What forms do the equations of motion for an idealized string take if either (a) the linear density varies with position, or (b)
the string hangs vertically supported only at the upper end?
1 answer:
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Answer:
Both angles B and C are equal to 40°
Step-by-step explanation:
The diagram tells you that the triangle is an isosceles triangle. From this we know that angles B and C will be equal to each other. To find what the angle measures are, we are going to set the two given expressions equal to each other, solve for x, and the plug x back in to get the two angle measures.
Now we are going to plug x back into each expression to solve for angles B and C.
Angle B
⇒
Angle C
⇒
Both angles B and C are equal to 40°
Answer:
a) There is a 99.99997% probability that at least one valve opens.
b) There is a 22.62% probability that at least one valve fails to open.
Step-by-step explanation:
For each valve, there are only two possible outcomes. Either it open, or it does not. So we use the binomial probability distribution to solve this problem.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
In this problem we have that:
(a) What is the probability that at least one valve opens?
Either no valves open, or at least one opens. The sum of the probabilities of these events is decimal 1. So
We want
So
There is a 99.99997% probability that at least one valve opens.
(b) What is the probability that at least one valve fails to open?
Either all valves open, or at least one does not open. The sum of the probabilities of these events is decimal 1. So
We want
So
There is a 22.62% probability that at least one valve fails to open.