A bucket that weighs 5 lb and a rope of negligible weight are used to draw water from a well that is 50 ft deep. The bucket is filled with 38 lb of water and is pulled up at a rate of 1.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.15 lb/s. Find the work done in pulling the bucket to the top of the well. Show how to approximate the required work by a Riemann sum. (Let x be the height in feet above the bottom of the well. Enter xi* as xi.)
Answers
Answer:
Part A
The work done in pulling the bucket to the top of the well is 1,775 ft.·lb
Part B
By Reimann approximation, the work done is 2,130 ft.·lb
Step-by-step explanation:
Part A
The parameters of the filled bucket of water being pulled upwards are;
The mass of the bucket = 5 lb
The mass of the rope = Negligible
The mass of water that fills the bucket = 38 lb
The rate at which the bucket is pulled up = 1.5 ft./s
The rate at which the bucket leaks, l = 0.15 lb/s
The height in feet above the bottom of the well = x
Therefore, we have;
Height of the bucket, x = 1.5·t
The weight of the bucket after a given time, t, W = 38 - 0.15·t
The time it takes to pull the bucket to the top of the well, t = d/v = 50/1.5 = 100/3 s. = [tex]33.\overline3[/tex] s
We have;
[tex]W = \int\limits^{t = 33.\overline 3}_{t = 0} {F} \, dx[/tex]
x = 1.5·t, F = Weight of the bucket, W = 38 - 0.15·t
[tex]W = \int\limits^{t = 33.\overline 3}_{t = 0} {(38-0.15\cdot t)} \, \cdot 1.5\cdot dt = \int\limits^{t = 33.\overline 3}_{t = 0} {(57-0.225\cdot t)} \, dt[/tex]
[tex]W = [57\cdot t - 0.225 \cdot t^2]_0^{33.\overline 3}[/tex]
Therefore, we have;
W = (57 × [tex]33.\overline3[/tex] - (0.225/2) × [tex]33.\overline3[/tex]²) - 0 = 1,775 ft.·lb
The work done in pulling the bucket to the top of the well, W = 1,775 ft.·lb
Part B
By summing the areas of the rectangular areas on the graph, we have
W = 10 × 38 + 10 × (38 - 0.1×10) + 10 × (38 - 0.1 × 20) + 10 × (38 - 0.1 × 30) + 10 × (38 - 0.1 × 40) + 10 × (38 - 0.1 × 50) = 2,130
Therefore, by left Reimann approximation, the work done, W = 2,130 ft.·lb
(More precisely, we have;
The weight at the bottom, F₁ = 38 lb.
The weight at the top of the well, F₂ = 38 - 0.15 × 100/3 = 33
∴ F₂ = 33 lb.
The average weight, [tex]F_{average}[/tex] = (F₁ + F₂)/2 = (38 lb. + 33 lb.)/2 = 35.5 lb.
Therefore, the work done, [tex]F_{average}[/tex] × d = 35.5 lb × 50 ft. = 1,775 ft.lb
The work done, W = 1,775 ft.lb)
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
What does it mean to be “in the red?”
a.
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b.
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c.
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d.
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Answer:
b.
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Step-by-step explanation
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Answers
Answer:
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Step-by-step explanation:
Giving the following information:
Growth rate (g)= 2% = 0.02
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Number of periods (n)= 20 years
To calculate the population in 2020, we need to use the following formula:
FV= PV*(1+g)^n
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Answer:
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Step-by-step explanation:
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Answers
An axiomatic system consists of some undefined terms (primitive terms) and a list of statements, called axioms or postulates, concerning the undefined terms. One obtains a mathematical theory by proving new statements, called theorems, using only the axioms (postulates), logic system, and previous theorems.
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
2.5 half-lives
Step-by-step explanation:
Find [tex]t_{h}[/tex] in [tex]N(t)=N_{0}e^{-kt}[/tex] given [tex]N(t) = 2, N_{0} =64,t=\frac{25}{2}[/tex]
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Simplifying gives [tex]\frac{1}{2} =e^{-kt_h} or k = -\frac{In(\frac{1}{2}) }{t_{h} } .[/tex]
Plugging this into the initial equation, we obtain that [tex]N(t)=N_{0}e^\frac{In(\frac{1}{2}) }{t_{h} }[/tex]or [tex]N(t)= N_{0} (\frac{1}{2})^\frac{t}{t_h}.[/tex]
Finally, just plug in the given values and find the unknown one.
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MARK ME AS BRAINLIEST IF YOU WISHThe number of half-lives that transpired during this time period is equal to 2.5 hours.
Given the following data:
Time = 12.5 hours.
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Remaining mass = 2.0 grams.
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[tex]ln(\frac{A}{A_0} )=ln(\frac{1}{2} )\frac{t}{H}[/tex]
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Answer:solutions, search about Complex Numbers
Step-by-step explanation:−2||=−6
−
2
|
x
|
=
−
6
||=−6−2=3
|
x
|
=
−
6
−
2
=
3
The value inside the absolute value brackets could be positive or negative and give a positive result.
()=3
(
x
)
=
3
OR −()=3
−
(
x
)
=
3
=3
x
=
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OR =−3
x
=
−
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A
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с
Map Scale
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225
200
175
150
125
100
75
Actual Distance (miles)
225
200
175
150
125
100
75
50
25
50
25
0 1 2 3 4 5 6 7 8 9
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0 1 2 3 4 5 6 7 8 9
Number of Inches on Map
B
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D
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y
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200
175
8 150
125
100
75
50
25
100
75
50
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0
0
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Answers
Given:
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The Number of people work for Hank’s Fried Chicken.
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We need to divide the total bonus by the bonus of each employee to get the number of people work for Hank’s Fried Chicken.
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Answers
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Answers
Step-by-step explanation:
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Hope it helps :)❤
Answer:
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Answers
Answer:6
Step-by-step explanation:
Angle 2, angle 6, angle 4, and angle 8 have the same measure that is 78 degrees and this can be determined by using the corresponding angle property.
GIven :
In the given figure, line a parallel to line b.Angle 2 = 78 degrees.The following steps can be used in order to determine the other angles whose measure is 78 degrees:
Step 1 - The corresponding angle property is used in order to determine the other angles whose measure is 78 degrees.
Step 2 - According to the given figure, angle 2 and angle 6 are corresponding angles. Therefore, the measure of angle 6 is also 78 degrees.
Step 3 - Angle 8 is the opposite angle of angle 6 therefore, the measure of angle 8 is 78 degrees.
Step 4 - Angle 4 is the opposite angle of angle 2 therefore, the measure of angle 2 is 78 degrees.
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О 99
042°
09°
0 48°
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Answer:Other person is correct. here are the summarized answer for my unit test right triangles and trigonometry unit test
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right
2. a is right angle m b = 45
14\/2
3.quilt squares hypotenuse 18
9\/2
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292.3
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105 feet
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912
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139 feet
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191.0
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6
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27.8
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42
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35.9
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31
Won't do written part.
Step-by-step explanation: