A bucket that weighs 3 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 42 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. 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 1

Answer:

the work done in pulling the bucket to the top of the well is 2125 ft-lb

Step-by-step explanation:

Given that;

Weight of the bucket is 3 lb

weight of water which can be filled in the bucket is 42 lb

Total weight of bucket and water = 3 + 42 = 45 lb

distance, the bucket filled with water is to be pulled 50 ft

now, let at any time t be the bucket at distance x ft from the bottom of the well

then, t = x/2 × S

where S is the rate at which water is leaking from the bucket

so at this time t, the amount pf water which leaked from the bucket is;

⇒ x ft / 2.5 ft/s × 0.25 lb/s

= 0.25 lb.s⁻¹ / 2.5 ft.s⁻¹ × x ft

= 0.1 lb/ft × x ft

= 0.1x lb

now, as x represent the distance that the bucket has been raised, we the force F applied to the bucket x to be;

F = ( 45 - 0.1x ) lb

so, the required worked by Riemann sum as;

[tex]\lim_{n \to \infty}[/tex]ⁿ∑_[tex]_{i=1}[/tex] ( 45 - 0.1x[tex]_i[/tex]* ) Δx

so, the work done, pulling the bucket up will be;

[tex]\lim_{n \to \infty}[/tex]ⁿ∑_[tex]_{i=1}[/tex] ( 45 - 0.1x[tex]_i[/tex]* ) Δx  =  [tex]\int\limits^{50}_0 {(45-0.1x)} \, dx[/tex]

= [ 45x - 0.1[tex]\frac{x^2}2}[/tex] ]⁵⁰₀

= 45 × 50 - 0.1/2 × (50)²

= 2250 - 125

= 2125 ft-lb

Therefore, the work done in pulling the bucket to the top of the well is 2125 ft-lb


Related Questions

Can someone please help and thank you:)

Answers

I have no idea Sorry

If YV = 28 in, find the length of the major arc VYX. Round to the nearest tenth ( one decimal place).

Answers

Answer:

[tex]VYX=84.3in[/tex]

Step-by-step explanation:

Given

[tex]YV = 28in[/tex]

[tex]\angle WZX = 15^\circ[/tex]

See attachment

Required

Determine the length of [tex]VYX[/tex]

First, calculate the major angle VZX

[tex]\theta = \angle VZX = 360 - \angle WZX[/tex]

[tex]\theta = \angle VZX = 360 - 15[/tex]

[tex]\theta = \angle VZX = 345[/tex]

[tex]\theta = 345[/tex]

The length of arc VYX, is:

[tex]L=\frac{\theta}{360} * 2\pi r[/tex]

Where

[tex]r = \frac{1}{2} * Diameter[/tex]

[tex]r = \frac{1}{2} * YV[/tex]

[tex]r = \frac{1}{2} * 28[/tex]

[tex]r = 14[/tex]

So:

[tex]L=\frac{\theta}{360} * 2\pi r[/tex]

[tex]L=\frac{345}{360} * 2 * \frac{22}{7} *14[/tex]

[tex]L=\frac{345}{360} * 2 * 22 *2[/tex]

[tex]L=\frac{345* 2 * 22 *2}{360}[/tex]

[tex]L=\frac{30360}{360}[/tex]

[tex]L=84.3in[/tex]

Hence, the length of VYX is:

[tex]VYX=84.3in[/tex]

Solve the question f/3+22=17

Answers

Answer:

f=-15

Step-by-step explanation:

Let's solve your equation step-by-step.

f /3 +22=17

Step 1: Simplify both sides of the equation.

1 /3 f+22=17

Step 2: Subtract 22 from both sides.

1/ 3 f+22−22=17−22

1/3f=-5

Step 3: Multiply both sides by 3.

3*(1/3f)=(3)*(-5)

f=−15

Answer:

f=−15

The value of the variable f for the given expression is f=-15.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is f/3+22=17. The value of f will be calculated as:-

f /3 +22=17

Step 1: Simplify both sides of the equation.

1 /3 f+22=17

Step 2: Subtract 22 from both sides.

1/ 3 f+22−22=17−22

1/3f=-5

Step 3: Multiply both sides by 3.

3*(1/3f)=(3)*(-5)

f=−15

Hence, the value of f will be -15.

To know more about an expression follow

https://brainly.com/question/25968875

#SPJ2

Need help and answer if you know it please

Answers

the answer is b. x=14

The point D(-3, 1) is reflected over the x-axis. What are the coordinates of the resulting point, D′?

