Answers
Answer:
1.314 MJ
Step-by-step explanation:
As water is removed from the tank, decreasing amounts are raised increasing distances. The total work done is the integral of the work done to raise an incremental volume to the required height.
There are a couple of ways this can be figured. The "easy way" involves prior knowledge of the location of the center of mass of a cone. Effectively, the work required is that necessary to raise the mass from the height of its center to the height of the discharge pipe.
The "hard way" is to write an expression for the work done to raise an incremental volume, then integrate that over the entire volume. Perhaps this is the method expected in a Calculus class.
Mass of waterThe mass of the water being raised is the product of the volume of the cone and the density of water.
The cone volume is ...
V = 1/3πr²h . . . . . . for radius 2 m and height 8 m
V = 1/3π(2 m)²(8 m) = 32π/3 m³
The mass of water in the cone is then ...
M = density × volume
M = (1000 kg/m³)(32π/3 m³) ≈ 3.3510×10^4 kg
Center of massThe center of mass of a cone is 1/4 of the distance from the base to the point. In this cone, it is (1/4)(8 m) = 2 m from the base.
Easy WayThe discharge pipe is 2 m above the base of the cone, so is 4 m above the center of mass. The work required to lift the mass from its center to a height of 4 m above its center is ...
W = Fd = (9.8 m/s²)(3.3510×10^4 kg)(4 m) = 1.3136×10^6 J
Hard Way
As the water level in the conical tank decreases, the remaining volume occupies a space that is similar to the entire cone. The scale factor is the ratio of water depth to the height of the tank: (y/8). The remaining volume is the total volume multiplied by the cube of the scale factor.
V(y) = (32π/3)(y/8)³
The differential volume at height y is the derivative of this:
dV = π/16y²
The work done to raise this volume of water to a height of 10 m is ...
(9.8 m/s²)(1000 kg/m³)(dV)((10 -y) m) = 612.5π(y²)(10 -y) J
The total work done is the integral over all heights:
[tex]\displaystyle W=612.5\pi\int_0^8{(10y^2-y^3)}\,dy=\left.612.5\pi y^3\left(\dfrac{10}{3}-\dfrac{y}{4}\right)\right|_0^8\\\\W=612.5\pi\dfrac{2048}{3}\approx\boxed{1.3136\times10^6\quad\text{joules}}[/tex]
It takes about 1.31 MJ of work to empty the tank.
Related Questions
Last week a painter painted 6 houses in 2 days. this week she painted 5 houses in 4 days. in which week was the painter more productive?
Answers
Answer:
The painter was more productive in week a.
Step-by-step explanation:
Find the unit rate. How many houses could be painted in 1 day?
6/2 means that she could paint 3 houses per day
5/4 means that she could paint 1.25 houses per day.
The painter was more productive in the last week.
Explanation:In this problem, we need to find in which week did the painter paint the most.
To find the solution to this problem, first, we need to divide 6 by 2 (last week)
which equals 3.
Next, divide 5 by 4 (this week)
which equals 1.25
Now, compare the two quotients and identify the larger number (3 and 1.25).
Basically, we can see that the number 3 is larger.
This means that the painter could paint 3 houses per day in the last week, and 1.25 houses per day in this week.
Therefore, we can say that the painter was more productive in the last week.
I hope this helps :)
What type of construction is illustrated in the figure?
A
The bisection of ∠D
B
A line segment congruent to segment AB
C
An angle congruent to ∠D
D
The bisection of segment BD
Answers
Option A is correct. The type of construction that we have here is the bisection of the <D.
What is the bisection of an angle?The bisection of angle can be defined to be the construction of a ray that would help to divide a particular angle into two equal halves.
In this diagram we can see that the angle here is at D. Hence the construction is aimed at dividing this particular angle into 2. Therefore the answer to the question is The bisection of ∠D.
The bisector does the job of creating an equal measure. The given bisector is known to have the midpoint of the segment. It cuts through this angle and creates two different angles that are of the same size.
If we draw the line in that shape, we will be having the division of that angle. From the explanation here, we can see the answer is the first option
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Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary Minimum: Lower quartile: Median: Upper quartile: Maximum: Interquartile range:
Answers
The five number summary can be calculated as follows:
lower quartile(Q₁) = 54 + 56 / 2 = 55
Median = 63.5
Upper quartile(Q₃) = 74
Maximum = 80
Interquartile range = Q₃ - Q₁ = 74 - 55 = 19
How to find the five number summary ?The five number summary can be found as follows;
48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80
minimum = 48
lower quartile(Q₁) = 54 + 56 / 2 = 55
The median is the middle number when the data is arranged in ascending or descending order.
