Answer:
(x+9)(3x+27)
Step-by-step explanation:
3x^2+54x+243 (243×3=729, Product=729, Sum=54) [27+27=54, 27×27=729]
3x^2+27x+27x+243
3x(x+9)+27(x+9)
=(x+9)(3x+27)
The distance from Baltimore to New York is about 171 miles this is about 189 miles less then the distance from Baltimore to Bost
1 answer:
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Answer:
The Fourier series of f(x) converges to 3 at the points x= π+2kπ, where k is an integer.
Step-by-step explanation:
First, recall that the function f(x) is extended 2π periodic to the whole real line, in order to obtain a valid Fourier expansion. Remember that a Fourier series is formed by a sines and cosines, which are 2π-periodic.
So, the 2π-periodic expansion of f(x) is discontinuous at the points π+2kπ, in particular π and -π. Check the attached figure to a better understanding.
Now, the Dirichlet theorem on the convergence of a Fourier series tells us that the series converges to the function at the points of continuity, and at points of discontinuity the sum of the series is
.
Here we understand the notation and
as
and
.
In this particular case
.
For the limit , with
recall that our function is 2π-periodic, so the values of f near π, with x>π are the same when x is near -π and x>-π. Again, check the attached figure. So,
.
Thus,
.
Note: In the attached figure we only have drawn three repetitions of the 2π-periodic extension of , recall that the extension is <em>ad infinitum</em>. Also, the points drawn in the dotted lines are the sum of the series at the points of discontinuity.
Answer:
Step-by-step explanation:
Given that a college senior who took the Graduate Record Examination exam scored 530 on the Verbal Reasoning section and 600 on the Quantitative Reasoning section.
Quantitative reasons scores are N (429, 148)
Hence Z score for the college senior =
The mean score for Verbal Reasoning section was 460 with a standard deviation of 105
Verbal reasoning score was N(460, 105)
The score of college senior = 530
Z score for verbal reasoning =
comparing we can say he scored more on quantiative reasoning.
Thus comparison was possible only by converting to Z scores.