Five jobs are to be scheduled on three machines (in series). Note jobs must be worked first on machine 1, then on machine 2, and finally on machine 3 (normal order!). Column PT1 is the processing time on the first machine, PT2 is the processing time on the second machine, and PT3 is the processing time on the third machine. What is the sequence that minimizes the makespan for these five jobs

Find the arc length parameter along the given curve from the point where tequals=0 by evaluating the integral s(t)equals=integral from 0 to t startabsolutevalue bold v left parenthesis tau right parenthesis endabsolutevalue d tau∫0tv(τ) dτ. then find the length of the indicated portion of the curve r(t)equals=1010cosine tcost iplus+1010sine tsint jplus+88t k, where 0less than or equals≤tless than or equals≤startfraction pi over 3 endfraction π 3.

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.

Acircle has a circumference of 7.850 units. what is its radius?