Median = 63 + 64 / 2 = 127 / 2 = 63.5
Upper quartile(Q₃)= 74 + 74 / 2 = 148 / 2 = 74
Maximum = 80
Interquartile range = Q₃ - Q₁ = 74 - 55 = 19
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Can someone help me with this? I cannot figure it out
Answers
Answer:
Step-by-step explanation:
To graph by hand I would first convert both equations into y=mx+b.
We start with:
[tex]\left \{ {{2x-2y=4} \atop {x+2y=8}} \right.[/tex]
Solve for y for 2x-2y=4
[tex]2x+2y=4\\2y=4-2x\\y=2-x[/tex]
Solve for y for x+2y=8
[tex]x+2y=8\\2y=8-x\\y=4-\frac{x}{2}[/tex]
Giving the new but equal system of equations:
[tex]\left \{ {{y=2x-x} \atop {y=4-\frac{x}{2} }} \right.[/tex]
From this point on you can graph the two functions to find where the two lines intersect, thats your solution.
I've gone ahead and graphed it on desmos for you
When comparing the f(x) = –x2 + 2x and g(x) = log(2x + 1), on which interval are both functions positive?
(–∞, 0)
(0, 2)
(2, ∞)
(∞, ∞)
Answers
Considering their graphs, the interval in which both functions are positive is:
(0, 2)
When are the functions positive?A function is positive when it's graph is positioned above the x-axis.
Looking at the graph, the functions are positive for x between 0 and 2, hence the interval in which both functions are positive is stated as follows:
(0, 2)
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Please help me solve!
Answers
Answer:
Step-by-step explanation:
Comment
There are a number of ways of doing this problem. I don't know which method you are intended to use. One sure way in this case is graphing the equation, I have done this for you. See below. The maximum volume occurs where x = 2
The graph shows that there is a peak at x = 2. That is where the maximum volume is,
Answer
x = 2
A substance decays so that the amount a of the substance left after t years is given by: a = a0 • (0.7)t, where a0 is the original amount of the substance. what is the half-life (the amount of time that it takes to decay to half the original amount) of this substance, rounded to the nearest tenth of a year?
Answers
The half-life of the substance is 1.94 years.
What is exponential decay formula?The exponential decay formula aids in determining the exponential drop, which is a rapid reduction over time. To calculate population decay, half-life, radioactivity decay, and other phenomena, one uses the exponential decay formula. F(x) = a [tex](1-r)^{x}[/tex] is the general form.
Here
a = the initial amount of substance
1-r is the decay rate
x = time span
The correct form of the equation is given as:
[tex]a=a_{0}[/tex]×[tex](0.7)^{t}[/tex]
where t is an exponent of 0.7 since this is an exponential decay of 1st order reaction
Now to solve for the half life, this is the time t in which the amount left is half of the original amount, therefore that is when:
a = 0.5 a0
Substituting this into the equation:
0.5 [tex]a_{0}=a_{0}[/tex]×[tex](0.7)^{t}[/tex]
0.5 = [tex](0.7)^{t}[/tex]
Taking the log of both sides:
t log 0.7 = log 0.5
t = log 0.5 / log 0.7
t = 1.94 years
The half life of the substance is 1.94 years.
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Use the figure to the right to identify each pair of angles as alternate exterior,
alternate interior, consecutive interior, or corresponding.
Answers
7. ∠I and ∠M are corresponding angles.
8. ∠J and ∠P are alternate exterior angles.
9. ∠K and ∠M are alternate interior angles.
10. ∠L and ∠M are consecutive interior angles..
11. ∠I and ∠O are alternate exterior angles.
12. 7. ∠K and ∠O are corresponding angles.
What are Alternate Exterior Angles?Angles that are formed outside the parallel lines that are intersected by a transversal and lie alternate to each other on along the transversal are alternate exterior angles.
What are Alternate Interior Angles?
Angles that are formed inside of the parallel lines that are intersected by a transversal and lie alternate to each other on along the transversal are alternate interior angles.
What are Consecutive Interior Angles?
Angles that are formed inside of the parallel lines that are intersected by a transversal and lie on the same side of the the transversal are consecutive interior angles.
What are Corresponding Angles?
Angles that are formed in relative corner position on each of the parallel lines that are intersected by a transversal and lie along the transversal in the same side are called corresponding angles.
Thus, from the image given, we have the following special angles:
7. ∠I and ∠M are corresponding angles.
8. ∠J and ∠P are alternate exterior angles.
9. ∠K and ∠M are alternate interior angles.
10. ∠L and ∠M are consecutive interior angles..
