Answer:
The total work done in pulling the bucket to the top of the well is approximately 3,139.1 ft·lb
Step-by-step explanation:
The given parameters are;
The mass of the bucket, W = 3.6 pounds
The depth of the well, h = 78 feet deep
The mass of water in the bucket = 38 ponds
The rate at which the water is pulled up = 2.9 feet per second
The rate at which water is leaking from the bucket, [tex]\dot m[/tex] = 0.1 pounds per second
We separate and find the work done for lifting the bucket and the water individually, then we add the answers to get the solution to the question as follows;
The work done in lifting bucket empty from the well bottom, [tex]W_b[/tex] = W × h
∴ [tex]W_b[/tex] = 3.6 pounds × 78 feet = 280.8 ft-lb
The work done in lifting bucket empty from the well bottom, [tex]W_b[/tex] = 280.8 ft-lb
The time it takes to lift the bucket from the well bottom to the top, 't', is given as follows;
Time, t = Distance/Velocity
The time it takes to pull the bucket from the well bottom is therefore;
t = 78 ft./(2.9 ft./s) ≈ 26.897
The time it takes to pull the bucket from the well bottom to the top, t ≈ 26.897 s
The mass of water that leaks out from the bucket before it gets to the top, m₂, is therefore;
m₂ = [tex]\dot m[/tex] × t
∴ m₂ = 0.1 lbs/s × 26.897 s = 2.6897
The mass of the water that leaks, m₂ = 2.6897 lbs
The mass of water that gets to the surface m₃ = m - m₂
∴ m₃ = 38 lbs - 2.6897 lbs ≈ 35.3103 lbs
Given that the water leaks at a constant rate the equation representing the mass of the water as it is lifted can b represented by a straight line with slope, 'm' given as follows;
The slope of the linear equation m = (38 lbs - 35.3103 lbs)/(78 ft. - 0 ft.) = 0.03448[tex]\overline 3[/tex] lbs/ft.
Therefore, the equation for the weight of the water 'w' can be expressed as follows;
w = 0.03448[tex]\overline 3[/tex]·y + c
At the top of the well, y = 0 and w = 38
∴ 35.3103 = 0..03448[tex]\overline 3[/tex] × 0 + c
c = 35.3103
∴ w = 0.03448[tex]\overline 3[/tex]·y + 35.3103
The work done in lifting the water through a small distance, dy is given as follows;
(0.03448[tex]\overline 3[/tex]·y + 38) × dy
The work done in lifting the water from the bottom to the top of the well, [tex]W_{water}[/tex], is given as follows;
[tex]W_{water} = \int\limits^{78}_0 {0.03448\overline 3 \cdot y + 35.3103 } \, dy[/tex]
[tex]\therefore W_{water} = \left [ {\dfrac{0.03448\overline 3 \cdot y^2}{2} + 35.3103 \cdot y\right ]^{78}_0[/tex]
[tex]W_{water}[/tex] = (0.034483/2 × 78^2 + 35.3103 × 78) - (0.034483 × 0 + 38 × 0) ≈ 2,859.1
The work done in lifting only the water, [tex]W_{water}[/tex] ≈ 2,859.1 ft-lb
The total work done, in pulling the bucket to the top of the well, W = [tex]W_b[/tex] + [tex]W_{water}[/tex]
∴ W = 2,859.1 ft.·lb + 280.8 ft.·lb ≈ 3,139.1 ft·lb
The total work done, in pulling the bucket to the top of the well, W ≈ 3,139.1 ft·lb.
A piece of art weighing 30 pounds is hung from two wires as shown below. Each wire is supporting half of the weight of the picture. However, since the wires extend out at an angle, they are also imparting force towards the left and right. Therefore, the force on each wire is greater than 15 pounds. Look at the diagram above with the vectors. Use trigonometry to find ||→ux||and ||→vx||.
||→ux||=____ pounds ||→vx||= ___ pounds What is the total force (in pounds) exerted on each wire?
||→u||= ____pounds ||→v||= ____pounds
Answer:
30 pounds + 15 pounds is 45 pounds is your total force
Which is the following statements CANNOT be true?
Midpoint, as the word suggests, means the point which lies in the middle of something. The correct option is C. P cannot be the midpoint.
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.
Since EN≅NG, therefore, the length of the two segments will be equal, which means P can not be the midpoint of the line segment EG.
Hence, the correct option is C. P cannot be the midpoint.
Learn more about Midpoint:
https://brainly.com/question/5127660
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The census is a survey of the population that gathers various details about individuals, such as age. This survey observed
that 155 out of every 200 people were 18 years old or older, Determine the probability of randomly selecting a person that
was 18 years old or older,
Express your answer as a fraction,
Answer:
31/40
Step-by-step explanation:
Just simplify the fraction
Answer:
31/40
Step-by-step explanation:
Simplify
please help me fast please
leo has 1 1/3 cups of sugar. He uses 3/4 cups of sugar in a recipe. How much sugar does leo have left
how do I show my work?