Answers

Answer:

The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.

Step-by-step explanation:

For example, when point P with coordinates (5,4) is reflecting across the X axis and mapped onto point P', the coordinates of P' are (5,-4).

Three friends drove radio controlled cars around a track. The table below shows the number of laps
completed by each person and the time it took.
Kaitlin
Keiko
Ann
Time (minutes)
9
7
5
Number of laps
54
28
25
Write the number of laps completed per minute for each person. Then determine who drove the fastest.
Number of laps completed per minute by Kaitlin:
Number of laps completed per minute by Keiko:
Number of laps completed per minute by Ann:
Select the person who drove the fastest.
Kaitlin
O keiko
Ann

Answers

kaitlyn:6
keiko: 4
ann: 5
keiko drive the fastest

The range of F(x) = 6x3^x is all positive real numbers,

Answers

True I believe possibly

2. Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of 3617 in3. One day, her sink clogged. She has to use one of two conical cups to scoop the water out of the sink. The sink is completely full when Carissa begins scooping. (a) One cup has a diameter of 2 in. and a height of 4 in. How many cups of water must Carissa scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number. *** Complete sentences

Answers

Answer:Yes, your answers are correct.

The volume of a cone is given by V = 1/3πr²h.  Since the diameter of the first cone is 4, the radius is 2; therefore the volume is

V = 1/3π(2²)(8) = 32π/3

We divide the volume of the sink, 2000π/3, by the volume of the cone:

2000π/3 ÷ 32π/3 = 2000π/3 × 3/32π = 6000π/96π = 62.5 ≈ 63.

The diameter of the second conical cup is 8, so the radius is 4.  The volume then is:

V = 1/3π(4²)(8) = 128π/3

Dividing the volume of the sink, 2000π/3, by 128π/3:

2000π/3 ÷ 128π/3 = 2000π/3 × 3/128π = 6000π/384π = 15.625 ≈ 16

Step-by-step explanation:

help me i am gonna give points to the people give me correct answer

Answers

Answer:

lol

Step-by-step explanation:

Answer:

Arjan should look for other cards that add up to $$94%

Step-by-step explanation:

I don't know it but I guess this one, let me know if it help

Joe has 16 pounds of fertilizer for his three gardens. He uses ⅜ of the fertilizer in his first garden and ¼ of the fertilizer in his second garden. What fraction of the fertilizer is left for the third garden? *

Answers

Answer:

3/8

Step-by-step explanation:

3/8 of 16 is 6

1/4 of 16 is 4

6+4 = 10

16-10 = 6

3/8 of 16 = 6

3x +2y=10 4x-y=6 using substitutional method​

Answers

Answer:

( 2 , 2 )

Step-by-step explanation:

Solve the eqaution :

3x +2y=10

4x-y=6

Solve the eqaution for y :

3x + 2y = 10

y = -6 + 4x

Substitute for y : 3x + 2 ( -6 + 4x ) = 10

x = 10

Substitute for the value of x : x = 2

Substitute the given value of x into the eqaution

y = -6 + 4x : y = -6 + 4 × 2

Solve the eqaution: y = -6 + 4 × 2

solve the eqaution for y : y = 2

y = 2 A possible solution : the ordered solution pair is

( 2 , 2 )

Tell whether c = 3 is a solution of c + 7 = 10.
a) Yes
b) No

Answers

Answer:

a) Yes

Step-by-step explanation:

Because, 3+7=10

Answer: yes

Explanation: In this problem, to determine whether c = 3

is a solution to the equation, we substitute 3 in for c.

So we have (3) + 7 = 10.

Simplifying the left side of the equation, (3) + 7 is 10.

So we have 10 = 10 which is a true statement so our answer is yes.

3.26 From a box containing 4 black balls and 2 green balls, 3 balls are drawn in succession, each ball being replaced in the box before the next draw is made. Find the probability distribution for the number of green balls.

Answers

Answer:

[tex]P(X = x) = \frac{2^{3-x}}{27}[/tex]

Step-by-step explanation:

Given

[tex]Black = 4[/tex]

[tex]Green = 2[/tex]

[tex]r = 3[/tex] --- selected balls (with replacement)

Required

Determine the probability distribution for the green balls.

