the steel pipe ab has a 102-mm outer diameter and a 6-mm wall thickness. knowing that arm cd is rigidly attached to the pipe, determine the principal stresses and the maximum shearing stress at point k.
Answers
At point K, the principal stresses are approximately 1.014 MPa, and the maximum shearing stress magnitude is approximately 0.0038 MPa.
To determine the principal stresses and the maximum shearing stress magnitude at point K, we can apply the equations of mechanics and stress analysis.
First, let's calculate the inner diameter of the steel pipe. The inner diameter is obtained by subtracting twice the wall thickness from the outer diameter:
Inner diameter = Outer diameter - 2 * Wall thickness
= 102 mm - 2 * 6 mm
= 90 mm
Next, we can calculate the area moment of inertia (I) for the cross-sectional shape of the pipe. For a hollow circular section, the area moment of inertia is given by:
I = (π/64) * \((D^4 - d^4)\)
where D is the outer diameter and d is the inner diameter.
I = (π/64) * \(((102 mm)^4 - (90 mm)^4)\)
\(= 334,029.2 mm^4\)
Given that the force applied (F) is 13 kN, we can now determine the bending moment (M) at point K. The bending moment is calculated by multiplying the force by the distance between the applied force and point K:
M = F * d
= 13 kN * (102 mm / 2)
= 663 kN·mm
Now, we can calculate the maximum normal stress (σ_max) using the formula:
σ_max = M * y / I
where y is the perpendicular distance from the neutral axis to point K. For a circular section, y equals half the radius, which is half the outer diameter.
y = 102 mm / 2
= 51 mm
σ_max = (663 kN·mm) * (51 mm) / \(334,029.2 mm^4\)
≈ 1.014 MPa
Finally, the maximum shearing stress (τ_max) can be calculated using the formula:
τ_max = (3/2) * V / A
where V is the shear force and A is the cross-sectional area.
For a circular section, the shear force V is equal to half the applied force F, and the cross-sectional area A is π/4 times the difference between the outer and inner radii squared.
V = F / 2
= 13 kN / 2
= 6.5 kN
A = (π/4) * \(((102 mm / 2)^2 - (90 mm / 2)^2)\)
≈ \(5067.14 mm^2\)
τ_max = \((3/2) * (6.5 kN) / 5067.14 mm^2\)
≈ 0.0038 MPa
Therefore, at point K, the principal stresses are approximately 1.014 MPa, and the maximum shearing stress magnitude is approximately 0.0038 MPa.
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Note: The question would be as
The steel pipe AB has a 102-mm outer diameter and a 6-mm wall thickness. Knowing that arm CD is rigidly attached to the pipe, determine the principal stresses and the maximum shearing stress magnitude at point K. (Round the final answers to one decimal place.) Given: F = 13 kN
Related Questions
625÷5×6=x what is x
Answers
Answer:
750
Step-by-step explanation:
trust
Which addition problems could be solved by adding 40+15?
39+16
38+13
37+18
36+17
35+19
Answers
Addition problems that could be solved by adding 40+15 include 39+16, 38+13, 37+18, 36+17, and 35+19.
What is Equation?Equation is a mathematical statement that consists of an expression set equal to a value or a series of values. It is usually written in the form of an equation, where the left side of the equation is equal to the right side. Equations can involve any combination of numbers, variables, and symbols, and are often used to represent relationships between physical and mathematical quantities. Equations can be used to solve problems, find unknown values, or describe the behavior of a system.
Each of these problems can be solved by first adding 40 and 15 together to get 55, then adding the remaining numbers to that sum. For example, to solve 39+16, first add 40+15 to get 55, then add 39+16 to get 55+55, or 110. This same strategy can be applied to any of the above problems to get the correct answer.
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Addition problems that can be solved by adding 40+15 include 39+16, 38+13, 37+18, 36+17, and 35+19. All of these problems can be solved by adding 55.
What is Equation?Equation is a mathematical statement that consists of an expression set equal to a value or a series of values. It is usually written in the form of an equation, where the left side of the equation is equal to the right side. Equations can involve any combination of numbers, variables, and symbols, and are often used to represent relationships between physical and mathematical quantities. Equations can be used to solve problems, find unknown values, or describe the behavior of a system.