Answer:
The answer is B 7/12
I attached a picture for your work.
how many distinct prime divisors does 132660 have
please help!!!1
Answer:
6?
Step-by-step explanation:
solve for x will give brainlest to anyone
2x=99
x=99/2
x=49.5
I hope you like my answer.
Convert 16/100 to decimal.
Answer: 0.16
Step-by-step explanation:
i dont know
A child tosses a baseball up into the air. On its way down, it gets caught in a tree for several seconds before falling back down to the ground.
Answer:
what is the question because I don't understand what you mean
Solve the following
NO BOTS!
Answer:
75/-3 = -25
Step-by-step explanation:
Numerator: -5^2 + 10^2 = 75
-5^2 = -25, since the minus sign is not in parentheses with the 5, it does not get squared so the negative is added on to five squared which is 25.
10^2 = 100,
-25 + 100 = 75
Denominator: (2 x (-5) x 3) + 3^3 = -3
2 x (-5) x 3 = -30, we can simply multiply these all together so 2 x -5 is -10, and -10 x 3 = -30
3^3 = 27, 3^3 = 3 x 3 x 3, which multiplied all together, 3 x 3 = 9, 9 x 3 = 27
-30 + 27 = -3
Total Fraction = 75/-3
Simplified = -25
Put the known terms together on one o
equation.
Example: 3x + 6 = 30
3x = 30 - 6
1. 2b10 =12
2.8 + 5x = 41
3 6 - 42 = 12.
4. 3n = 60 +n
5. 7a+ 5 = 54
ale
ACTIVITY 2:
Solve and check. Show your complete solutions.
1. x+ 5 = 2
2 X – 10 = 22
3. 41 + 3x = -29-18
4. x-27 = 8 + 10
5. 5x + (-55) = 20
ACTIVITY 3:
Solve each problem. Show your solution.
1. What is the number if twice a number is increased by 9
2. If twelve less than a thrice a number is 3, what is the n
(Hypothetical.) Suppose a certain person's reaction time, in seconds, for pressing a button on a visual cue has the following cumulative distribution function: F (x )equals 1 minus fraction numerator 1 over denominator (x plus 1 )cubed end fraction space x greater than 0 What is the probability the person's reaction time will be between 0.9 and 1.1 seconds
Answer:
the probability the person's reaction time will be between 0.9 and 1.1 seconds is 0.0378
Step-by-step explanation:
Given the data in the question;
the cumulative distribution function F(x) = [tex]1 - \frac{1}{(x + 1)^3}[/tex] ; [tex]x > \theta[/tex]
probability the person's reaction time will be between 0.9 and 1.1 seconds
P( 0.9 < x < 1.1 ) = P( x ≤ 1.1 ) - P( x ≤ 0.9 )
P( 0.9 < x < 1.1 ) = F(1.1) - F(0.9)
= [ [tex]1 - \frac{1}{(x + 1)^3}[/tex] ] - [[tex]1 - \frac{1}{(x + 1)^3}[/tex] ]
we substitute
= [ [tex]1 - \frac{1}{(1.1 + 1)^3}[/tex] ] - [[tex]1 - \frac{1}{(0.9 + 1)^3}[/tex] ]
= [ [tex]1 - \frac{1}{(2.1)^3}[/tex] ] - [[tex]1 - \frac{1}{(1.9)^3}[/tex] ]
= [ [tex]1 - \frac{1}{(9.261)}[/tex] ] - [[tex]1 - \frac{1}{(6.859)}[/tex] ]
= [ 1 - 0.1079796998 ] - [ 1 - 0.1457938 ]
= 0.8920203 - 0.8542062
= 0.0378
Therefore, the probability the person's reaction time will be between 0.9 and 1.1 seconds is 0.0378
Can someone help me? I’ll reward points + brainalist (btw In need help with 8, & 9)
Answer:
8. X=108.
9. X= 14.
Step-by-step explanation:
Hope it was helpful ;)
Help me with this problem please
Answer:
[tex](a)\ A_1 = s^2[/tex]
[tex](b)\ A_2 = 4s^2[/tex]
(c) 4 small squares
Step-by-step explanation:
Given
Small Square:
[tex]Dimension: s[/tex]
Large Square:
[tex]Dimension: 2s[/tex] i.e. twice as long as the small square
Solving (a): The area of the small square.
This is calculated as
[tex]Area = Length^2[/tex]
So, we have:
[tex]A_1 = s^2[/tex]
Solving (b): The area of the large square.
This is calculated as
[tex]Area = Length^2[/tex]
So, we have:
[tex]A_2 = (2s)^2[/tex]
[tex]A_2 = 4s^2[/tex]
Solving (c): Number of small square to cover the large square
To do this, we simply divide their areas.
