A transformer has 18 turns of wire in its primary coil and 90 turns in its secondary coil. An alternating voltage with an effect
1 answer:
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Given Information:
Mean length of aluminum rods = μ = 10 cm
Standard deviation of length of aluminum rods = σ = 0.02 cm
Required Information:
a) P(9.98 < X < 10.02) = ?
b) P(9.90 < X < 10.1) = ?
Answer:
a) P(9.98 < X < 10.02) = 68.27%
b) P(9.90 < X < 10.1) = 100%
Explanation:
What is Normal Distribution?
Normal Distribution or also known as Gaussian Distribution, is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability
a) We want to find out the probability that the length of aluminum rods is between 9.98 and 10.02 cm.
The z-score corresponding to -1 is 0.15866 and 1 is 0.84134
Therefore, the probability that the length of aluminum rods is between 9.98 and 10.02 cm is 68.27%
b) We want to find out the probability that the length of aluminum rods is between 9.90 and 10.1 cm.
The z-score corresponding to -5 is 0 and 5 is 1
Therefore, the probability that the length of aluminum rods is between 9.90 and 10.1 cm is 100%
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.0, 2.2, 0.5 etc.)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 1.00 then go for 0.00 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.
In order to accelerate the dragster at a speed 
, its engine must do a work equal to the increase in kinetic energy of the dragster. Since it starts from rest, the initial kinetic energy is zero, so the work done by the engine to accelerate the dragster to 100 m/s is
however, we must take into account also the fact that there is a frictional force doing work against the dragster, and the work done by the frictional force is:
and the sign is negative because the frictional force acts against the direction of motion of the dragster.
This means that the total work done by the dragster engine is equal to the work done to accelerate the dragster plus the energy lost because of the frictional force, which is
:
So, the power delivered by the engine is the total work divided by the time, t=7.30 s:
And since 1 horsepower is equal to 746 W, we can rewrite the power as
however, we must take into account also the fact that there is a frictional force doing work against the dragster, and the work done by the frictional force is:
and the sign is negative because the frictional force acts against the direction of motion of the dragster.
This means that the total work done by the dragster engine is equal to the work done to accelerate the dragster plus the energy lost because of the frictional force, which is
So, the power delivered by the engine is the total work divided by the time, t=7.30 s:
And since 1 horsepower is equal to 746 W, we can rewrite the power as