4. The general Reynolds Transport Theorem (RTT) for conservation of momentum is expressed as: dB =ΣF= dpdv + √p(v•n) dA (4.1) dt Where; Bsys = Extensive property in terms of momentum of a rigid b
Answers
The general Reynolds Transport Theorem (RTT) for conservation of momentum is expressed as:
dB = ΣF = dpdv + √p(v•n) dA (4.1) dt
The general Reynolds Transport Theorem (RTT) is a mathematical expression used in fluid mechanics to describe the conservation of momentum in a system. In this equation, dB represents the change in the extensive property Bsys, which is related to the momentum of a rigid body. ΣF represents the sum of forces acting on the system.
The right-hand side of the equation consists of two terms. The first term, dpdv, represents the rate of change of momentum within the control volume. It accounts for the change in momentum due to the net inflow or outflow of mass through the control surface.
The second term, √p(v•n) dA, represents the surface forces acting on the control volume. Here, p is the pressure, v is the velocity vector, n is the outward normal vector to the control surface, and dA is an elemental area on the control surface. This term captures the momentum flux across the control surface due to pressure forces.
The equation is valid for both steady and unsteady flows and provides a comprehensive representation of momentum conservation within a system.
The general Reynolds Transport Theorem (RTT) expressed by equation (4.1) represents the conservation of momentum in a system. It considers the change in momentum within the control volume and the surface forces acting on the control surface. Understanding and applying this theorem is essential in analyzing and predicting fluid flow behavior and its impact on momentum within a given system.
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Related Questions
ABCD is a rectangle and AC and BD are its diagonals. If AC = 10 cm, then BD is?
A. 10 cm
B. 5 cm
C. 15 cm
Or D. 20 cm
Lemme know, take ur timeee
Answers
Answer:
A. 10 cm
Step-by-step explanation:
In a right angled triangle, a² + b² = c² where c is the diagonal or hypotenuse. If you split a rectangle diagonally into two right angle triangles, the a and b of both triangles would be the same length. Therefore, the c or diagonals would also be the same length - 10 cm.
Hope this helps!
T
15
the
2
-2
y
0
(4.3)
2
(4.-2),
**
Which is the equation of the given line?
Answers
1. What is the domain and range of the
graph shown?
-10 S
2799
-24
Answers
Answer:
D: (-∞,∞)
R: (0,∞)
Step-by-step explanation:
This is a parabola, so the domain of this function is always:
D:(-∞,∞)
The y-values of this parabola do not go any lower than 0, and it goes upwards in the positive y-direction. So, the range for this function is:
R:(0,∞)
50 p o i n t s H U R R Y
Answers
Answer:
1 1/6
Step-by-step explanation:
Answer:
1 1/6
Step-by-step explanation:
have a good one
Sorry if I'm wrong
Fill in the blank with the correct response.
3
of a =
then I
5
24
Answers
Answer:
8 is the answer
have a great day
Answer:
x = 8
Step-by-step explanation:
Hi there!
\(\displaystyle\frac{9}{24}=\frac{3}{x}\)
9/24 can be simplified by dividing both the numerator and denominator by 3:
\(\displaystyle\frac{9\div3}{24\div3}=\frac{3}{x}\\\\\\\frac{3}{8} =\frac{3}{x} \\\\\\x=8\)
Therefore, x is 8.
I hope this helps!
susan monitors the number of strep infections reported in a certain neighborhood in a given week. the recent numbers are shown in this table: week number of people 0 20 1 26 2 34 3 44 according to her reports, the reported infections are growing at a rate of 30%. if the number of infections continues to grow exponentially, what will the number of infections be in week 10?
Answers
Therefore, the predicted number of infections in week 10 is approximately 276 (rounded to the nearest whole number).
To predict the number of infections in week 10, we first need to find the growth factor.
Using the formula for exponential growth, we have:
\(N = N0 * (1+r)^t\)
where:
N0 = initial number of infections (week 0) = 20
r = growth rate = 30% = 0.3
t = number of weeks
To find the growth factor (1+r), we add 1 to the growth rate:
1+r = 1 + 0.3 = 1.3
So the formula becomes:
\(N = N0 * (1.3)^t\)
To find the number of infections in week 10, we substitute t = 10 into the formula and solve for N:
\(N = 20 * (1.3)^{10}\)
= 20 * 13.784
= 275.68
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the sat and act college entrance exams are taken by thousands of students each year. the mathematics portions of each of these exams produce scores that are ap- proximately normally distributed. in recent years, sat mathematics exam scores have averaged 480 with standard deviation 100. the average and standard deviation for act mathematics scores are 18 and 6, respectively.