Let n represents the required number; n is calculated as:
[tex]n = \frac{A_2}{A_1}[/tex]
[tex]n = \frac{4s^2}{s^2}[/tex]
[tex]n = 4[/tex]
Hence, 4 small squares is required to cover the large square
The overall distance traveled by a golf ball is tested by hitting the ball with Iron Byron, a mechanical golfer with a swing that is said to emulate the distance hit by the legendary champion, Byron Nelson. Ten randomly selected balls of two different brands are tested and the overall distances were measured. If the data of these two random samples were provided, what type of hypothesis test would be most appropriate to determine if both balls have the same mean overall distance?Group of answer choices
Answer:
The tabulated value is less than the calculated value, therefore we accept the null hypothesis and It show that there is a difference in the mean overall distance of brands.
Step-by-step explanation:
What is the distance between the points (-4 , -12) and (-4 , 20) in the coordinate plane?
Answer:
26 units i think
Step-by-step explanation:
Answer:
32 units
Step-by-step explanation:
from -12 to 0 it is 12 units, and from 0 to 20 it is 20 units.
12 + 20 = 32 units
Please help before 7 min
Answer:
The Value of x = 23.1 unit
Step-by-step explanation:
Given:
Parallel line intersect
Find:
The value of "X"
Computation:
We know that given lines are parallels
So, by using Ratio theorem we can find the value of "x"
Ratio theorem of parallel lines say
AB / BC = AD / DE
So,
14 / 20 = x / 33
x = [14 x 33] / 20
The Value of x = 23.1 unit
A pool can be filled by one pipe in 6 hours and by a second in 12 hours . How long will it take using both pipes to fill the pool?
Answer:
4 hours
Step-by-step explanation:
Part of the pool filled by first pipe in an hour = 1/6
Part of the pool filled by second pipe in an hour = 1/12
Part of the pool filled by first pipe and second pipe in an hour = 1/6 +1/12
[tex]=\frac{1*2}{6*2}+\frac{1}{12}\\= \frac{2}{12}+\frac{1}{12}\\\\=\frac{3}{12}\\\\=\frac{1}{4}[/tex]
Time taken by both the pipes to fill the pool = 4 hours
help pls what is 10,000 - 9,745 =
Answer:
10,000 - 9,745 = 255
Step-by-step explanation:
UwU Hope that helps
Answer: 255
→Hope this helps!←
a car is moving 70 miles per hour. how far does it travel in 16 seconds
Answer is what in miles
PLEASE HELP ME!!!!
Answer:
0.311 miles
Step-by-step explanation:
Convert 16 seconds to hours :
16 /60×60
= 16÷3600
= .004444hrs
Distance = Speed × time
= 70 × 0.00444444
= 0.311 miles
Find the area of the shape below.
Answer:
The is 5000 centimeters^2??
There are 120 children at a school assembly. 15 are 3rd graders; 45 are 4th graders; and 60 are 5th graders. Each student has entered their name in a drawing for a prize.
What is the probability that the winner will be a 3rd grade student?
Answer:
1/8 for a third grader to win
Step-by-step explanation:
15/120=1/8
Which equation has a constant of proportionality equal to
There are many equations that has a constant of
proportionality, might want to make it more specific.
Answer:
i can answer this if you tell me whay the constant of proportionality is. or you can add a attachment
Step-by-step explanation:
Find the values of X and why. Dragon drop the answers into the box is below.
Answer:
1 3/4 1
Step-by-step explanation:
Dave is splitting 3 quarts of ice cream with 9 members of the team. If the ice cream is split evenly, how many cups will each person get?
Answer:
Its will be 27 if we are multiplying
Step-by-step explanation:
But I don't think so but if u look up 3 quarts to 9 it will be 4.75 so yea HOPE THIS HELPS!
The measure of angle ABC is 84, find the measure of angle ADC.
Answer:
Step-by-step explanation:
uhhh i think so its 84 is abc but adc is missing try 48 i dont know but i try
Geometry Question! WORTH 20 POINTS
Answer:
x = 65
Explanation:
A whole circle equals 360*
half of that is 180*
180 - 115 = 65
How many more sides does a quadrilateral have than a triangle?
Answer:
1
Step-by-step explanation:
Quadrilateral=4sides
Triangle=3sides
Difference=4-3=1
Tivo families planned to go to the zoo. The entry ticket for one adult was $7.31 and
the entry ticket for one child was $5.66. There were two adults in the group. The
families intend to spend no more than $46.00. What is the greatest number of child
tickets that can be purchased?
Answer:
5 children
Step-by-step explanation:
Solve
$7.31 x2 = $14.62
$46 - 14.62 =$32
5.66 divided by 5 = 28.3
5.66 divided by 6 = 33
$33 is bigger than $31
Therefore, the greatest number of children tickets can be purchased is only 5.
How many points of intersection do the graphs of these two equations have [2x+3y=7 4x+6y=14
Answer:
infinitely many they are the same line
Step-by-step explanation:
Determine whether the given value makes a true statement.
NO LINKS-DRIVES-DOCS ETC.
WILL MARK BRAINLYEST
EARN LOTS OF POINTS
Answer:
Yes it is true
Step-by-step explanation:
cause 11 + 8 = 19
now give me the brainliest lol
