A regular 18-sided polygon is rotated with the center of rotation at its center. What is the smallest degree of rotation needed
2 answers:
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Answer:
Part A.
Let f(x) = 0;
suppose x= a+h
such that f(x) =f(a+h) = 0
By second order Taylor approximation, we get
f(a) + hf'±(a) + f''(a) = 0
±
So, we get the succeeding equation for Newton's method as
±
Part B.
It is evident that Newton's method fails in two cases, as:
1. if f''(x) = 0
2. if f'(x)² is less than 2f(x)f''(x)
Part C.
In case is close to
, the choice that shouldbe made instead of ± in part A is:
f'(x) = ⇔
Part D.
As given =
= h
or h = -
We get,
f(a) + hf'(a) +(h²/2)f''(a) = 0
or h² = -hf(a)/f'(a)
Also, (-
)² = -(
-
)(f(
)/f'(
))
So, f(a) + hf'(a) - (f''(a)/2)(hf(a)/f'(a)) = 0
It becomes h = -f(a)/f'(a) + (h/2)[f''(a)f(a)/(f(a))²]
Also, =
-f(
)/f'(
) + [(
-
)f''(
)f(
)]/[2(f'(
))²]
Answer:
Mean =26.2
Median=27
Mode=32
Range=38
Step-by-step explanation:
From the stem and leaf plot, we obtain the original data as:
9,11,12,12,14,17,25,25,27,32,32,32,33,35,41,42,47
The median is middle observation of the array.
Thebefore the median is 27
The mode is the number that occurs most.
The mode is 32.
The range is the highest observation minus the least observation.
The range is 47-9=38
The mean is given by: