A tank in the shape of a hemisphere with a radius r = 13 ft is full of water to a depth of 11 ft. Set up the integral that would find the work W required to pump the water out of the spout. Use the location of the origin and the direction of the positive axis as specified in the different parts. hemisphere
Note: Use 62.5 lb/ft^3 as the weight of water.
a. The origin is at the top of the tank with positive y variables going down.
b. The origin is at the bottom of the tank with positive y-values going up.
Answers
Answer:
(a). The integral is \(W=62.5\pi\int_{0}^{11}(169-y^2)ydy\)
(b). The integral is \(W=62.5\pi\int_{0}^{11}{48+22y-y^2(11-y)}dy\)
Step-by-step explanation:
Given that,
Radius = 13 ft
Depth = 11 ft
Weight of water = 62.5 lb/ft³
(a). The origin is at the top of the tank with positive y variables going down.
We need to calculate the volume of the strip
Using formula of volume
\(dV=\pi r^2dy\)
Put the value into the formula
\(dV=\pi(\sqrt{13^2-y^2})^2dy\)
\(dV=\pi({169-y^2})dy\)
We need to calculate the mass of the strip
Using formula of mass
\(W=\rho dVgy\)
Put the value into the formula
\(W=\pi({169-y^2})dy\times62.5\ y\)
We need to calculate the work done to pump the water out of the spout
Using formula of work done
\(W= \int_{0}^{11}(\pi({169-y^2})dy\times62.5\ y)\)
\(W=62.5\pi\int_{0}^{11}(169-y^2)ydy\)
(b). The origin is at the bottom of the tank with positive y-values going up
We need to calculate the volume of the strip
Using formula of volume
\(dV=\pi r^2dy\)
Put the value into the formula
\(dV=\pi(\sqrt{13^2-(11-y)^2})^2dy\)
\(dV=\pi(169-(121-22y+y^2))dy\)
\(dV=\pi(169-121+22y-y^2)dy\)
\(dV=\pi(48+22y-y^2)dy\)
We need to calculate the mass of the strip
Using formula of mass
\(W=\rho Vg\)
Put the value into the formula
\(W=dV\rho g(11-y)\)
\(W=\pi(48+22y-y^2)dy\rho g(11-y)\)
\(W=62.5\pi(48+22y-y^2)(11-y)dy\)
We need to calculate the work done to pump the water out of the spout
Using formula of work done
\(W=\int_{0}^{11}{62.5\pi(48+22y-y^2)(11-y)dy}\)
\(W=62.5\pi\int_{0}^{11}{48+22y-y^2(11-y)}dy\)
Hence, (a). The integral is \(W=62.5\pi\int_{0}^{11}(169-y^2)ydy\)
(b). The integral is \(W=62.5\pi\int_{0}^{11}{48+22y-y^2(11-y)}dy\)
Related Questions
An airplane descends 2.3 miles to an elevation of 7.05 miles. Find the elevation of the plane before its
descent.
Answers
Answer:
Hope it help
Step-by-step explanation:
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What is the value of x for the triangle shown to the right?
Answers
Answer:
x = 6.24
Step-by-step explanation:
x =
Tan32° = OPP/ADJ
Tan32° = x/10
0.624 = x/10
cross-multiply
x = 6.24
A local school has was evaluated the the Education Department and received the
following scores. Given the weights, what should be the school's overall grade for this
evaluation? Round to a whole number.
Graduation Rates
Grade:82
Weight: 50%
Passing Rates
Grade: 75
Weight: 30%
Enrollment
Numbers
Grade: 60
Weight: 10%
Career readiness
Grade: 95
Weight: 10%
Answers
Answer: 79
Step-by-step explanation:
Given the following :
Graduation Rates:
Grade:82
Weight: 50%
Passing Rates:
Grade: 75
Weight: 30%
Enrollment Numbers:
Grade: 60
Weight: 10%
Career readiness:
Grade: 95
Weight: 10%
Overall score : Σ(grade × weight)
(82 × 50%) + (75 × 30%) + (60 × 10%) + (95 × 10%)
= (41 + 22.5 + 6 + 9.5)
= 79
Hence, overall score is 79
Which of the following correctly defines a population parameter?
