The maximum shearing stress for case (a) is approximately 9.10 ksi, and for case (b) it is approximately 6.13 ksi.
For the given state of plane stress, the maximum shearing stress can be determined using the formula:
τmax = (σx - σy) / 2 + sqrt[((σx - σy) / 2)^2 + τxy^2]
where σx and σy are the normal stresses in the x and y directions respectively, and τxy is the shearing stress.
(a) When σx = 20 ksi and σy = 10 ksi, the in-plane shearing stress (τxy) is given as:
τxy = 0.4 * (σx - σy) = 0.4 * (20 - 10) = 4 ksi
The out-of-plane shearing stress is assumed to be zero, since there is no information given about it. Therefore, the maximum shearing stress is:
τmax = (20 - 10) / 2 + sqrt[((20 - 10) / 2)^2 + 4^2] = 5 + sqrt(25 + 16) = 5 + sqrt(41) ≈ 9.10 ksi
(b) When σx = 12 ksi and σy = 5 ksi, the in-plane shearing stress is
τxy = 0.4 * (σx - σy) = 0.4 * (12 - 5) = 2.8 ksi
Again, assuming the out-of-plane shearing stress to be zero, the maximum shearing stress is:
τmax = (12 - 5) / 2 + sqrt[((12 - 5) / 2)^2 + 2.8^2] = 3.5 + sqrt(12.25 + 7.84) = 3.5 + sqrt(20.09) ≈ 6.13 ksi
Therefore, the maximum shearing stress for case (a) is approximately 9.10 ksi, and for case (b) it is approximately 6.13 ksi.
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What is the equation of the line that passes through the point (-6, 5) and has a slope of 1/2
The equation of a line passes through the point (-6, 5) and
has a slope of 1/2 is y = (1/2)x + 8.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, A line passes through the point (-6, 5) and has a slope of 1/2.
First, we need to determine the y-intercept 'b'.
5 = (1/2)(-6) + b.
5 = - 3 + b.
b = 8.
y = (1/2)x + 8 is the required equation of the line.
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A small object slides along the frictionless loop-the-loop with a diameter of 3 m. What minimum speed must it have at the top of the loop?.
The minimum speed object must have at the top of the loop is 3.8m/s.
Friction is the force that resists the motion of an object, it works in the opposite direction of applied force. Centripetal force is the force applied to the center of the body moving in a circular motion, whereas gravitational force is the pull of gravity on a body i.e., it attracts a body toward the ground.
Diameter of loop= 3m
thus radius = 1.5m
Centripetal force =< gravitational attraction the object has.
Centripetal force ,F=mv^2/r ----1
where M= mass v= velocity and r= radius
gravitational force is F=ma -----2
let 1=2
mv^2/r=ma
m is common so can be canceled out
a=v^2/r
for v= 9.8m/s^2
a= 9.8^2/1.5
a=3.834057903
Therefore, the minimum speed object must have at the top of the loop is 3.834m/s.
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Which of the following is the value of discriminant for the equation √ 2x² 5x+ √ 2 0 *?-517√22 √2−5
Discriminant of the eqaution √2x²-5x+√2 is 17
what is discriminant?The discriminant of a polynomial in mathematics is a number that relies on the coefficients and allows inference of some root features without computing them. It is basically a polynomial function of the original polynomial's coefficients.
To calculate the Discriminant of a quadratic equation which is generally expressed as
ax² + bx + c = 0
The quadratic equation's discriminant, indicated by the letter D, is defined as
D = b² - 4ac
So D= 5*5 -4 * √ 2 *√ 2
=> 25 -4 *2
=> 25-8
=> 17
so discriminant of the eqaution √2x²-5x+√2 is 17
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Complete question :
For √2x²-5x+√2=0 find the value of discriminant
What is 2 exponent called?
2 exponent is also known as the "square" of a number. When a number is raised to the power of 2, it means that the number is multiplied by itself.
For example, 2^2 means 2 multiplied by 2, which is equal to 4. The term "square" is used because the result of raising a number to the power of 2 is the same as finding the area of a square with that number as the length of each side.
This notation is widely used in mathematics, particularly in algebra and geometry. When we see a number with exponent 2, we can understand it as the number is multiplied by itself, which is the square of the number.
