Voltage sags and swells. refer to the electrical engineering (vol. 95, 2013) study of transformer voltage sags and swells, exercise 2.76 (p. 86). recall that for a sample of 103 transformers built for heavy industry, the mean number of sags per week was 353 and the mean number of swells per week was 184.
assume the standard deviation of the sag distribution is 30 sags per week and the standard deviation of the swell distribution is 25 swells per week. suppose one of the transformers is randomly selected and found to have 400 sags and 100 swells in a week. a. find the z-score for the number of sags for this transformer. interpret this value. b. find the z-score for the number of swells for this transformer. interpret this value.

a. z-score for the number of sags for this transformer is  ≈ 1.57 . The number of sags found in this transformer is within the highest 6% of the number of sags found in the transformers.  

b. z-score for the number of swells for this transformer is ≈ -3.36. The number of swells found in the transformer is extremely low and within the lowest 1%

Step-by-step explanation:

z score of sags and swells of a randomly selected transformer can be calculated using the equation

z= where

z-score for the number of sags for this transformer is:

z= ≈ 1.57

the number of sags found in the transformer is within the highest 6% of the number of sags found in the transformers.  

z-score for the number of swells for this transformer is:

z= ≈ -3.36

the number of swells found in the transformer is extremely low and within the lowest 1%

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

hello :

70y^8 + 30y^6 = 2 ( 35 y^8 + 15y^6)

the lenght is : 35 y^8

the width is : 15y^6