A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is 60 ft deep. The bucket is filled with 38 lb of water and is pulled up at a rate of 2.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.25 lb/s. Find the work done in pulling the bucket to the top of the well.

The work-done required to pull the bucket to the top of the well = 2340 ft-lb

Step-by-step explanation:

From the information given:

The water is pulled at a rate of 2.5 ft/s

Also, water leaks out of a hole in the bucket at a rate of 0.25 lb/s.

Thus, the rate of water leaking out of the bucket is:

= 0.1 lb/ft

The work done needed to pull the bucket to the top of the well can be expressed by using the integral:

where;

F(x) is read as the function of x = total weight of the bucket and water

i.e

F(x) = 4 + ( 38 - 0.1x)

F(x) = 42 - 0.1x

and a which is inital height = 0 and b which is th final height = 60

Thus: we can compute the workdone as follows:

W = 2520 - 180

W = 2340 ft-lb

Package of tulip bulbs = $12

Package of crocus = $19

Step-by-step explanation:

Let b = cost of a package of bulbs

     c = cost of a crocus package

Mark:   (1)   9b + c = 127          Huong:  (2)   6b + 6c = 186

                          c = 127 - 9b                        6b + 6(127 - 9b) = 186

                                                                      6b + 762 - 54b = 186

                                                                                      - 48b = -576

                                                                                           b = 12

                          c = 127 -9(12)

                          c = 127 - 108 = 19