A. a characteristic of the population
B. the difference between the maximum and minimum value of a sample
C. the difference between the maximum and minimum value of the population
D. a characteristic of a sample
Answers
The correct answer is A. a characteristic of the population.
A population parameter refers to a specific characteristic
A population parameter refers to a specific characteristic or numerical value that describes the entire population being studied. It is a fixed value that is typically unknown and estimated using sample data. Examples of population parameters include the population mean, population standard deviation, population proportion, etc.
Help Asap I will give brainliest
Answers
Answer:
I didn't want to type it, but it is on the image.
Step-by-step explanation:
Solve for x 15+5x=20x
Answers
Answer:
Step-by-step explanation:
15+5x=20x
-5x -5x => Subtract 5x from each side
You get
15 = 15x
Divide both sides by 15
1=x
how many ft is equal to 1.66m
Answers
Answer:
5.44 meters
Step-by-step explanation:
We Know
0.3048 meter = 1 ft
How many ft makes a height of 1.66m?
We Take
1.66 ÷ 0.3048 ≈ 5.44 meters
So, the answer is 5.44 meters.
solve for x!!!!!!!!!!!!!!!!
Answers
Answer:
cross multiplication\(6(3x + 1) = 5(2x - 2) \\ 18x + 6 = 10x - 10 \\ 18x - 10x = - 10 - 6 \\ 8x = - 16 \\ x = \frac{ - 16}{8} \\ x = - 2\)
hope it helps you<3Given equation is {(3x+1)/5} = {(2x-2)/6}
On applying cross multiplication then
⇛6(3x+1) = 5(2x-2)
Multiply the numbers outside the bracket with numbers in bracket.
⇛18x + 6 = 10x - 10
Shift the variable value on LHS and the constant value on RHS.
⇛18x - 10x = -6-10
Subtract the values on LHS and RHS.
⇛8x = -16
Shift the value 8 from LHS to RHS.
⇛x = -16÷8 = -16/8
⇛x = -2
Therefore, x = -2
Answer: Hence, the value of x for the given problem is -2
Please let me know if you have any other questions.
A book Probably cost $21.50 today it was on sale for $15.05 percent discount was offered during the sale
Answers
A can has 50 marbles in it.every hour, 7 marbles are taken out.after 4 hours,how many marbles are left in the can.
Answers
Answer:
22 marbles
Step-by-step explanation:
you do 7 times 4 and subtract the awnser from 50
What is the value of y?
Answers
Answer:
A
Step-by-step explanation:
Remember that the sum of the interior angles of a triangle is always 180 degrees. We are given that two of the interior angles of the triangle are y and the exterior angle that is connected to the missing interior angle is 130 degrees. We can see from the image that the given exterior angle and the missing interior angle are supplementary, or they add up to 180. Knowing this, we can find the missing interior angle:
130 + a = 180
a = 50
So we now know that the missing interior angle is 50 degrees. Since the sum of the interior angles for a triangle is 180 degrees, we can make the equation:
50 + y + y = 180
and solve for y.
50 + y + y = 108
50 + 2y = 180
2y = 130
y = 65
So now we know that y = 65.
I hope you find my answer and explanation to be helpful. Happy studying. :)
3
Select the correct answer.
Cora, her sister, and four friends are going to share a bag of candy equally. There are 120 candies in the bag. How many candles will each person
get?
OA 20
OB. 24
OC. 30
Reset
Next
21 Edmentum. All rights reserved.
Answers
Cora, her sister, and four friends. So there are 6 people, 120 candies are divided equally in the bag, so each person gets 20 candies
Each person will get 20 candles.
What is division?The division is one of the four basic mathematical operations, the other three being addition, subtraction, and multiplication.
