Numerical Mathematics Problems (Matlab)
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Mathematics
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There are 4 problems. The answer should include Matlab code.
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2. Find the polynomial of degree 10 that interpolates the function arctan x at 11 equally
spaced points in the interval [1, 6]. Print the coefficients in the Newton form of the
polynomial. Compute and print the difference between the polynomial and the function
at 33 equally spaced points in the interval [0, 8]. What conclusion can be drawn?
6. Write routines analogous to Coef and Eval using the Lagrange form of the interpolation
polynomial. Test on the example given in this section at 20 points with h/2. Does the
Lagrange form have any advantage over the Newton form?
11. Use mathematical software such as Matlab, Maple, or Mathematica to find an interpo-
lation polynomial for the points (0,0), (1, 1), (2, 2.001), (3, 3), (4,4), (5,5). Evaluate
the polynomial at the point x = 14 or x = 20 to show that slight roundoff errors in the
data can lead to suspicious results in extrapolation.
8(x) =
17. (Padé interpolation) Find a rational function of the form
a+bx
1+cx
that interpolates the function f(x) = arctan (x) at the points Xo = 1, x1 = 2, and
x2 = 3. On the same axes, plot the graphs of f and g, using dashed and dotted lines,
respectively.
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Homework 3Homework 3 focuses on the application of concepts addressed in Exercises 13 and 28. Homework 3 is due SUNDAY at 11:59pm.Homework 3 involves survey data from the Centers for Disease Control (CDC) that focused on residential care facilities in the United States in 2010 (CDC, 2010). Residential care facilities primarily consist of persons in assisted living communities who receive housing and supportive services because they cannot live independently but generally do not require the skilled level of care provided by nursing homes. The focus of the first national study of acute care use in residential care facilities by Kahveci and Cipher (2014) was on acute care use (emergency department visits and hospitalizations) among persons in various disease categories, and information regarding the residents’ length of stay and visitor frequency was also collected. Length of stay in the facility was coded as 1 =0 to 3 months; 2 =3 to 6 months; 3= 6 months to a year; 4= 1 to 3 years; 5 =3 to 5 years; 6 =More than 5 years. Visitor frequency was coded as 1 =Every day; 2 =At least several times a week; 3 =About once a week; 4 =Several times in past month; 5 =At least once in past month; 6 =Not at all in the last 30 days. Therefore, higher values of the length of stay variable represent longer stays in the facility. Higher values of visitor frequency represent fewer visitor frequencies, which are considered inverse scoring.The null hypothesis is “There is no correlation between length of stay and visitor frequency among residents of residential care facilities.” The data are presented in HW3.sav. A subset of 15 residents was randomly selected for this example so that the computations would be small and manageable. In actuality, studies involving Pearson correlations need to be adequately powered (Aberson, 2010; Cohen, 1988) and in the case of CDC survey data, adjusted for complex sampling. Download the file: HW3.savOpen in SPSS. Use the dataset to answer the following questions.Calculate the Pearson r between LOS and visitor frequency, using the formula presented in Exercise 28. List the SOLVED numerator and the denominator. See attached for starter calculations. HW3 Starter Calculations.xlsxCompute the Pearson r with SPSS. Paste the correlation matrix table into your homework.What was the exact likelihood of obtaining the r value at least as extreme or as close to the one that was actually observed, assuming that the null hypothesis is true? (this question is asking you for the exact p value, converted to a percentage.) How would you characterize the magnitude of the effect between length of stay and visitor frequency? Refer to Table 28-1 for the size of the effect. State your rationale. Write your interpretation of the results, as you would in an APA-formatted journal. Remember that visitor frequency is REVERSE coded, with larger values represented FEWER visitors.Help for Homework 3:Please watch my video ‘What is a p value‘ in Module 2. When comparing the obtained r to the tabled r, the obtained must be higher than the tabled r to achieve significance. The other way to determine significance is to look at the exact p value presented in statistical software output. If the exact p is LESS THAN .05 thenthe result is significant.
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11 pages
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1. SDJ, Inc., has net working capital of $1,760, current liabilities of $5,670, and inventory What is the current ratio? ( ...
Finance Course
1. SDJ, Inc., has net working capital of $1,760, current liabilities of $5,670, and inventory What is the current ratio? (Do not round intermediate ...
Week 4 discussion
Read/review the following resources for this activity:
OpenStax Textbook Readings
...
Week 4 discussion
Read/review the following resources for this activity:
OpenStax Textbook Readings
Lesson in Canvas
Assignments in Knewton
Graphing Linear Equations
Solving Systems of Linear Equations by Graphing
Solving Systems of Linear Equations by Substitution
Solving Systems of Linear Equations by Elimination
Initial Post Instructions
Before we begin graphing systems of equations, a good starting point is to review our knowledge of 2-D graphs. These graphs are known as 2-D because they have two axes. Find an online image of a graph to use as the foundation of your discussion. (This is easily accomplished by searching within Google Images.)
Using your graph as the example:
Select any two points on the graph and apply the slope formula, interpreting the result as a rate of change (units of measurement required); and
Use rate of change (slope) to explain why your graph is linear (constant slope) or not linear (changing slopes).
Embed the graph into the post by copying and pasting into the discussion. You must cite the source of the image. Also be sure to show the computations used to determine slope.
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