The term "square" is widely used in mathematics, particularly in algebra and geometry. Understanding this concept is important for solving mathematical problems, especially in algebra and geometry.
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The volume of gas a balloon can hold varies directly as the cube of its radius. Imagine a balloon with a radius of 4 inches can hold 192 cubic inches of gas. How many cubic inches of gas must be released to reduce the radius down to 3 inches?
Answer:
The volume of a balloon is directly proportional to the cube of its radius, so we can use the formula:
V1/V2 = (R1/R2)^3
Where V1 is the initial volume, V2 is the final volume, R1 is the initial radius, and R2 is the final radius. We know that when the radius is 4 inches, the volume is 192 cubic inches, so we can use this information to find the final volume when the radius is 3 inches.
V1 = 192 cubic inches
R1 = 4 inches
R2 = 3 inches
V1/V2 = (R1/R2)^3
V2 = V1 / (R1/R2)^3
V2 = 192 / (4/3)^3 = 192/ (4/27) = 192 * 27/4 = 192 * 6.75 = 1296 cubic inches
So, 1296 cubic inches of gas must be released to reduce the radius down to 3 inches.
graph
16. 2y – 4x < 8
17. -4y > -x + 12
18. | x + 3 |= y
19. |2x – 6| + 2 = y
To graph the inequality 2y - 4x < 8, we can start by isolating the y variable on one side of the inequality. To do this, we add 4x to both sides:
An explanation graph is what?
A graph is a representation of the relationship between two variables that are normally measured along one of a pair of axes at right angles.
2y - 4x < 8
2y < 4x + 8
Next, we divide both sides by 2 to get y by itself:
y < 2x + 4
To graph this inequality, we can start by plotting the y-intercept, which is the point where x = 0. In this case, y = 2(0) + 4 = 4, so the y-intercept is (0, 4). Next, we can find the slope of the line, which is -2.
To graph the inequality -4y > -x + 12, we can start by isolating the y variable on one side of the inequality. To do this, we add x to both sides:
-4y > 12 - x
Next, we divide both sides by -4 to get y by itself:
y < -3 + (1/4)x
To graph this inequality, we can start by plotting the y-intercept, which is the point where x = 0. In this case, y = -3 + (1/4)(0) = -3, so the y-intercept is (0, -3). Next, we can find the slope of the line, which is (1/4).
The equation | x + 3 |= y represent a vertical line with x = -3
The equation |2x – 6| + 2 = y represent a V shape with the vertex at (-3,2)
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Haley started by putting $862 in her account, and she will deposit an additional $71 each week. Ezra made an initial deposit of $58, and he will add $473 more each week. Eventually, Haley and Ezra will each have the same amount saved. How many weeks will that take? What is that amount?
The amount that they will have saved after 2 weeks is $1,737.
What is Amount?Tom, you can refer to a quantity or number of something using the word "amount." It is typically used to refer to an amount of money, like when people discuss their income, but it can also be used to describe a quantity of something, such as the volume of water in a tank or the time required to complete a task.
We must divide the difference between Ezra and Haley's initial deposits by the difference between their weekly installments to figure out how many weeks it will take them to save the same amount of money. In this instance, their initial deposits differed by $804 ($862 - $58), while their weekly installments differed by $402 ($71 - $473). We can calculate that it will take them two weeks to save the same amount of money by dividing $804 by $402.
After two weeks, they will have $1,737 in savings. Haley will have $1,737 ($862 + $71 + $71 + $703) and Ezra will have $1,737 ($58 + $473 + $473 + $733) in their accounts after two weeks.
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Given that 4,p,q,13 are consecutive terms of a a.p find the value of p and q
value of p = 7 and value of q = 10.
what is consecutive term?The word consecutive implies an unbroken sequence that means terms approaches forward by following a specific order. Within a consecutive sequence the gap between each term is the same.
What is the value of p and q?
given, 4, p, q, 13 are consecutive terms, find the value of P and Q.
As the above four are consecutive number so starting from the 4 we write the list in an unbroken sequence.
At first difference between highest and lowest number = 13- 4 = 9
now this difference is divided by the number of gaps between the sequence, we find there are 3 gaps between four numbers.
order of sequence = 9/ 3 = 3
now the next number after 4 will be 4+3 = 7
in the next, 7+3 =10
finally, we get 10+3 =13
so, the consecutive numbers are 4, 7, 10, 13.
