Answer:
The solution is in the attached file
Answer:
The answer is 48 units³
Step-by-step explanation:
If we simply draw out the region on the x-y plane enclosed between these lines we realize that,if we evaluate the integral the limits all in all cannot be constants since one side of the triangular region is slanted whose equation is given by y=x. So the one of the limit of one of the integrals in the double integral we need to evaluate must be a variable. We choose x part of the integral to have a variable limit, we could well have chosen y's limits as non constant, but it wouldn't make any difference. So the double integral we need to evaluate is given by,

Please note that the order of integration is very important here.We cannot evaluate an integral with variable limit last, we have to evaluate it first.after performing the elementary x integral we get,

After performing the elementary y integral we obtain the desired volume as below,

Answer:
Minimum cycle time = time for longest task = 2.4 minutes
Maximum cycle time = sum of the times to complete all the tasks = 18 minutes
Step-by-step explanation:
For the minimum cycle time, the reasoning is that all the tasks can be done simultaneously, at some during the assembling task. Hence, minimum time to complete one cycle is the time it takes to complete task that takes the longest time to complete.
For the maximum cycle time, the reasoning here is that each task is done after the completion of the previous task. The total time taken to finish the task will then be the sum of the time taken to complete each task. This usually is at the beginning of operations.
55,57,59
Let the smallest integer = x
171= (x) + (x+2) + (x+4)
171= 3x + 6
3x = 165
x= 55
therefore the integers are 55, 57, 59