Reference no: EM131008059
Problem- Brutus is working on a new space telescope-called Scarlet Eye-to help detect exoplanets. The telescope works by focusing on one star and recording the star's brightness. (Brutus hopes to locate exoplanets by measuring the differences in a star's brightness. If the brightness significantly decreases at regular intervals, then its change in brightness is probably caused by a planet passing in front of the star.)
Scarlet Eye is launched into space and starts returning data on its first star. Unfortunately, Brutus discovers that before the launch Sparty has hacked the telescope! Sparty's hack forces the telescope to only return functions and not their graphs.
The telescope returns
f (x) = 3sin (x/2)
for its first star. Undeterred Brutus's knows calculus and so knows how to convert this function into its graph.
The Scarlet Eye tells Brutus that the domain of this function is [-2π, 2π]. (Brutus knows that usually Brutus should always figure out the domain of the function first.)
(A)
(i) True or False: this function is an even function. (ii) True or False: this function is an odd function.
(B) Find the first derivative of f.
(C) Find all critical points of f.
(D) Identify those intervals where f is increasing and those intervals where f is decreasing.
(E) Use the first derivative test to identify local extrema.
(F) Find the second derivative of f.
(G)
(i) Identify those intervals where f is concave up and those intervals where f is concave down. (ii) Find all the inflection points of f
(H) Sketch the graph of f over the interval [-2π, 2π]. In your graph be sure to mark critical points, inflection points, local extrema, global extrema, and x-intercepts and y-intercepts.
|
Conduct a test to determine whether the two variables
: In one variation of the experiment, two variables were measured: active head movement (x, percent per degree) and body plus head rota- tion (y, percent per degree). The data for n = 39 trials were subjected to a simple linear regres- sion analysis..
|
|
Would you expect the correlation to be positive or negative
: GPA and IQ. Do you believe that the grade point average of a college student is correlated with the student's intelligence quotient (IQ)? If so, will the correlation be positive or negative? Explain.
|
|
Is the estimated slope of the line
: Data collected for n = 426 University of Maine instructors yielded a correla- tion between RMP and SET ratings of .68. Give the equation of a linear model relating SET rating (y) to RMP rating (x).
|
|
How integrate information into safety management system
: Conclusion - what are your thoughts and/or conclusions about the topic. How would integrate this information into a Safety Management System? How will it support it? How will your new knowledge make the SMS better
|
|
Compute the first derivative of given function
: Find the first derivative of f. Find all critical points of f. Identify those intervals where f is increasing and those intervals where f is decreasing. Use the first derivative test to identify local extrema.
|
|
What was the inventory turnover
: Maple Leaf, Inc., a television manufacturer, would like to reduce its inventory. In addition, the cost of goods sold last year was $15 million. What was the inventory turnover
|
|
Compute and interpret the coef?cient of determination r2
: For the 13 obese young adults, the researchers reported a correlation of r = .50 between base- line and follow-up physical activity, with an associated p-value of .07. Give a practical interpretation of this correlation coef?cient and p-value.
|
|
Determining the potential downside results
: Investing in equipment, maxes and mins. Shawn Over- growth, whom we met in Exercise 31, is an entrepreneur who is optimistic about the growing season. What choice should he make to maximize his return? His assistant, Lance Broadleaf, is very conse..
|
|
Disclosure of non cash investing and financing activities
: Disclosure of interest and income taxes paid if the indirect method is used.
|