As a result, p = 7 and q = 10
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For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 6 N acts on a certain object, the acceleration
of the object is 3 m/s². If the force is changed to 20 N, what will be the acceleration of the object?
00
8
X
Ś
PLEASEEEE HELPPP MEEEEEEE
When the object's acceleration reaches 6.67 m/s2, the force is 20 N.
The mass of an object determines the acceleration it experiences.
The force is 6 N if the object's acceleration increases to 3 m/s2.
Reason:
The parameters listed are;
The occupying force the object's acceleration.
The acceleration produced by a force, F, of 18 N is equal to 6 m/s2.
Newton's Second Law of Motion states that;
F = M × A
Where;
m = The object's mass
In light of the parameters, F = 18 N and a = 6 m/s2, we may determine the mass of the
the following is the provided object;
Weight = F/A
Therefore, the force acting when the acceleration is an is;
20 = 3 kg, where a = a = 6.67 m/s2.
When the object's acceleration reaches 6.67 m/s2, the force is 20 N.
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Rose purchased a total of 17 books and toys for the Rupert play school. earn book cost $11 and each toy cost $6.How many books and toys did she buy for $157?
Answer: 11 Books, 6 Toys
Step-by-step explanation:
Let the number of books be B, and the number of toys be T
B+T=17
11B+6T=157
Let's use the elimination method:
11B+6T=157
6B+6T=102
And finally you get
5B=55
B=11
Use the value of B to get T
11+T=17
T=6
Therefore, the answer is
B=11,T=6
3 (2x - 4) = 3 (2x + 4)
[tex]3 (2x - 4) = 3 (2x + 4)[/tex]
Distribute:
[tex](3)(2x)+(3)(-4)=(3)(2x)+(3)(4)[/tex]
[tex]6x-12=6x+12[/tex]
Subtract 6x from both sides:
[tex]6x-12-6x=6x+12-6x[/tex]
[tex]-12=12[/tex]
Add 12 to both sides:
[tex]-12+12=12+12[/tex]
[tex]0=24[/tex] (false)
[tex]\fbox{No solution}[/tex]
Answer:
False Expresion, Wrong , Error
Step-by-step explanation:
if solving for x
3 (2x - 4) = 3 (2x + 4) insert the 3 into the parenthesis [remember to imput for each element])
6x - 12 = 6x +12 False expression
if we decide to go further we would get
0x = 24
help me with this please
Answer: D
Step-by-step explanation:
The amount needs to be saved 8 times, and the phrase "at least" means the value can be greater than or equal to. So, the answer's the 4th option.
The principal claims he only loses about 30 students a year. Do the values in the table support his claim? explain.
Indeed, the values in the table back up his assertion.
What is unitary method?
This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.
A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.
We typically utilize this technique for math calculations.
This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.
According to our question-
2% of 250 = 5, 4% of 200 = 8, and 8% of 150 = 12.
5 + 8 + 12 = 25
Hence, Indeed, the values in the table back up his assertion.
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Triangle ABC ~ triangle DEF. Use the image to answer the question.
Determine the length of sides AB and BC in triangle ABC.
AB = 9.68, BC = 7.04
AB = 8.8, BC = 6.4
AB = 9.152, BC = 6.656
AB = 7.92, BC = 5.76
Answer:
AB = 9.68, BC = 7.04
Step-by-step explanation:
AC/DC = 6.71/6.1 = 1.1 This is the proportionality factor
6.4(1.1) = BC = 7.04
8.8(1.1) = AB = 9.68
Find the distance between the two points rounding to the nearest tenth (if necessary).
(−6,4) and (−1,−8)
So on solving provided question we can say that given coordinates are
(−6,4) and (−1,−8)so equation is x - y +10 = 0
what are coordinates?A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.
given coordinates are
(−6,4) and (−1,−8)
so equation is
y-y1 = m(x-x1)
y-4 = x +6
x - y +10 = 0
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the ratio of the number of boys to the number of girls at school is 4:5. If there are 120 boys, how many students are there together?