Addition problems that could be solved by adding 40+15 include 39+16, 38+13, 37+18, 36+17, and 35+19. Adding 40+15 is the same as adding 55. Therefore, all of the above addition problems can be solved by adding 55.
For example, 39+16 can be solved by adding 40+15, which is the same as adding 55. 39 + 16 = 55. Similarly, 38+13 can be solved by adding 55. 38 + 13 = 55. The same is true for the other addition problems, which can all be solved by adding 55.
In conclusion, addition problems that can be solved by adding 40+15 include 39+16, 38+13, 37+18, 36+17, and 35+19. All of these problems can be solved by adding 55.
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(Rabbitsus. foxes) Themodel\dot{R}=a R-b RF, \dot{F}=-c F+d RF isthe Lotka - Volterrapredator-preymodel. Here R(t)isthenumberofrabbits. F(t) is, thenumberof foxes, anda, b, c, d>0
areparameters. a)Discussthebiologicalmeaningofeachofthetermsinthemodel. Commentonanyunrea
x^{\prime}=x(1-y) y^{\prime}=\mu y(x-1)$ c) Find a conserved quantity in terms of the dimensionless variables.
d) Show that the model predicts cycles in the populations of both species, for almost all initial conditions.
Answers
The Lotka-Volterra predator-prey model is a set of differential equations used to describe the interactions between two species, a predator and its prey, in a given ecosystem. The model assumes that the population sizes of both species are influenced by factors such as predation, reproduction, and carrying capacity.
a) In the Lotka-Volterra predator-prey model, the terms have the following biological meanings:
- R(t) represents the number of rabbits (prey) at time t.
- F(t) represents the number of foxes (predators) at time t.
- a is the rabbit's reproduction rate.
- b is the predation rate at which rabbits are consumed by foxes.
- c is the natural death rate of foxes.
- d is the rate at which foxes consume rabbits and convert them into new foxes.
b) To make the equations dimensionless, we introduce dimensionless variables x and y, and a constant µ:
x = R/a, y = F/c, µ = ac/bd
The equations become:
x' = x(1 - y)
y' = µy(x - 1)
c) A conserved quantity in terms of the dimensionless variables can be found using the following function:
H(x, y) = - ln(x) + y - ln(y) + µx
The conserved quantity is dH/dt = 0.
d) The model predicts cycles in the populations of both species for almost all initial conditions, as indicated by the oscillatory behavior of the solutions in the phase plane. The trajectories in the phase plane are closed curves around a fixed point (x*, y*), showing that both species' populations will experience periodic fluctuations.
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Jenny drove 660 miles in 12 hours at the same rate how long would it take her to drive 385 miles
Answers
Answer:
7 hours
Step-by-step explanation:
Hi! I need help with my maths the question is 69x420=? (i dont have calculator)
Answers
Answer:
69×420=28980
just use calculator
Step-by-step explanation:
i hope this will help you :)
Answer:
28,980
Step-by-step explanation:
Given: Triangle ABC is similar to triangle DEF, side BC = 19, angle ABC = 48, angle BCA = 73.
If the side DF = 15, then AB - EF = ?
Answers
Answer:
We are given two similar triangles, triangle ABC and triangle DEF, and some measurements of triangle ABC. We are also given that DF, one of the sides of triangle DEF, is equal to 15 units. Using this information, we are asked to find the difference between the lengths of sides AB and EF.
To solve the problem, we can first use the angle-angle similarity theorem to determine that the corresponding angles of the two triangles are equal. Therefore, angle DEF is equal to angle BCA, and angle ABE is equal to angle DFE.
Next, we can use the law of sines to find the length of side AB. The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all sides and angles in the triangle. Applying this to triangle ABC, we have:
AB/sin(73) = BC/sin(48)
Substituting the value of BC as 19 units, we can solve for AB to get:
AB = 22.78 units
Similarly, we can use the law of sines to find the length of side EF. Since angle DFE is equal to angle ABE, we can use the same ratio as above to get:
EF/sin(73) = DF/sin(48)
Substituting the value of DF as 15 units, we can solve for EF to get:
EF = 18.20 units
Finally, we can subtract EF from AB to get:
AB - EF = 22.78 - 18.20 = 4.58 units
Therefore, the difference between the lengths of sides AB and EF is 4.58 units.
