Calculate u and v and show working out. Suppose that u and v are two unit vectors in 3D and the angle between themis =.i. What is |u × v[?ii. If u = j and if v lies in the y-z plane with vz > 0, find v.

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Answered: Suppose that u and v are two unit…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Q/Fit (y = ax² + (b/x)) to the following data: (x:1, 2, 3, 4), (y: -1.51, 0.99, 3.88, 7.66). *
You work at a company called 'PulseTech'. The startup is about to launch a new smart wristband that has a photoplethysmogram (PPG) sensor that monitors heart rhythms. This sensor captures a reading every 60 seconds, represented by beats per minute (bpm). Imagine you possess this heart rate information for N individuals, gathered over a span of one day, and you save it in a vector hi for i = 1, 2, 3, ..., N.
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Loblolly is a built-in R dataset that that records the growth of Loblolly pine trees. We are interested in the height column of Loblolly. The values in the height column can be converted into a vector of name x by the assignment: x <- Loblolly$height We can see the values in x by typing x and Return or Enter. Remember x <- Loblolly$height After this assignment, we can see the first six values in x by typing head(x) and Return or Enter a. Give the R code to assign the values in in the height column of Loblolly to the vector named x. (Easy-see above) b. Calculate the interquartile range of x using the R, IQR() function. c. Calculate the sum of the squares of the values in x. d. Calculate the sample mean of x. e. Calculate the sample variance of x. f. Calculate the sample standard deviation of x. f. Using R, calculate a trimmed mean of x. [ h.Enter your R script in the box below.
Exercise 4 In this regression we presented the results of the consumption fitted to the income in the period 1980-2005. We divide the data in two periods as 1980-1992 and 1993-2005. Decide if there is a structural change in the consumption-income regression in the two periods. The results for all data are as follows cons = 179 + 0.85 Income RSSfull = 265277 The results for 1980-1992(1) and 1993-2005 (2) are as follows 143 - 0.85 Income RSSfull = 13310 (1) cons = cons = 110 + 0.18 Income RSSfui = 163505 (2) fll
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Suppose that u and v are two unit vectors in 3D and the angle between them 6 i. What is |u x v[? ii. If u = j and if v lies in the y-z plane with vz > 0, find v. %3D