Answers
a) 75.80 percentage of students will be scoring below 550 in a typical year.
b) 22.2 marks should be set by the engineering school setas a comparable standard on ACT math test.
Here we have been mentioned that in the recent years, sat maths exam scores have averaged 480 with standard deviation 100. the average and standard deviation for act mathematics scores are 18 and 6, respectively.
a) The percentage of the students scoring below 550 marks in a typical year is calculated as follows:
Let x be the SAT score
So, x follows normal distribution
Given above,
mean (μ) = 480
standard deviation (σ) = 100
we will find P ( x < 550)
We will use the excel function NORM.DIST to find the required probability
P(x < 550) = NORM.DIST\((550, 480, 100, TRUE)\)
= 0.7580
= 75.80%
Hence the percentage of the students who are scoring below 550 in a typical year = 75.80%
b) We calculate the score to be set by the engineering school as a comparable standard on the ACT math test as follows:
Let Z be the ACT score
Z follows the normal distribution
Given above, μ = 18 and σ = 6
Let Z' be the ACT score comparable to the standard set for SAT
Then we need to find Z' such that P(Z < Z') = 75.80% = 0.758
From standard normal tables we get Y' such that
Z' = NORM.INV\((0.758, 18, 6)\)
= 22.2
The ACT score that needs to be set by the college = 22.2 marks
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At the beach, Ayana and her sister both built sandcastles and then measured their heights. Ayana's sandcastle was 1/2 of a foot tall and her sister's was 3/8 of a foot tall. How much taller was Ayana's sandcastle than her sister's?
Write your answer as a fraction or as a whole or mixed number.
Answers
Ayana's sandcastle is 1/8 foot taller than her sister's.
What is fraction?Fractions in Math, represent a numerical value that expresses a part of a whole. The whole can be any number, specific value, or a thing.
Given,
Ayana's sandcastle was 1/2 of a foot tall
Her sister's was 3/8 of a foot tall.
Difference between the height of the both sandcastle
= 1/2 - 3/8
= (4 - 3)/8
= 1/8
Hence, Ayana's sandcastle is taller than her sister's by 1/8 foot.
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HELPPPPPPP
For each graph below, state whether it represents a function.
Answers
Answer:
No, No, Yes, No, Yes, Yes
Step-by-step explanation:
A graph is a function if it passes the vertical line test (in other words, every vertical line that can be drawn intersects the graph at no more than one point).
This is because for a function, each input must map onto no more than one output.
A rectangular garden has a length of 20 yards and a width of 42 yards. A diagonal path runs from one end of the garden to the other. How long is the diagonal path? a. B. C. 50 yd. D.
Answers
When the rectangular garden has a length of 20 yards and a width of 42 yards the diagonal path will be \(\sqrt{2164}\) .
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.
Since we have a right-angled triangle, we can use the Pythagorean Theorem to find our answer. The Pythagorean Theorem states the following:
\(a^{2} +b^{2} =c^{2}\)
In this formula a and b represent the legs of the triangle and c represents the length of the hypotenuse.
Let's substitute our data from the question.
\(42^{2} +20^{2} =c^{2}\)
Square.
1764 + 400 = \(c^{2}\)
And finally take the root of both sides. We only need to use the positive solution, since the length of the hypotenuse can't be negative.
\(c = \sqrt{2164}\)
When the rectangular garden has a length of 20 yards and a width of 42 yards the diagonal path will be \(\sqrt{2164}\) .
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Answer: 53
Step-by-step explanation:
The length and width of the garden represent the legs of a right triangle, and the diagonal path represents the hypotenuse.
The Pythagorean Theorem states that a squared plus b squared equals c squared, where a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse.
Let p equal the length of the diagonal path in yards.
Applying the Pythagorean Theorem gives us p squared equals forty-five squared plus twenty-eight squared.
Now square forty-five and twenty-eight to get p squared equals two thousand twenty-five plus seven hundred eighty-four.
Next, find the sum of two thousand twenty-five and seven hundred eighty-four, which is two thousand eight hundred nine.
Finally, calculate the square root of two thousand eight hundred nine to find that p equals fifty-three.
So the length of the diagonal path is fifty-three yards.
Can someone please help me? Thanks!
Answers
Answer:
Step-by-step explanation:
0
Help someone please I need this one correct to get a good grade
Answers
1) The square root of 8 is the least, since 3^2 equals 9, and 8 is less than 9, so its the least.
2) Then the cube root of 27, because 3 cubed is equal to 27
3) Finally, pi is the largest since it equals 3.142.