11. ∠I and ∠O are alternate exterior angles.
12. 7. ∠K and ∠O are corresponding angles.
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If 12 oz. of sausage contains 300 calories, how many calories w ould 7 oz, contain? how would i write a formula
Answers
Answer:
175 cal
Step-by-step explanation:
if 12oz = 300 cal
then, 7 oz = ?
cross multiplication
12×?= 7×300
? = 2100/12
? = 175 cal
NB: you can replace the question mark with any variable.
what is 2^c=8 (please help)
Answers
Answer:
c=3.
Step-by-step explanation:
∵2*2*2=8,
∴2^3=8.
∵2^c=8,
∴c=3.
johns first three test scores out of 100 are 84,78,82. what did he score on his fourth test if the average for all four tests is 80 out of 100
Answers
Answer:
76
Step-by-step explanation:
Formula
[tex]\sf Average=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}[/tex]
Given values:
First three test scores: 84, 78 and 82Total number of tests = 4Average score for all four tests = 80Let x be the score of the fourth test.
To find the score of the fourth test, substitute the given values into the formula and solve for x:
[tex]\begin{aligned} \sf Average & =\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}\\\\\implies \sf 80 & = \sf \dfrac{84+78+82+x}{4}\\\sf 80 & = \sf \dfrac{244+x}{4}\\\sf 80 \cdot 4 & = \sf 244 + x \\\sf 320 & = \sf 244 + x\\\implies \sf x & = \sf 320 - 244\\& = \sf 76\end{aligned}[/tex]
Therefore, John scored 76 on his fourth test.
What expression represents the volume of the prism, in cubic units? one-halfx3 one-halfx2 x 2x3 2x2 x
Answers
Volume of prism = [tex]\frac{1}{2x^{3} } + x^{2}[/tex]
Given that:
The oblique prism below has an isosceles right triangle base and the length of the base is x
=> the area of the base: [tex]\frac{1}{2}[/tex] × x × x = [tex]\frac{1}{2}[/tex]
The vertical height of the prism is (x + 2)
=> The volume of the oblique prism is:
V = the base area * the vertical height
<=> V = [tex]\frac{1}{2}[/tex] [tex]x^{2}[/tex] (x + 2)
<=> V = [tex]\frac{1}{2x^{3} } + x^{2}[/tex]
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What is the 7th term of an AP: 50+45+40
Answers
Answer:
20
Step-by-step explanation:
using the arithmetic progress formula
tn=a+(n-1)d
from the series given above a which is your first term is 50
the d which is the common difference.. you minus the first term from the second term which is 45-50=-5
so the 7th term which our n=7
we have:
t7=50+(7-1)(-5)
t7=50+(6)(-5)
t7=50-30
t7=20
Answer:
a₇ = 20
Step-by-step explanation:
the nth term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 50 and d = 45 - 50 = - 5 , then
a₇ = 50 + (6 × - 5) = 50 + (- 30) = 50 - 30 = 20
Two students compared the scores on their math tests. Their results on 9 tests are shown in the box plots below.
Which statements are true?
Ben has the smaller range of test scores.
The lower quartile and upper quartile of Nadia’s data are both higher than the lower quartile and upper quartile of Ben’s data.
The median of Nadia’s data is equal to the median of Ben’s data.
Nadia had the highest score on a test.
Ben’s lowest score was equal to Nadia’s lowest score.
Answers
The statements which are true regarding the students whose results on 9 tests are as shown are; The median of Nadia's data is equal to the median of Ben's data.
Nadia had the highest score on a test.
Which statements are true regarding the scores on the tests?According to the task content, it follows that the results of the students in discuss are indicated by means of a box plot as in the attached image.
Consequently, it follows from observation that the median of Nadia and Ben as indicated in the attached box plot is 92 in both cases as indicated by the vertical line in both boxes.
Additionally, the highest score by Nadia is 100 while that for Ben is; 99.
Hence, Nadia had the highest score on a test.
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Choose the division problem represented by this model.
Answers
Answer:
The answer is C
Step-by-step explanation:
What is the tenth term in the sequence 9, 13, 17, 21, 25…?
Answers
Step-by-step explanation:
its 29 9x4=29 9+4=13 13+4=17
Kamden is a mind-reading alien. He had each friend draw and look at a card, then he guessed whether the card had a star on it.
The two-way frequency table below shows data on guess and true status of the cards the friends drew.
Complete the following two-way table of column relative frequencies.
Answers
The completed table will have values filled into it accordingly from left to right and the downwards.
What values are required to complete the table?The concept of relative frequencies involves expressing the frequency of occurrence of events as a fraction of a whole frequency.
