Calculate the circulation, ∫CF⃗ ⋅dr⃗ , in two ways, directly and using Stokes' Theorem. The vector field F⃗ =(8x−y+5z)(i⃗ +j⃗ ) and C is the triangle with vertices (0,0,0), (8,0,0), (8,3,0) , traversed in that order. Calculating directly, we break C into three paths. For each, give a parameterization r⃗ (t) that traverses the path from start to end for 0≤t≤1. On C1 from (0,0,0) to (8,0,0), r⃗ (t)= On C2 from (8,0,0) to (8,3,0), r⃗ (t)= On C3 from (8,3,0) to (0,0,0), r⃗ (t)=

F(x)=|x| is shifted down 4 units and to the right 3 units.

Analyze the data sets below. data set a 25,25,25,26,26,26,27,28,28,29,30,31 ,31,32,33,33,34,35,35,35 data set b 25,25,25,26,26,26,26,27,27,27,27,28 ,28,29,29,30,31,31,32,34 which of the following statement are true? select all that apply. a. data set a is relatively symmetric and data set b is skewed left. b. the means of the data sets are within 3 units from eachother. c. the data sets have the same standard deviation. d. the mean of data set a is 27.95 and the mean of data set b is 30. e. the data set b has a higher standard deviation than data set a. f. the mean and median of data set a are close in value.

Simplify the expression. -2/5(10+15m-20n)