Answer:
200/3
Step-by-step explanation:
4+5=9
5\9*120=200/3
=
Is (3,4, -2) a solution of the following system? 5x1 X2 + 2x3 = 7 -2x1 + 6x2 + 9x3 = 0 – 7x1 + 5x2 – 3x3 = -7
Yes, (3,4, -2) is a solution of the system. You can find the solution by substituting the values.
To check if (3,4,-2) is a solution of the system, we can substitute those values into each of the equations and see if they are true.
5x1 + 2x3 = 7
becomes
5(3) + 2(-2) = 7
which simplifies to
15 - 4 = 7
-2x1 + 6x2 + 9x3 = 0
becomes
-2(3) + 6(4) + 9(-2) = 0
which simplifies to
-6 + 24 - 18 = 0
-7x1 + 5x2 - 3x3 = -7
becomes
-7(3) + 5(4) - 3(-2) = -7
which simplifies to
-21 + 20 + 6 = -7
As we can see all the equation are true, (3,4,-2) is a solution of the system.
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expand and simplify, 7(3p+4)+5(2p-3)
Answer:
31p+13
Step-by-step explanation:
After expanding: 21p+28+10p-15
After simplifying: 31p+13
the hieghts of the people if the plant Ixx are normally distributed with a mean of 40 inches and a standard deviation of 5 inches. [ they are vertically diverse people.]
The percentage and the z-scores for specific heights of the given normal distributions are as detailed below.
How to Interpret normal distribution?
The first step is to draw the Normal curve with 8 regions, and then we now label the 7 vertical dividing lines with the mean plus/minus one/two/three standard deviations:
By adding the percentage values in the areas indicated in the question, we will arrive at;
The percentage of Ixxians that are;
i) Over 30 inches tall = 100% - (2.35% + 0.15%) = 97.5%
ii) Over 45 inches tall = 13.5% + 2.35% + 0.15% = 16%
iii) Under 50 inches tall = 100% - (2.35% + 0.15%) = 97.5%
iv) under 40 inches tall = 34% + 13.5% + 2.35% + 0.15% = 50%
v) between 35 and 55 inches tall = 34% + 34% + 13.5% + 2.35% = 83.85%
vi) between 25 and 35 inches tall = 13.5% + 2.35% 15.85%
The z-score is defined as the number of standard deviations above the mean corresponding to the given value. Thus;
i. For a height of 32 inches, the z-score is;
z = [32-40]/5
z = -1.6
ii. For a height of 47 inches, the z-score is;
z = [47 - 40]/5
z = 1.4
iii. For a height of 51 inches, the z-score is;
z = [51 - 40]/5
z = 2.2
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Complete question is;
The hieghts of the people if the plant Ixx are normally distributed with a mean of 40 inches and a standard deviation of 5 inches. [ they are vertically diverse people.]
a) What percentage of Ixxians are
i over 30 inches tall?
ii over 45 inches tall?
iii under 50 inches tall?
iv under 40 inches tall?
v between 35 and 55 inches tall?
vi between 25 and 35 inches tall?
b) What is the z-score for an Ixxian of height?
i. 32 inches?
ii. 47 inches
iii. 51 inches
Write the equation of the line that passes through the points (-2,-3) and (-4,17)
Answer: y=−2.8x + 11.4
Clare has $150 in her bank account. She withdraws $110 to buy a bike. What is Clare's account balance now?
Clare's account balance is $40
How to calculate the amount of money in Clare's account balance ?Clare has $150 in her bank account
She withdraws $110 from this money to purchase a bike
The amount of money left in her account after purchasing the bike can be calculated as follows
150-110
= 40
Hence Clare has $40 in her account after purchasing the bike
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How do you find the 1st and 2nd element of a pair?
An ordered pair is a set of two values, (x,y), where x and y are the coordinates. In an ordered pair, the first element is typically referred to as the x-coordinate, or the "first component" and it represents the horizontal position of the point on a coordinate plane. The second element is typically referred to as the y-coordinate, or the "second component" and it represents the vertical position of the point on a coordinate plane.
So, to find the first and second element of a pair, you can refer to the first element as the x-coordinate or the first component and the second element as the y-coordinate or the second component.
For example, in the ordered pair (4,3), the first element is 4, which represents the x-coordinate, and the second element is 3, which represents the y-coordinate.
Use the drop-down menus to complete the statement about the inequality d>3.