Picture attached help please!
Answers
The missing lengths in the triangles are h = 3/2√2 and b = 4√3
How to determine the missing lengthsTriangle a and b
From the question, we have the following parameters that can be used in our computation:
A special right triangle
For a right triangle with an angle of 45 degrees
The measure of the leg is
h = Hypotenuse/√2
So, we have
h = 3/√2
Evaluate
h = 3/2√2
For the other triangle, we have
sin(60) = b/6
So, we have
b = 6/sin(60)
Evaluate
b = 4√3
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A statistics student hypothesised that the time spent waiting in a queue at a grocery store is exponentially distributed. To test her hypothesis, she collected data. Based on the collected data and her hypothesis, she created the following table: [0,5) [5, 10) [10, 15) 7 [15, 20) 3 [20,00) 31 Frequency 16 12 Expected 15.2627 7,2096 25.3837 NOTE: Expected cell counts in the table are correct to four decimal places. 0.05. Unfortunately, She used the data to estimate the rate parameter of an exponential distribution. Her estimate of the rate parameter was = due to a computer crash, the raw data are not available. Answer the following questions. You may round off numerical answers to four decimal places. Where applicable, select only the most correct answer. 1. What statistical test would you use to assess whether the data in the table are from an exponentially distributed population? O Anderson-Darling test O Chi-squared test of independence O Binomial test O Shapiro-Wilk test O Median test O McNemar's Chi-squared test Chi-squared goodness-of-fit test O Jarque-Bera
Answers
The correct answer is:
Chi-squared goodness-of-fit test.
The Chi-squared goodness-of-fit test is used to compare observed frequencies with expected frequencies to determine if there is a significant difference between them. In this case, the observed frequencies are the counts in each interval, and the expected frequencies are the hypothesized values based on the exponential distribution.
To perform the Chi-squared goodness-of-fit test, you would calculate the test statistic by comparing the observed and expected frequencies. The formula for the test statistic is:
χ² = Σ((O - E)² / E)
Where:
O is the observed frequency
E is the expected frequency
In this case, the expected frequencies are given in the table, and you can calculate the observed frequencies by summing the counts in each interval.
After calculating the test statistic, you would compare it to the critical value from the Chi-squared distribution with degrees of freedom equal to the number of intervals minus 1. If the test statistic exceeds the critical value, you would reject the null hypothesis that the data follows an exponential distribution.
Therefore, the correct answer to the question is:
Chi-squared goodness-of-fit test.
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The scatter diagram shows the age and yearly salary of a sample of seven surgeons in a hospital.
Answers
Answer:
a) Point (42, 30,000)
b) The salaries are directly proportional to the age of a surgeon to a large extent
c) By performing regression analysis
Step-by-step explanation:
a) From the given information;
Given that Igor is an experienced surgeon that just completed his medical training, Igor has;
1) Years of experience
2) Redid his medical training to obtain the same qualification with more time spent
3) Able to work only with his newly acquired re-qualification
Therefore, Igor will receive wages similar to other recently trained surgeons that have similar years of experience post Igor's re-qualification
The point that most likely will represent Igor's data will have his years of experience and wage commensurate with his UK based post qualification experience, which is the point (42, 30,000)
b) Because from the graph apart from the two points, (that of Igor and (34, 44,000)), the salaries of the other points vary proportionately with the age of the Surgeon
c) By carrying out a regression analysis as follows;
A = 50, 55,000
B = 42, 46,000
C = 38, 42,000
D = 34, 44,000
E = 42, 30,000
F = 26, 30,000
G = 22, 28,000
Analyzing the above data using excel regression analysis gives Which gives
R² = 0.5739 which shows that approximately 60% of the data fit the Managing Directors data
The equation is as follows;
y = 790·x + 10620
Where
y = Salary
x = Age of surgeon.