Now it is given that,
Number of candles in the bag = 120
Cora, her sister, and four friends are going to share.
So, Number of person = 6
Thus, candles each person gets = Number of candles in the bag / Number of person
⇒ candles each person gets = 120 / 6
⇒ candles each person gets = 20
Thus, each person will get 20 candles.
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Part of the proceeds from a garage sale was $340 worth of $5 and $20 bills. If there were 3 more $5 bills than $20 bills, find the number of each denomination.
Answers
There are 13 $20 bills and 16 $5 bills 6 in the collection.
System of linear equations:A system of linear equations is a set of two or more linear equations involving the same variables. The solution to a system of linear equations is the values of the variables that satisfy all the equations in the system.
To solve the following problem use variables and form linear equations according to the given conditions in the problem. Solve the equation for the values of variables.
Here we have
Part of the proceeds from a garage sale was $340 worth of $5 and $20 bills. There were 3 more $5 bills than $20 bills
Let's use variables to represent the number of $5 and $20 bills.
Let x be the number of $20 bills, then the number of $5 bills is x + 3.
The total value of the $20 bills is 20x,
The total value of the $5 bills is 5(x + 3) = 5x + 15.
According to the problem,
The total value of the bills is $340, so we can set up the equation:
20x + 5x + 15 = 340
Simplifying and solving for x, we get:
25x = 325
x = 13
Therefore,
There are 13 $20 bills and 16 $5 bills 6 in the collection.
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there are 25 student in a class. five of then scored A and 10 of them score B while the other scored C for Biostatistics. if a student is selected at random, calculate the probability that the selected student scored A or B in biostastics.
Answers
There is a 60% probability that a randomly selected student from the class scored either an A or B in Biostatistics.
To calculate the probability that a randomly selected student scored either an A or B in Biostatistics, we need to consider the number of students who scored A and B and divide it by the total number of students in the class.
Given that there are 25 students in the class, 5 of them scored an A and 10 scored a B. To calculate the probability, we add the number of students who scored A (5) to the number of students who scored B (10):
Number of students who scored A or B = Number of students who scored A + Number of students who scored B = 5 + 10 = 15.
Therefore, the probability that a randomly selected student scored A or B
in Biostatistics is:
Probability = Number of students who scored A or B / Total number of students = 15 / 25 = 0.6 or 60%.
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lighting, inc. uses direct labor hours as a basis for allocating overhead. next year's estimated total overhead is $180000 and direct labor hours are predicted to be $30000 hours. the average labor cost is $10 per. what is the predetermined overhead rate
Answers
Answer:
The predetermined overhead rate is calculated as follows:
Predetermined overhead rate = Estimated total overhead / Estimated total direct labor hours
In this case, the estimated total overhead is $180,000, and the estimated total direct labor hours are 30,000. Therefore:
Predetermined overhead rate = $180,000 / 30,000 hours
Predetermined overhead rate = $6 per direct labor hour
So, the predetermined overhead rate is $6 per direct labor hour.
Share #720 among A, B and C in the ratio 2:3
Answers
Answer:
A will receive 288, B will receive 432, and C will receive 144.
Step-by-step explanation:
The total ratio of the parts is 2+3=5. This means that the whole amount represents 5 parts.
To find the size of one part, we can divide the total amount by the total number of parts:
One part = 720/5 = 144
Now that we know the size of one part, we can use the ratio to find the amounts that A, B, and C will receive:
A will receive 2 parts: 2 × 144 = 288
B will receive 3 parts: 3 × 144 = 432
C will receive 1 part: 1 × 144 = 144
Therefore, A will receive 288, B will receive 432, and C will receive 144.
Find the exact surface area of a sphere with a diameter of 13cm
Answers
Answer:
A = 530.929158457
Answer:
Area = 706.8583471
Explanation:
The used law to measure the surface area of the sphere is
\(area \: = 4\pi \: {r}^{2} \)
Where (r) is the radius. The radius is half the diameter, so it will be half 13 which is equal to 7.5. By using this law:
\(4\pi \: {7.5}^{2} = 706.8583471\)
If you like my explanation please give me 5 stars.what is the property of 3x(5x7)=(3x5)7
Answers
The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.