The inequality d > 3 has infinitely many solutions because 4 and any number to the right of 3 on the number line can be substituted for d to make this inequality true.
What are infinitely many solutions?In Mathematics, an equation or an inequality is said to have an infinitely many solutions when the left hand side and right hand side of the equation or inequality are the same and equal.
This ultimately implies that, an equation or an inequality would have infinitely many solutions when both sides of the equal sign are the same, and both the slope and y-intercept for the two lines are the same.
The given inequality d > 3 simply means that the variable d is greater than three (3). Therefore, d represents the set of all possible real numbers that are greater than 3 and from the right of 4 on the number line for d > 3 because it has infinitely many solutions.
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Complete Question:
Use the drop-down menus to complete the statement about the inequality d > 3.
The inequality d > 3 has _____ solutions because ______ can be substituted for d to make this inequality true.
Options: for the first one 0 1 2 8 9 Infinitely many
For the second one: No numbers only 1 number 4 and any number to the right of 3 on the number line
I’ll give brainliest please help! Using point slope form find the equation of the line with the given slope that passes through the given point
Answer:
it’s A
Step-by-step explanation:
I graphed it out
9) 60x-42y=0
-100x + 70y=0
ELIMATION
We solved using elimination method, For the given set of equations, no solution exists.
To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
Given,
two equations as
60x-42y=0 ........... (1)
-100x + 70y=0 ............(2)
Now, multiplying the equation (1) by 10 and (2) with 6
we get the equation as
⇒ (60x-42y=0) × 10
⇒ 600x - 420y = 0 ............(3)
⇒ (-100x + 70y=0 ) × 6
⇒ -600x + 420 = 0
Solving equation 2 and 3 simultaneously
⇒ 600x - 420y = 0
⇒ -600x + 420 = 0
⇒ x = y = 0
∴ No Solution exists for this problem
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Is √ 3x² 2x a polynomial?
Because it has a variable and that variable is raised to a certain power, the expression 3x2+2x is a polynomial.
A polynomial is a mathematical formula that involves only the operations addition, subtraction, multiplication, and powers of positive integers of the variables and is composed of coefficients and indeterminates.
A polynomial term, a series term, or an expression's multiplicative factor is known as a coefficient in mathematics. In addition to being any statement, it is frequently a number. If the coefficients are variables in and of themselves, they may also be known as parameters.
The fact that the above phrase 3x2+2x contains a variable makes it a polynomial. The power of that variable is likewise increased. The mathematical expression that results becomes a polynomial.
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PLEASE HELP (picture provided)
Answer:
Step-by-step explanation:
its the next one down
What are the 3 types of equality?
Equality is a fundamental component of a just and equitable society. It encompasses legal, social, and economic aspects, all of which are essential to ensure that all citizens are treated fairly and have access to the same rights and opportunities.
The 3 types of equalityLegal Equality: This type of equality is based on the laws and regulations of a society, which are designed to protect the rights of all citizens regardless of their gender, race, religion, or other characteristics.Social Equality: This type of equality focuses on the outcomes of a society in terms of how the members are treated. It looks at the quality of life, access to education, and economic opportunity for all citizens.Economic Equality: This type of equality looks at the distribution of wealth within a society. It examines how income and wealth are shared among various groups, and how this affects their ability to access resources and opportunities.Learn more about equality: https://brainly.com/question/9873909
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Which could be the missing first term of the expression that, when fully simplified, would be a binomial with a degree of 4? Select three options.
________ – 5xy3 + 9x2y
0
5xy3
9x2y
8y4
4xy3
its a multiply chose
The missing first term of the expression that, when fully simplified, would be a binomial with a degree of 4 include the following:
A. 0
C. 9x^2y
E. 4xy^3
What is a polynomial function?In Mathematics, a polynomial function simply refers to a type of mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.
In Mathematics, the canonical form for a polynomial in one variable (x) is given by this mathematical expression:
[tex]a_n x^n + a_{n-1} x^{n-1} +a_1 x^1 +a_0=0[/tex]
Since the degree of a polynomial function is the sum of exponents in each of its term, the required answer options must have exponents that are equal to those of the given polynomial function and these include the following:
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Answer: A C E
Step-by-step explanation:
Find the measure of each numbered angle.
Answer 50 for the bottom and 48 for the sides