Let x be a [tex]random\ variable[/tex] such that:

[tex]x = 0, 1, 2, 3[/tex]

Because it is a selection with replacement

The probability of a green ball being drawn is always:

[tex]P(G) = \frac{Green}{Total}[/tex]

[tex]P(G) = \frac{2}{6}[/tex]

[tex]P(G) = \frac{1}{3}[/tex]

The probability of a black ball being drawn is always:

[tex]P(B) = \frac{Black}{Total}[/tex]

[tex]P(B) = \frac{4}{6}[/tex]

[tex]P(B) = \frac{2}{3}[/tex]

So, the probability distribution of green is:

[tex]P(X = x) = (P(B))^{3-x} * (P(G))^x[/tex]

[tex]P(X = x) = (\frac{2}{3})^{3-x} * (\frac{1}{3})^x[/tex]

Apply law of indices

[tex]P(X = x) = \frac{2^{3-x}}{3^{3-x}} * \frac{1^x}{3^x}[/tex]

[tex]P(X = x) = \frac{2^{3-x}*1^x}{3^{3-x}*3^x}[/tex]

[tex]P(X = x) = \frac{2^{3-x}*1}{3^{3-x+x}}[/tex]

[tex]P(X = x) = \frac{2^{3-x}*1}{3^3}[/tex]

[tex]P(X = x) = \frac{2^{3-x}}{27}[/tex]

Can you guys help plsssss I’m tireddddd

Answers

Answer:

#8 - 52°, #9 - 29°

Step-by-step explanation:

8. The two angles added together are a straight line, so they sum up to 180 degrees.

x + (2x + 24°) = 3x + 24° = 180°

3x + 24° = 180°

3x = 156°

x = 52°

9. Similar to #8. "Supplementary" means they add up to 180° (whether they are actually next to each other or not).

So,     4x + (2x + 6°) = 180°

                 6x + 6° = 180°

                     6x = 174°

                        x = 29°

Hope this helps. Get some rest. Zzzzz  :)

What is the median of this set of data?

362, 187, 211, 298, 331, 250, 347, 199

Answers

Answer:

274

Step-by-step explanation:

Hey There!

So if you didnt know the median is the middle number ( in value) of the set

So first we would like to arrange the numbers in order from least to greatest

187 , 199 , 211 , 250 , 298 , 331 , 347 , 362

Then we take the middle number(s)

if there is just one then that is the answer but if there is two than we add them together and divide that by 2

In this case there are two which would be 250 and 298

So we add them together

250+298=548

Then we just divide that by 2

[tex]\frac{548}{2} =274[/tex]

Therefore the median is 274

hope this helps :)

Step-by-step explanation:

l hope this answer is helpful to you

All of the items in a bicycle shop are on sale for 30% off the regular price. Rene spends $74.90 to buy a bicycle and a
helmet (without taxes). If the regular price of the bicycle is $85, which equation can be used to find the regular price of the
helmet, h?
0.3(74.90+ h) - 85
0.3(85+) - 74.90
0.7(74.90+h) - 85
0.7(85+1) - 74.90

Answers

Answer:

0.7(85+)-74.90

Step-by-step explanation:

Answer:

D - 0.7(85+)-74.90

Step-by-step explanation:

Got 100% on the quiz! Have a good day!! :)

On three days, Ben throws darts at a target.

Here are his results.

Number of hits

Number of misses

30

10

Number of throws

Monday

40

Tuesday

30

Wednesday

50

Total

120

18

12

36

14

84

36

(1)

a) Use Tuesday's results to estimate the

probability of Ben hitting the targe.

b) Use the total of the results to estimate the

probability of Ben of hitting the target.

c) Which estimate would give the most reliable probability?

A- the one from Tuesday or B - the one from the Total?

(1)

(1)

Total marks: 3

Answers

Answer:

0.6 ;

0.7

Reaukt in B will give a better estimate because it has a larger sample size (120) than the result on A ,with sample size (30)

Step-by-step explanation:

Probability of hitting the target using Tuesday's result :

P(hitting the target):

Probability = required outcome / Total possible outcomes

Required outcome = number of hits = 18

Total possible outcomes = number of throws =. 30

Hence, Probability of hitting the target using Tuesday's result : 18 / 30 = 0.6

B.)

Probability of hitting the target using Total result:

Required outcome = number of hits = 84

Total possible outcomes = number of throws =. 120

= 84 / 120

= 0.7

20% of the middle school students decided not to go skiing. How many middle school students are there if 40 stayed in the lodge?

Write a proportion for the situation.

Solve the problem. Show your work.