In the equation you provided: 3x(5x7) = (3x5)7
The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.
You deposit $300 in an account that earns simple interest at an annual rate of 6.5%.
If no other deposits or withdrawals were made, what is the total amount of money in the account at the end of 8 years?
Answers
Total amount of money in the account will be $456.
How much money will be in the account after 8 years?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest.
The formula for simple interest is: Simple Interest = Principal × Rate × Time
Principal (P) is $300
Rate (R) is 6.5%
Time (T) is 8 years.
Simple Interest = $300 × 0.065 × 8
Simple Interest = $156
Total Amount = Principal + Simple Interest
Total Amount = $300 + $156
Total Amount = $456.
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if you earn 1425 dollars by working 5 days a week and get a bonus of 200 how much money do i earn a day
Answers
Answer:
You will earn $285 a day but with the bonus you will earn $485.
Step-by-step explanation:
Do you need an explanation?
1) Kelly has 15 blue bracelets and 12 green bracelets. What is the ratio of Kelly’s blue bracelets to green bracelets?
2) Over the winter it snowed 36 days out of 40 days. What is the snow days to days ratio in simple form?
3) The ratio of girls to boys who participated in the quiz bowl was 7:5. There were 42 girls in the competition. How many boys participated?
Answers
1)The ratio of Kelly’s blue bracelets to green bracelets is 5:4.
2)The snow days to days ratio is 20:1
3)There are 42 girls in the competition. The ratio of girls to boys who participated in the quiz bowl was 7 : 5. Solving the two ratios, Therefore, There are 30 boys in the competition.
Define ratio?A ratio is a ratio that compares two quantities.A proportion is the difference between two ratios. To write a ratio, do the following: Determine whether the ratio is a part-to-part or a part-to-whole ratio. If necessary, compute the parts and total.The ratio is defined as the division of two numbers or quantities. The ratio is a relationship between the quantities of two or more objects that indicates how much of one is contained in the other. The ratio formula can be used to convert a ratio into a fraction. a:b = a/b is the ratio formula for any two quantities, say a and b.To learn more about ratio refer to:
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1)The ratio of Kelly’s blue bracelets to green bracelets is 5:4.
2)The snow days to days ratio is 20:1
3)There are 42 girls in the competition. The ratio of girls to boys who participated in the quiz bowl was 7 : 5. Solving the two ratios, Therefore, There are 30 boys in the competition.
Define ratio?
A ratio is a ratio that compares two quantities.A proportion is the difference between two ratios.To write a ratio, do the following: Determine whether the ratio is a part-to-part or a part-to-whole ratio. If necessary, compute the parts and total.The ratio is defined as the division of two numbers or quantities.The ratio is a relationship between the quantities of two or more objects that indicates how much of one is contained in the other.The ratio formula can be used to convert a ratio into a fraction. a:b = a/b is the ratio formula for any two quantities, say a and b.To learn more about ratio refers to:
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If the surface area of the cube is 70 cm^2 what is the approximate length of one side of the cube
Answers
Answer:
3.41565
Step-by-step explanation:
What is 4h when h=25?
Answers
Answer:
100
Step-by-step explanation:
When h has the value 25, the expression 4h has the value 4(25), or 100.
Answer:
100
Step-by-step explanation:
4(25)=100
Which value is closest to (2.4×103)+(5.7×102)?
2.97×102
2.97×103
8.1×105
8.1×106
Answers
Answer:
C
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
A college basketball player makes 80% of his freethrows. Over the course of the season he will attempt 100 freethrows. Assuming free throw attempts are independent, the probability that the number of free throws he makes exceeds 80 is approximately:____________.