Answer:
the answer for C is
use a larger sample of surgeons
Step-by-step explanation:
A(7,-10), B(-3, 4) and C(8,-9)
Find the centroid of the triangle with the given vertices
Answers
Take the average of the three points. Add their coordinates together:
(7, -10) + (-3, 4) + (8, -9) = (7 - 3 + 8, -10 + 4 - 9) = (12, -15)
Divide each coordinate by 3:
(12, -15) / 3 = (4, -5)
can you help me to find the values of abc and cde ?
Answers
Answer:
88° and 132°
Step-by-step explanation:
The sum of angles in a pentagon ( a 5-sided shape) is given as
= (5 - 2) 180°
= 540°
The angles ∠EAB and ∠AED are supplementary hence the sum is 180° Therefore,
∠AED + 110 = 180
∠AED = 180 - 110
= 70°
Given that the sum of the angles in a pentagon is 540° then
110 + 70 + 2k + 140 + 3k = 540
5k + 320 = 540
5k = 540 - 320
5k = 220
k = 220/5
= 44°
Hence the angle ∠ABC
= 2 × 44
= 88°
∠CDE
= 3 × 44
= 132°
The figure above shows the graph of f', the derivative of a function f. The domain of f is the set of all real numbers x such that -3 < x < 5. a. For what values of x does f have a relative maxlmum? Why? b. On what intervals is the graph of concave upward? Use ' to justify your answer. C. Suppose that f(1) = 0. In the xy-plane provided, draw a sketch that shows the general shape of the graph of the function f on the open interval 0 < x < 2. у X O 2
Answers
a) For value of x=-2 given function have a relative maximum.
b) The graph is concave upward in the interval of (-1,1) and (3,5)
c)
What is a function?A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
What is Differentiation?Finding a function's derivative, or rate of change, is the process of differentiation in mathematics. The practical approach of differentiation may be performed utilizing just algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.
solution of above questions are:
a)Function 'f' has relative maximum at x=-2 because f'(x)=0 and f' is changing from +ve to -ve
b) (-1,1 ) and (3,5) are intervals of graph that is concave upward because f' is increasing and f'' is +ve.
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How to solve pls. I need help really bad I don’t understand
Answers
Answer:
The answer for the question is 3.7
Almost sooo close guys just 5 more left sorry if it’s taking long
Answers
Answer:
As a decimal its 6.34, If you round up then its 6.35
As a fraction its 400/63
As a mixed number its 6 22/63
Can someone solve this for me? I’m stuck
Answers
Answer:
Look below.
Step-by-step explanation:
Bill: 5, 10, 15, 20, 25, 30...
Daughter: 3, 6, 9, 12, 15...
And so on.
Every 5 Bill does, add 3 to the number before in the daughter boxes..
What is the product of (9) (negative 9) (negative 1)?
Answers
Answer:
81
Step-by-step explanation: 9 * 9 = -81 * -1 = 81
What’s - 46.15 as a mixed number
Answers
Answer: -46 15/100
Explanation: (see pic attached)
Answer:
46 3/20
Step-by-step explanation:
Rewrite the decimal number as a fraction with 1 in the denominator
46.15=46.15/1
Multiply to remove 2 decimal places. Here, you multiply top and bottom by 10^2 = 100
46.15/1 x 100/100= 4615/100
Find the Greatest Common Factor (GCF) of 4615 and 100, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 5
4615/100 divided by 5/5= 923/20
Simplify the improper fraction
46 3/20
In conclusion
46.15= 46 3/20
I hope that helped ;)
kamala has 2.73 liters of lemonade. She wants to have about 5.5 liters for her party. About how much more lemonade does Kamala need? Does this situation require an exact answer or is it the estimate enough?
Answers
Answer:
The estimate is enough because; 1. The amount needed for the party 5/5 liter is not exact (about 5.5 liters) 2/ 2/73 + 2.7 = 5.53 liters, 5.53 liters is approximately 5.5 liters
Step-by-step explanation:
Present poises = 2.73 liters The estimated need = 2.8 liters Estimated + amount posses = 2.8 f2.73 = 5.54 The total amount (5.53 liter) is also about 5.5 liter, i.e, 5.53 liter is approximately 5.5 liters
Brianna went on a trip to the art museum and sketched a scale drawing of a rectangular wall mural. She used a scale factor of 0.2. The sketch was 12 inches wide and 18 inches long. What was the length of the mural? 3.6 inches 18.2 inches 60 inches 90 inches
pls answer quick this is worth 65 points
Answers
Answer:
90 inches
Step-by-step explanation:
18 divided by 0.2 is 90
Answer:
D: 90 inches
Step-by-step explanation:
Got it right on edge!