Answers

Answer:

Step-by-step explanation:

s(20/100)=40

20s=4000

s=200

So there are a total of 200 students.

Answer:

There are 200 middle school students

Step-by-step explanation:

The equation for this question can be: 40 is 20% of what. This can be simplified to 40 = 0.2x and then to get x by itself you divide 40 by 0.2 which is 200.

What is 0.64 divided by 248?

Answers

Answer:

0.00258064516

Step-by-step explanation:

Answer:

0.64 divided my 248 = 0.00258064516129

the problem is set up incorrectly what you should have put is 248 divided my 0.64 the answer to that is = 387.5

Your welcome!

Step-by-step explanation:

Write in expression form:
Seven times the quotient of 8 and 5

Answers

Answer:

7 x (8 ÷ 5)

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what are the special purpose books?​

Answers

Answer:

hi Plz Subscribe Sameer Duos Channel

They give you knowledge somehow

Explain step by step how to use the horizontal method the multiple the two polynomials

Answers

Answer:

Step-by-step explanation:

Multiply each term of the first polynomial with   the second polynomial. Then combine the like terms.

(3a² + 5a - 2)* (5a² -3a + 4)

= 3a² *(5a² -3a + 4)  + 5a*(5a² -3a + 4)  - 2*(5a² -3a + 4)

=3a²*5a² - 3a*3a² + 4*3a² +  5a*5a² - 3a*5a  + 4*5a + 5a²*(-2) - 3a*(-2) + 4*(-2)

=15a⁴ - 9a³  + 12a² + 25a³ - 15a² + 20a - 10a² + 6a - 8

= 15a⁴ - 9a³ + 25a³   + 12a² - 15a² - 10a²   + 20a +6a - 8

= 15a⁴ + 16a³  - 13a² +26a  - 8

Find the missing angle according to the Triangle Sum Theorem.

Answers

Answer:

k = 140 degrees.

The missing INTERIOR angle is 40 degrees.

Step-by-step explanation:

The missing interior angle would be 40.

Triangle angle sum theorem states the 3 interior angles of a triangle sum to 180.

64+76+40 = 180

The exterior angle theorem states the exterior angle of a triangle is equal to the sum of the two remote interior angles of the triangle.

Exterior angle k = 64+76

k= 140

Can some on help me not sure thanks

Answers

Answer:

13 I think

Step-by-step explanation:

So basically all i did was double what the gate had. 5=15 3=13 I dont know if that makes lol

HELP !!!!!!!!!! PLEASEEEEEEE

Answers

Answer:

13.825, 13, -13 25/40

Answer:

13.825, 13, and -13 25/40

Step-by-step explanation:

Hope this helps :)

Estimate by rounding each mixed number to thenearest whole number 5 1/3 - 3 7/9

Answers

Answer:

1.6 or 2?

Step-by-step explanation:

5-3 =2

1/3 - 7/9 LCD

3/9 - 7/9 =-4/9

2-4/9 = 1 5/9

16/3-34/9 LCD

1 5/9 = 1.5555555555 rounded is 1.6 or 2? Not sure if decimals count.

Factor
2x3 + 6x2 - 36x

Answers

Answer:

23+62−36

2(3+32−18)

Step-by-step explanation:

Compare the areas. What is the ratio of the areas? SHOW YOUR WORK

Answers

Answer:

Ratio of the area of MIKE to TEAM = 9 : 1

Step-by-step explanation:

Ratio of similar shapes = square of the ratio of their corresponding sides

Since TEAM ~ MIKE, therefore the ratio of their areas = square of the height of MIKE : square of the height of TEAM

Ratio = 33² : 11²

Ratio = 1089 : 121

Ratio = 9 : 1

What's the value of x
(3x-5) and (x+10)

Answers

3x-5+x+10+x=180 (property of a triangle (angles add up to 180°))
5x+5=180 (simplify)
5x=175 (subtraction property of equality)
x=35 (division property of equality)

Therefore, x is equal to 35.

Dont know this question I am 2nd grade math 2 quarters = how many coins

Answers

Answer:

Well, 2 quarters are 2 coins. But, if you are asking the value of 2 quarters, then your answer will be, 50.

Step-by-step explanation:

So, 1 quarter = 25 cents. So that means that, 25 x 2 or 25 + 25 = 50. So, your answer will be 50. Hope that helps! :)

Answer:50

Step-by-step explanation:if a quarter equals 25cents and you have 2 quarters,you have to add .25+25 that equals 50 this is a simple way to do it.

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