In addition to being computed directly, the following integrals may be computed by applying one or more of the following theorems. (a) −0.1 r · d r c where c is the line segment from (3, 0, 8) to (−2, 7, 1). which of the following theorems can be used? select all that apply. fundamental theorem of line integrals green's theorem divergence theorem stokes' theorem (b) 2x i + 4y j + 18z k · d a s where s is the sphere of radius 4 centered at (0, 5, −4). which of the following theorems can be used? select all that apply. fundamental theorem of line integrals green's theorem divergence theorem stokes' theorem (c) (−9x+20y) i + (7x−8y) j · d r c where c is a square of side 8 in the xy-plane, traversed counterclockwise with center at (3, 5, 0). which of the following theorems can be used? select all that apply. fundamental theorem of line integrals green's theorem divergence theorem stokes' theorem

Which of the following represents the length of a diagonal of this trapezoid?

Susie wants to take her friend out for lunch. she wants to spend $9.75 each person. how much will she spend in all.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.