Good luck with your grades.
root 8 < pi < cube root 27
the vector sum of two or more other vectors is called the
Answers
Answer: resultant
Step-by-step explanation:
James, John and Jane decided to buy a piece of land. James paid 3/5 of the total cost while John paid 3/8 of the reminder. if Jane paid 30000.what was the total cost of the piece of land?
Answers
The total cost of the piece of land for which James, John and Jane decided to buy a piece of land is 1,200,000.
What is the total cost?Total cost or the final cost is the summation of all the cost spend while buying any good or taking any service.
James, John and Jane decided to buy a piece of land. James paid 3/5 of the total cost while John paid 3/8 of the reminder. Thus, the fraction of amount paid by Jane is,
\(x=1-\dfrac{3}{5}-\dfrac{3}{8}\\x=\dfrac{40-24-15}{40}\\x=\dfrac{1}{40}\)
The Jane paid, 30000 of total cost which is 1/40 part of it. Thus, the total cost of the piece of land is,
\(\dfrac{1}{40}x=30000\\x=30000\times40\\x=1200000\)
Thus, the total cost of the piece of land for which James, John and Jane decided to buy a piece of land is 1,200,000.
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Consider the statement "Worldwide in 2014, there are more than $2.5 trillion in credit card transactions." Make sure that you fill in each answer area before checking "How Did I Do?". What was the daily average dollar amount of transactions? Round to the nearest hundred million dollars. $ Number How many dollars were spent in credit card transactions each day?
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given that:
In 2014:
Worth of credit card transaction = $2.5 trillion
The daily average dollar amount of transaction:
Number of days in a year = 365
(Yearly worth of transaction / number of days in a year)
$(2,500,000,000,000) / 365
= $6,849315068.4931
= $6,849, 000,000 (nearest 100 million dollars)
Amount spent in transaction daily :
= $6,849,315,058
A triangle has vertices at A (−2, −2), B (−1, 1), and C (3, 2). Which of the following transformations produces an image with vertices A′ (−2, 2), B′ (−1, −1), and C′ (3, −2)?
Answers
Show the family of conics with the same focus
x^2/a^2+C + y^2/b^2+C = 1
is its own orthogonal family of curves.
Answers
The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.
To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.
First, we take the derivative of the equation with respect to x:
2x/a^2 = -2y/b^2 * dy/dx
Simplifying, we get:
dy/dx = -b^2*x/a^2*y
Now, we set this equal to -1/b^2:
-b^2*x/a^2*y = -1/b^2
Cross-multiplying and simplifying, we get:
x/a^2*y = 1/b^2
Finally, we can rearrange this equation to get:
y = b^2*x/a^2
This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.
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How are viruses used in biotechnology?
Answers
Viruses are widely used in biotechnology for gene therapy, vaccine production, protein expression, phage therapy, and biocontrol.
Viruses have been used extensively in biotechnology for a variety of purposes. Here are some examples:
1. Gene therapy: Viruses can be used as vectors to deliver therapeutic genes to specific cells in the body. This is done by modifying the virus so that it can enter the target cells and deliver the therapeutic gene without causing harm. This approach has been used to treat a variety of genetic disorders and is a promising area of research.
2. Vaccines: Many vaccines are made using weakened or inactivated viruses. These vaccines help the immune system recognize and fight off the virus in case of future exposure.
3. Phage therapy: Bacteriophages are viruses that infect bacteria. They can be used to treat bacterial infections by targeting and killing specific bacteria. This approach has been used as an alternative to antibiotics in cases where bacteria have developed resistance to traditional antibiotics.
4. Biocontrol: Viruses can be used to control the population of certain pests, such as insects or fungi. This is done by infecting the pest with a virus that is specific to that species. The virus will then replicate inside the pest, eventually killing it.
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which of the following statements is true of the sample size for nonprobability samples
Answers
The statement that is true of the sample size for nonprobability samples is that it is typically small.
Nonprobability sampling methods are often used when it is not feasible or practical to obtain a large sample that is representative of the population.
Nonprobability samples are selected based on criteria other than random selection, such as convenience, judgment, or purposive sampling. These methods are commonly used in qualitative research or when studying hard-to-reach populations.
Since nonprobability samples do not guarantee representativeness, the focus is often on in-depth exploration rather than generalization to a larger population. As a result, researchers often work with smaller sample sizes that are more manageable and allow for in-depth analysis of the selected cases or individuals.
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Need help soon!!!! Will give 100 points
Answers
The mistake is in the second step, the slope of the perpendicular line is 2.
How to find the error in Julia's math?Here we can see that Julia is trying to find a linear equation that is perpendicular to the graphed in the given coordinate axis, and that passes through R.