The owner of a bookstore buys used books from customers for $1.50 each. The owner then resells the used books
for 400% of the amount he paid for them.
What is the price of a used book in this bookstore?
need the answer
Answers
The price of a used book in the bookstore after the percentage increase in its price is $7.50.
What are percentages?
Percentage can be described as the fraction out of an amount that is usually expressed as a number out of hundred. Percentages are represented with this sign - %.
What is the price of the used book?Price = 1.50 x ( 1 + 4)
1.5 x 5 = $7.50
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Answer:
j 6.00
Step-by-step explanation:
i took the test hope this helps good luck
Please can i have help with the last question
Answers
Answer:
.
Step-by-step explanation:
PLEASE HELP!!
During take off, a plane leaves the ground and travels in a straight line until it reaches a height of 9 km. The distance the plane flies during take-off should be in the range of 49 km to 53 km. What is the smallest possible angle that the path of the plane could make with the ground? Give your answer in degrees to 1 d.p.
Answers
On solving the provided question, we can say that angle, by trigonometry. angle = cos(x) = 50+53 /9; x = \(cos^{-1}(11.45)\)
what are angles?In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays can generate an angle that is in the plane where the rays are located. The meeting of two planes also creates an angle. They are referred to as dihedral angles. An angle is the shape created by two rays or lines that have a shared termination in plane geometry. The Latin word "angulus," which meaning "horn," is the source of the English term "angle." The vertex is the common terminal of the two rays, which are referred to as the sides of the angle.
to find the .
height = 9 km
base = 50
by trigonometry,
angle = cos(x) = 50+53 /9
cos(x) = 50+53 /9
cos(x) = 103/9
cos(x) = 11.45
angle, x = \(cos^{-1}(11.45)\)
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Select all expressions are equivalent to 3^8
83
310
32
3.8
(34)
o (3.3)
3
Answers
Answer:
\(\frac{3^{10} }{3^{2} }\) , \((3*3)^{4}\), \((3^{4})^{2}\)
Step-by-step explanation:
The expressions 3¹⁰/3², (3⁴)², and (3·3)⁴ are equivalent to the given expression. which is the correct answer would be options (B), (D), and (E).
What are exponential expressions?Exponential expressions, as the name indicates, involve exponents. We already know that the exponent of a number (base) specifies how many times the number (base) has been multiplied. To answer the exponential expressions, we may need to apply the relationship between exponents and logarithms.
As per option (B), we have
3¹⁰/3²
3¹⁰⁻²
Apply the subtraction operation in the exponent
3⁸
As per option (D), we have
(3⁴)²
3⁴ˣ²
Apply the multiplication operation in the exponent
3⁸
As per option (E), we have
(3·3)⁴
(3²)⁴
3⁴ˣ²
3⁸
Thus, the expressions 3¹⁰/3², (3⁴)², and (3·3)⁴ are equivalent to the given expression.
Hence, the correct answer would be options (B), (D), and (E).
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After randomly selecting 1,009 adults and surveying each of them, 545 of them indicated that they were not comfortable with a drone delivering packages to them. The pollster concluded from the data that precisely 54 percent of all American adults are therefore not comfortable having drones make deliveries to them.
Determine whether the pollster’s conclusion makes sense. Address whether the pollster is correct in drawing this conclusion based upon the given information. In preparing your answer, include the following terms:
statistics and parameters,
estimation,
margin of error,
and any other concepts from the assigned readings and/or class sessions you deem helpful and appropriate.
Answers
Based on the information, the pollster's conclusion makes sense.
How do you know if the pollster is right with his conclusion?To know if the pollster is right with his conclusion we must perform the following operation.