Hence, it follows that the blank space on the top-leftmost corner of the table can be filled with the value; 4/5 = 0.8.
For the top-rightmost blank space in the table, the required value is; 2/754 = 0.0027.
For the bottom-leftmost blank space, the required value to fill the table is; 1/5 = 0.2.
For the bottom-rightmost blank space, the required value is; 752/754 = 0.9973.
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The half life of a substance is defined as the time required for the substance to decrease by half. If the weight of a substance begins at 128 grams, and the half life is 7 years, what will be the weight of the substance after 28 years?
Answers
the weight of the substance after 28 years is 8 grams.
How to determine the amountWe have that the half life of a substance is defined as the time required for the substance to decrease by half
The formula for calculating the half - life of a material is given as;
[tex]N(t) = N0 (\frac{1}{2} )^\frac{t}{t^\frac{1}{2} }[/tex]
Where
N(t) is final amountNo is the initial amount = 128 gramst1/2 is the half life = 7 yearst is the time elapsed = 28 yearsSubstitute into the formula
N(t) = 128 × (0. 5) ^28/ 7
N (t) = 128 × ( 0. 5) ^ 4
N(t) = 128 × 0. 0625
N(t) = 8 grams
Thus, the weight of the substance after 28 years is 8 grams.
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If a 650-cm leader is placed against a building at a certain angle, it just reaches a point on the building that is 520 cm above the ground. If the ladder is moved to reach a point 80 cm higher up, how much closer will the foot of the ladder be to the building
Answers
Answer:
140 cm
Step-by-step explanation:
The distance of the foot of the ladder from the building can be found using the Pythagorean theorem (or your knowledge of Pythagorean triples). Once the two distances are found, their difference can be found.
Position 1The 650 cm ladder reaches 520 cm up the side of the building. The ratio of these side lengths is 650/520 = 5/4, suggesting these are the sides of a 3-4-5 right triangle. The distance from the building is ...
(3/5)×650 cm = 390 cm.
Alternatively, the distance (a) from the building can be found using the Pythagorean relation ...
a² +b² = c²
a² +520² = 650²
a = √(422500 -270400) = √152100 = 390 . . . cm
Position 2The 650 cm ladder reaches 520 +80 = 600 cm up the side of the building. The ratio of these side lengths is 650/600 = 13/12, suggesting these are the sides of a 5-12-13 right triangle. The distance from the building is ...
(5/13)×650 cm = 250 cm
Again, the Pythagorean theorem can be used to obtain the same result:
a = √(422500 -360000) = √62500 = 250 . . . cm
DifferenceThe difference between the two distances is ...
390 cm -250 cm = 140 cm
The foot of the ladder will be 140 cm closer to the building.
Which equation can be solved by using this system of equations?
[y=3x5 - 5x³ + 2x² - 10x+4
y=4x4 +6x³-11
Answers
the equation that we can solve using the given system of equations is:
3x^5 - 4x^4 - 11x^3 + 2x^2 - 10x + 15 = 0
Which equation can be solved using the given system of equations?
Here we have the system of equations:
y = 3x^5 - 5x^3 + 2x^2 - 10x + 4
y = 4x^4 + 6x^3 - 11
Notice that both x and y should represent the same thing in both equations, then we could write:
3x^5 - 5x^3 + 2x^2 - 10x + 4 = y = 4x^4 + 6x^3 - 11
If we remove the middle part, we get:
3x^5 - 5x^3 + 2x^2 - 10x + 4 = 4x^4 + 6x^3 - 11
Now, this is an equation that only depends on x.
We can simplify it to get:
3x^5 - 4x^4 - 11x^3 + 2x^2 - 10x + 15 = 0
That is the equation that we can solve using the given system of equations.
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what is the Pythagorean theorem
Answers
Answer:
a^2+b^2=c^2
Step-by-step explanation:
leg1=a
leg2=b
hypotenuse=c
a^2+b^2=c^2
Answer:
u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D
Step-by-step explanation:
1/?
Which number produces a rational number when Multiplied 1/5
Answers
Answer:
-2/3
Step-by-step explanation:
A rational number is a number that can be expressed as a fraction so when you add 2 fractions it’s a rational number
7. Which of these statements is true?
A. 1-(-4)<4- (-2)
B. (-2)(3) > (-1)(-6)
C. 6÷
D.-(5-3)=-5-3
Answers
Answer:
A. because 5 < 6. 1-(-4)=5. and 4-(-2) =6
Ahmed made a fruit smoothie in his blender, shown below. He gave 320 milliliters of the smoothie to his brother. How much smoothie is left for Ahmed to drink?
