A chain fits tightly around two gears as shown. What is the radius of the smaller gear? Round your answer to the nearest tenth.
1 answer:
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Answer:
We have been given a unit circle which is cut at k different points to produce k different arcs. Now we can see firstly that the sum of lengths of all k arks is equal to the circumference:
Now consider the largest arc to have length \small l . And we represent all the other arcs to be some constant times this length.
we get :
where C(i) is a constant coefficient obviously between 0 and 1.
All that I want to say by using this step is that after we choose the largest length (or any length for that matter) the other fractions appear according to the above summation constraint. [This step may even be avoided depending on how much precaution you wanna take when deriving a relation.]
So since there is no bias, and \small l may come out to be any value from [0 , 2π] with equal probability, the expected value is then defined as just the average value of all the samples.
We already know the sum so it is easy to compute the average :
Answer:
Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel
And the anfle is approximately
Step-by-step explanation:
For this case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.
a=[1,2,-2], b=[4,0,-3,]
The dot product on this case is:
Since the dot product is not equal to zero then the two vectors are not orthogonal.
Now we can calculate the magnitude of each vector like this:
And finally we can calculate the angle between the vectors like this:
And the angle is given by:
If we replace we got:
Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel
And the anfle is approximately