Given the function f(x) = 3x + 1, what is the value of f(-2/3)? show work
1 answer:
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Answer:
4.1 N
Step-by-step explanation:
We can solve this problem by using considerations about energy.
At the moment the stone is dropped, it has only gravitational potential energy:
where
is the weight of the stone
h = 10 m is the initial height of the stone
As the stone falls, part of this energy is converted into kinetic energy, while part into thermal energy due to the presence of the air friction, acting opposite to the motion of the stone:
where:
is the mass
v = 13 m/s is the final speed of the stone
is the thermal energy
The thermal energy is actually equal to the work done by the air friction on the stone:
where
F is the average force of friction
h = 10 m
Since the total energy must be conserved, we can combine the three equations, so we find:
And solving for F, we find the average force of air friction:
Answer:
Top 5% is 5.84 milliters and the bottom 5% is 5.60 millimeters.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Top 5%:
X when Z has a pvalue of 0.95. So X when Z = 1.645
Bottom 5%:
X when Z has a pvalue of 0.05. So X when Z = -1.645
Top 5% is 5.84 milliters and the bottom 5% is 5.60 millimeters.