1,009 / 100 = 10.0910.09 * 54 = 544.86In accordance with the above, we can infer that the pollster concludes that 54% of the people surveyed are equivalent to 545 people correctly because 0.86 is a minimum margin of error for this type of statistics. In addition, it can be inferred that the pollster correctly uses the statistics and study parameters of a sample to establish a correct conclusion.
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A survey asked high shcool students to pick their favorite subject. THe results are shown in the table
Answers
Answer:
Sorry there is no table or picture to show the subjects ;-;
Step-by-step explanation:
Answer:
Step-by-step explanation:
35
Add.
(6x³ + 3x² − 2) + (x³ - 5x² − 3)
Express the answer in standard form. (Please and thank you)
Answers
Answer:
\(\\\sf7x^3 - 2x^2 - 5\)
Step-by-step explanation:
\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)
Remove parenthesis.
6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3
Rearrange:
6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3
Combine like terms to get:
7x^3 - 2x^2 - 5----------------------------------------
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Hope this helps! :)
Answer:
7x³ - 2x² - 5
Step-by-step explanation:
(6x³ + 3x² - 2) + (x³ - 5x² - 3)
Remove the round brackets.
= 6x³ + 3x² - 2 + x³ - 5x² - 3
Put like terms together.
= 6x³ + x³ + 3x² - 5x² - 2 - 3
Do the operations.
= 7x³ - 2x² - 5
____________
hope this helps!
A tire is hung from a tree. The outside diameter is 34 inches and the inside diameter is 14 inches. You throw a baseball toward the opening of the tire. Your baseball is equally likely to hit any point on the tire or in the opening of the tire. What is the probability that you will throw the baseball through the opening in the tire?
Answers
The required answer is the probability of throwing the baseball through the opening in the tire is approximately 0.1556, or 15.56%.
To solve this problem, we need to find the area of the opening in the tire and the area of the entire tire. Then, we can divide the area of the opening by the area of the entire tire to get the probability of throwing the baseball through the opening.
First, we need to find the radius of the tire. The outside diameter is 34 inches, so the radius is 17 inches. The inside diameter is 14 inches, so the inner radius is 7 inches.
The area of the opening is the area of a circle with radius 7 inches. Using the formula for the area of a circle (A = πr^2), we get:
A(opening) = π(7)^2
A(opening) = 49π
The area of the entire tire is the difference between the area of the outer circle and the area of the inner circle. Using the same formula, we get:
A(tire) = π(17)^2 - π(7)^2
A(tire) = 225π
Now we can find the probability of throwing the baseball through the opening by dividing the area of the opening by the area of the entire tire:
P(through opening) = A(opening) / A(tire)
P(through opening) = (49π) / (225π)
P(through opening) = 7/45
P(through opening) ≈ 0.1556
So the probability of throwing the baseball through the opening in the tire is approximately 0.1556, or 15.56%.
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if it takes 24 minutes to walk 2 miles how long would it take to walk 6 miles
Answers
Step-by-step explanation:
24min= 2miles
? 6miles
it will be 6×24min÷2= 72minutes or 1hr 12min
10) Alicia, an employee of Dunkin' Donuts, receives 23+ days per year of vacation time. So far
this year she has taken 3 days in January, 5 days in May, 6 days in July, and 4+ days in
September. How many more days of vacation does Alicia have left?
Alicia has
more days of vacation left.
Answers
Answer:
Alicia has 5 days of vacation left
Step-by-step explanation:
add the number of days she has used and subtract that from her 23 days of vacation time
solve please :3 will mark brainliest !!
Answers
__________
\( \: \)
6f = $15
8f = $20
10f = ?
Soo :
2f = 5
f = 2,5
10f = 10(2,5) = $25✔
The cost of the wire of the third length in the table is, 25 dollars
We have to give that,
The cost of a certain type of wire varies directly with its length.
Now, From the table the equation between cost and length is,
y - 15 = (20 - 15)/(8 - 6) (x - 6)
y - 15 = (5/2) (x - 6)
y - 15 = 2.5x - 15
y = 2.5x
Where y represents the cost and x represent the length.
Hence, At x = 10 feet
y = 2.5 (10)
y = 25 dollars
So, The cost of the wire is, 25 dollars
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