First she gets the slope of the graphed line, and remember that two lines are perpendicular if the product between the slopes is -1.
Then if the slope of the graphed line is -1/2, the slope of the perpendicular one is:
a*-1/2 = -1
a = -1/(-1/2)
a = 2
That is the slope that she should have used, instead of -2.
so the mistake is in the second step.
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y = 6x; (2,12) tell weather the ordered pair is a solution of the equation
Answers
Hi!
I can help you with joy!
Plug in the values and solve:Instead of y, plug in 12 (the y-coordinate)Instead of x, plug in 2 (the x-coordinate)Then, if we end up with a true statement, then the ordered pair is a solution of the equation.12=6(2)12=12Yeah! It worked! :)Answer:
Yes, (2,12) is a solution of the equation y=6x.
Hope it helps.
Do comment if you have any queries regarding my answer.
~Misty~
Which is the approximate measure of angle yzx? 34.8° 39.4° 50.6° 55.2°
Answers
The approximate measure of angle YZX is 39.4°. Option(B) is the correct answer.
we know that
In the right triangle XYZ
\(tan(Y Z X)= \frac{opposite side angle YZX}{adjacent side angle YZX}\)
In this problem,
Opposite side angle YZX= XY = 12.4cm
Adjacent side angle YZX= YZ = 15.1cm
substitute the values,
\(tan ( Y Z X) = \frac{12.4}{15.1}\)
\(Angle ( Y Z X) = arc tan( \frac{12.4}{15.1} )\)
Angle ( Y Z X) = 39.4°
So, the approximate measure of angle YZX is 39.4°.
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The complete question is:
In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm. Which is the approximate measure of angle YZX?
A .34.8°
B .39.4°
C .50.6°
D. 55.2°
L
The cost of 3 pounds of strawberries
is $6.57. What is the constant of
proportionality that relates the cost in
dollars, y, to the number of pounds of
strawberries, x?
A 3
B
6.57
C 2.19
D
Not here
help please lol it has to be one of the answer choices btw
Answers
Answer: A
Step-by-step explanation: Hi
What is the value of 7(3x-4) + 4^3,when x = 6
Answers
Answer:
162
Step-by-step explanation:
Answer:
162
Step-by-step explanation:
7(3x-4)+4^3 if x = 6
-> 7(3)(6)-4)+4^3
-> 162
Write an equation for the following:
A number increased by 6 is 22.
Solve your equation (show steps) to find the number.
Answers
Answer:
16
Step-by-step explanation:
Steps: x + 6 = 22
-6 -6
x = 16
What IS the slope of a line that is perpendicular to the line y= --x + 5?
• -2
-1/2
1/2
• 2
Answers
Let k: y = a₁x + b₁ and l: y = a₂x + b₂. Then
k ║ l ⇔ a₁ = a₂k ⊥ l ⇔ a₁ · a₂ = -1We have the line y = -x + 5 ⇒ a₁ = -1.
Therefore
a₂ · (-1) = -1
-a₂ = -1 Ichange the signs
a₂ = 1Let's say someone is conducting research on whether people in the community would attend a pride parade. Even though the population in the community is 95% straight and 5% lesbian, gay, or some other queer identity, the researchers decide it would be best to have a sample that includes 50% straight and 50% LGBTQ+ respondents. This would be what type of sampling?
A. Disproportionate stratified sampling
B. Availability sampling
C. Snowball sampling
D. Simple random sampling
Answers
The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."
A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.
B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.
C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.
D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.
Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.
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A spinner is divided into five colored sections that are not of equal size: red, blue,
green, yellow, and purple. The spinner is spun several times, and the results are
recorded below:
Spinner Results
Color Frequency
Red
Blue
Green
Yellow
Purple
14
6
12
4
16
Based on these results, express the probability that the next spin will land on purple
as a fraction in simplest form.
Answers
Answer:
4/13
Step-by-step explanation:
total = 14 + 6 + 12 + 4 + 16 = 52
purple = 16
p(purple) = 16/52 = 4/13
Can some help simplify this question, with positive exponents
Answers
Answer:
4\(a^{9}\)\(b^{8}\)
Step-by-step explanation:
\(\frac{8a^{6}b^{12} x 4a b^{3} }{8x^{-2}b^{7} }\)
\(\frac{32a^{7} b^{15} }{8a^{-2} b^{7} }\)
4\(a^{9}\)\(b^{8}\)
Helping in the name of Jesus.
a diameter measures has a radius of 8 ft
Answers
Answer:
The radius is 4
You have to do half what 8 it 4 an that your answer