if we open the circumference of the circle into a straight line segment, the length of this segment is C=2πR≈2*3.14*R=6.28R

4 rotations mean 4 circumferences that is 4 segments of length 6.28R, 
which makes a linear distance of 4*6.28R=25.12R


i: the radius of the smaller wheel is R=r, thus it covers a distance of 25.12r feet

ii: the radius of the smaller wheel is R=2r, thus it covers a distance of  25.12*2r=50.24r (feet)

50.24r is twice 25.12r, thus the larger wheel traveled Twice the distance of the smaller one.


Answer: the larger covered twice the distance of the smaller.
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a. What is the probability that a disk has exactly one missing pulse?

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This is P(X = 1).

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0.164 = 16.4% probability that a disk has exactly one missing pulse

b. What is the probability that a disk has at least two missing pulses?

P(X \geq 2) = 1 - P(X < 2)

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P(X < 2) = P(X = 0) + P(X = 1)

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P(X = 0) = \frac{e^{-0.2}*0.2^{0}}{(0)!} = 0.819

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P(X < 2) = P(X = 0) + P(X = 1) = 0.819 + 0.164 = 0.983

P(X \geq 2) = 1 - P(X < 2) = 1 - 0.983 = 0.017

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Two disks, so binomial with n = 2.

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P(X = 0) = C_{2,0}.(0.181)^{0}.(0.819)^{2} = 0.671

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