Answers
625 ml is the amount of smoothie is left for Ahmed to drink.
According to the statement
we have given that the
Ahmed made a 625 ml fruit smoothie in his blender and out of this he gave
320 milliliters of the smoothie to his brother and we have to find that the
How much smoothie is left for Ahmed.
So, For this purpose,
The total smoothie = 625 ml
Smoothie he gave to his brother = 320 ml
Now, we have to find the Amount of smoothie left for ahmed.
So, Smoothie left for ahmed = 625 ml - 320 ml
Smoothie left for ahmed = 305 ml
So, 625 ml is the amount of smoothie is left for Ahmed to drink.
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Question:
Ahmed made a fruit smoothie in his blender, shown below. He gave 320 milliliters of the smoothie to his brother. How much smoothie is left for Ahmed to drink? check the image below.
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The data set below has a lower quartile of 13 and an upper quartile of 37.
1, 12, 13, 15, 18, 20, 35, 37, 40, 78
Which statement is true about any outliers of the data set?
Answers
The dataset 78 is an outlier of the dataset
How to determine the true statement about the outlier?The dataset is given as:
1, 12, 13, 15, 18, 20, 35, 37, 40, 78
Where
Q1 = 13
Q3 = 37
The boundaries of the outliers are given as:
L = Q1 - 1.5 * (Q3 - Q1)
U = Q3 + 1.5 * (Q3 - Q1)
Substitute the known values in the above equation
L = 13 - 1.5 * (37 - 13) = -23
U = 37 + 1.5 * (37 - 13) = 73
This means that the data elements outside the range -23 to 73 are outliers.
78 is outside this range
Hence, 78 is an outlier of the dataset
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define ratio (maths short definition)
Answers
Answer:
division
Step-by-step explanation:
ratio compares 2 numbers by dividing them
example
2 out of 3 dentists like gum
2 ÷ 3 = .67 = 67%
so you can say
67% of dentists like gum
A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. For example, if the number of marks scored in a test is 7 out of 10, then the ratio of marks obtained to the total number of marks is written as 7:10.
Find the surface area of the figure.
2 m
2 m
11 m
11 m
2 m
5 m
5 m
SA = [? ]m²
Answers
Answer:
174m²
Step-by-step explanation:
SA = 2(wl + hl + hw)
= 2(5m x 11m + 2m x 11m + 2m x 5m)
= 2(55m² + 22m² + 10m²)
= 2 x 87m²
=174m²//
Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles
Answers
The height of the triangle is 11.3 in. The correct option is C. 11.3 in
Calculating height of triangleFrom the question, we are to determine the height of the given triangle
The height of the given triangle is x in.
Now, we will determine the value of x
In the diagram, we can observe that the height divides the triangle into two equal halves
Thus,
By the Pythagorean theorem, we can write that
12² = x² + 4²
144 = x² + 16
144 - 16 = x²
∴ x² = 144 - 16
x² = 128
x = √128
x = 11.3
Hence, the height of the triangle is 11.3 in. The correct option is C. 11.3 in
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Which option is the fraction 28/31 closest to? 0, 1/2 or 1?
Answers
Answer:
1 is the closest to 28/31
Step-by-step explanation:
0 is technically 28 spaces away and 1/2 is around 13 spaces away but 1 is only 3. :)
Estimate each of these square roots.
a) √80
b) √27
c) √110
d) √0.03
e) √0.12
Answers
Answer:
a) √80 ≈ 9
b) √27 ≈ 5
c) √110 ≈ 10
d) √0.03 ≈ 0.2
e) √0.12 ≈ 0.3
Step-by-step explanation:
a) √8080 is close to 81
Therefore, √80 can be estimated as √81
√81 = 9
[tex]\Large\boxed{\sqrt{80}\approx9 }[/tex]
b) √2727 is close to 25
Therefore, √27 can be estimated as √25
√25 = 5
[tex]\Large\boxed{\sqrt{27}\approx5 }[/tex]
c) √110110 is close to 100
Therefore, √110 can be estimated as √100
√100 = 10
[tex]\Large\boxed{\sqrt{110}\approx10 }[/tex]
d) √0.030.03 is close to 0.04
Therefore, √0.03 can be estimated as √0.04
√0.04 = 0.2
[tex]\Large\boxed{\sqrt{0.03}\approx0.2 }[/tex]
e) √0.120.12 is close to 0.09
Therefore, √0.12 can be estimated as √0.09
√0.09 = 0.3
[tex]\Large\boxed{\sqrt{0.12}\approx0.3 }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