A) 0.2000
B) 0.2266
C) 0.5000
D) 0.7734
Answers
Answer:
The probability that the number of free throws he makes exceeds 80 is approximately 0.50
Step-by-step explanation:
According to the given data we have the following:
P(Make a Throw) = 0.80%
n=100
Binomial distribution:
mean: np = 0.80*100= 80
hence, standard deviation=√np(1-p)=√80*0.20=4
Therefore, to calculate the probability that the number of free throws he makes exceeds 80 we would have to make the following calculation:
P(X>80)= 1- P(X<80)
You could calculate this value via a normal distributionapproximation:
P(Z<(80-80)/4)=1-P(Z<0)=1-50=0.50
The probability that the number of free throws he makes exceeds 80 is approximately 0.50
The probability that the number of free throws he makes exceeds 80 is approximately 0.5000.
Given that,
A college basketball player makes 80% of his free throws.
Over the course of the season, he will attempt 100 free throws.
Assuming free throw attempts are independent.
We have to determine,
The probability that the number of free throws he makes exceeds 80 is.
According to the question,
P(Make a Throw) = 80% = 0.80
number of free throws n = 100
Binomial distribution:
Mean: \(n \times p = 0.80 \times 100 = 80\)
Then, The standard deviation is determined by using the formula;
\(= \sqrt{np(1-p)} \\\\=\sqrt{80\times (1-0.80)}\\\\= \sqrt{80 \times 0.20 } \\\\= \sqrt{16} \\\\= 4\)
Therefore,
To calculate the probability that the number of free throws he makes exceeds 80 we would have to make the following calculation:
\(P(X>80)= 1- P(X<80)\)
To calculate this value via a normal distribution approximation:
\(P(Z<\dfrac{80-80}{4})=1-P(Z<0)=1-0.50=0.5000\)
Hence, The probability that the number of free throws he makes exceeds 80 is approximately 0.5000.
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Find the Area of the shaded region. Round your answer to the nearest tenth.
Answers
Answer:
610 m^2
Step-by-step explanation:
Area of the shaded region = area of the outer rectangle - area of the inner rectangle
Area of the outer rectangle
l = 42
b = 25
a = l*b = 42*25 = 1050m^2
Area of the inner rectangle
l = 22
b = 20
a = l*b = 22*20 = 440m^2
Therefore, the area of the shaded region is = 1050 - 440
= 610m^2
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A weighted coin has a 0.599 probability of landing on heads. What is the probability that it takes 5 flips for the first head to occur?
Answers
Answer:
0.411^5 times 0.599
Step-by-step explanation:
0.599 chance of landing on heads.
0.411 chance of not landing on heads.
0.411 times 0.411 times 0.411 times 0.411 times 0.411 (for the 5 flips that do not land on heads) times 0.599 (for the time that it does land on heads).
Question 4 of 10
Evaluate: 2-4 =
A. -8
B.
1
16
C. -16
D.
-ico
Answers
A park has a triangular sandbox. Todd wants to create a smaller sandbox at his backyard having the same angles as the park sandbox.
What is the perimeter in feet of Todd’s sandbox?
Answers
What type of correlation exists? Is the model linear or non-linear?
The graph shows a negative correlation, and it is a linear model.
O The graph shows a positive correlation, and it is a linear model.
The graph shows a negative correlation, and it is a non-linear model.
The graph shows a positive correlation, and it is a non-linear model.
Answers
Answer:
The graph shows a positive correlation, and it is a linear model.
Hope this helps! :]
The given graph shows a positive correlation, and it is a linear model. The correct answer would be an option (B).
What is the Scatter plot?The variables in the scatter plot made from the data are described by the independent variable, time, which is graphed along the horizontal axis. The independent variable will be time, and the dependent variable will be the number of calories provided.
As per the given scatter plot,
The slope of the line is positive (small values of length correspond to small values of width; large values of length correspond to large values of width), so there is a positive co-relation (that is, a positive correlation) between length and width.
Thus, the given graph shows a positive correlation, and it is a linear model.
Hence, the correct answer would be option (B).
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