A tank is full of water. Find the work required to pump the water out of the spout. Use the fact that water weighs 62.5 lb/ft3
1 answer:
The work required to pump the water out of the spout is 5000ft⋅lb
Given
The volume V=12(4ft)(5ft)(6ft)=60ft3,
Then the weight is w = γV = (62.5lb /ft³) (60ft³) = 3750lb.
Since work is force × distance, you need a distance here, and the appropriate one is the distance you must raise the center of mass to get the H2O out of the spout.
Since the center of mass of a uniform triangular area is 13 of the way from any side, the distance is (4ft)/3 so the work is (3750lb) (4ft)/3=5000 ft-lb.
In calculus, the area of a horizontal section yft from the lowest point is (5ft) × (6ft) × y / (4ft) = 7.5y ft2.
We have to lift that slice 4ft−y, so work is
w = (62.5)(4 − y) (7.5y)
dy = (62.5)[15y2−2.5y3]40 = 5000ft⋅lb
The work required to pump the water out of the spout is 5000ft-lb
Learn more about calculus here: brainly.com/question/24430269
#SPJ4
You might be interested in
Answer:
- 25000 seats in section A
- 14100 seats in sectin B
- 10900 seats in section C
Step-by-step explanation:
The problem statement tells you half the total number of seats are in section A, so you already know that there are 25000 A seats. The revenue from those seats is
... 25000×$25 = $625,000
so the revenue from B and C seats must total
... $1,070,500 - 625,000 = $445,500
If all 25000 of the B/C seats were C seats, the revenue would be
... 25000×$15 = $375,000
The actual revenue from those seats is $445,500 -375,000 = $70,500 more than that. We know each B seat generates $5 more revenue, so there must be ...
... $70,500/$5 = 14,100 . . . . B seats
Then the balance of the 25000 B and C seats are C seats:
... 25,000 - 14,100 = 10,900 . . . . C seats
_____
<em>Alternate Solution Method</em>
The new Brainly answer format requires the answer be supplied before the working. In order to find the answer quickly so that I can fill in that section, I used a matrix method for solving the problem. The problem equations can be written ...
- a + b + c = 50000
- a - b - c = 0
- 25a + 20b + 15c = 1070500
so the augmented matrix is ...
A graphing calculator can be used to find the solution to this, generally using a function that produces the reduced row-echelon form. The attachment shows the solution using a TI-84 calculator.
___
<em>Comment on the Working</em>
Since the number of A seats is equal to the total of B and C seats, the number of A seats must be half the total number of stadium seats. Having figured that out, the problem is reduced to one of finding the mix of B and C seats that will produce the remaining revenue.
As with many mixture problems, it is convenient to look at differences. Start with the assumption that all of the desired revenue comes from the least contributor. Here, that is C seats. Then figure the difference that using a B seat makes ($20 -15 = $5) and the difference of the actual revenue and the amount that you got by assuming all C seats: 445,500 -375,000 = 70,500. Since replacing a C seat by a B seat adds $5 to the revenue, it is easy to figure the number of such replacements required in order to raise the revenue by $70,500.
If you write the equation for B seats, you find the solution to the equation mirrors this verbal description:
... 20b + 15(25000-b) = 445,500
... 5b = 445,500 - 375000 . . . . simplify, subtract 375000
... b = 70500/5 = 14100
Answer:
THE AMOUNT OF LABOR TO BE USED IS 2,244.28
THE AMOUNT OF CAPITAL TO BE USED IS 2,619.33
THE MINIMUM PRODUCTION COST IS $374,047
Step-by-step explanation:
PLEASE CHECK ATTACHMENT FOR COMPLETE SOLUTION AND STEP BY STEP EXPLANATION
