The number of pounds of the chemical container can hold with given dimension is, 3600 pounds
What is Volume?In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.
Given that,
1 ft³ = 60 pounds
A container which has dimensions,
length = 6 ft
height = 4 ft
width = 5/2 ft
Volume of container = length × height × width
= 6 × 4 × 5/2
= 60 ft³
1 ft³ = 60 pounds
60 ft³ = 60 × 60 pounds
= 3600 pounds
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Guess the value of the limit (if it exists) by evaluating the function at the given numbers. (It is suggested that you report answers accurate to at least six decimal places.) Let f(x) : (cos(12x) - cos(3x))/x^2 We want to find the limit lim x=0 from (cos(12x) - cos(3x))/x^2 Start by calculating the values of the function for the inputs listed in this table. x fx 0.2 24.987664 0.1 -98.998848 0.05 -19.923683 0.01 -99.853172 0.001 -998.62855 0.0001 -9989.29525 0.00001 -99862.9534' Based on the values in this table, it appears : lim x=0 from (cos(12x) - cos(3x))/x^2=
The limit of the function (cos(12x) - cos(3x))/x^2 as x approaches 0 is approximately -99862.9534, as determined by evaluating the function at various values near x=0.
Let f(x) : (cos(12x) - cos(3x))/x^2
We want to find the limit lim x=0 from (cos(12x) - cos(3x))/x^2
Step 1: Calculate the value of the function for x=0.2
fx = (cos(12(0.2)) - cos(3(0.2)))/(0.2)^2
fx = (cos(2.4) - cos(0.6))/0.04
fx = (0.92358 - 0.95105)/0.04
fx = -24.987664
Step 2: Calculate the value of the function for x=0.1
fx = (cos(12(0.1)) - cos(3(0.1)))/(0.1)^2
fx = (cos(1.2) - cos(0.3))/0.01
fx = (0.9589 - 0.9511)/0.01
fx = -98.998848
Step 3: Calculate the value of the function for x=0.05
fx = (cos(12(0.05)) - cos(3(0.05)))/(0.05)^2
fx = (cos(0.6) - cos(0.15))/0.0025
fx = (0.9802 - 0.9657)/0.0025
fx = -19.923683
Step 4: Calculate the value of the function for x=0.01
fx = (cos(12(0.01)) - cos(3(0.01)))/(0.01)^2
fx = (cos(0.12) - cos(0.03))/0.0001
fx = (0.9999 - 0.9998)/0.0001
fx = -99.853172
Step 5: Calculate the value of the function for x=0.001
fx = (cos(12(0.001)) - cos(3(0.001)))/(0.001)^2
fx = (cos(0.012) - cos(0.003))/0.000001
fx = (0.999983 - 0.999971)/0.000001
fx = -998.62855
Step 6: Calculate the value of the function for x=0.0001
fx = (cos(12(0.0001)) - cos(3(0.0001)))/(0.0001)^2
fx = (cos(0.0012) - cos(0.0003))/0.00000001
fx = (0.99999983 - 0.99999971)/0.00000001
fx = -9989.29525
Step 7: Calculate the value of the function for x=0.00001
fx = (cos(12(0.00001)) - cos(3(0.00001)))/(0.00001)^2
fx = (cos(0.00012) - cos(0.00003))/0.0000000001
fx = (0.9999999983 - 0.9999999971)/0.0000000001
fx = -99862.9534
Therefore, the limit of the function
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Evaluate ∭ (x + y + z) dV , where E is the solid in the first octant that lies under the paraboloid z = 9 − x^2 − y^2.
By evaluating ∭ (x + y + z) dV, the final answer is 342.
What is the change of variables method?
In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better-understood problem.
We can evaluate the triple integral by using the change of variables method. We can set u = x, v = y, and w = z, and find the corresponding bounds for each variable in terms of the original bounds.
Then, we have
∭ (x + y + z) dV = ∭ (u + v + w) det(J) du dv dw,
where J is the Jacobian matrix of the transformation and det(J) is its determinant.
We know that 0 <= x <= 3, 0 <= y <= 3, and 0 <= z <= 9 - x^2 - y^2. Therefore, we have:
u = x, 0 <= u <= 3
v = y, 0 <= v <= 3
w = z, 0 <= w <= 9 - u^2 - v^2
The determinant of the Jacobian matrix is 1, so we can simplify the integral to:
∭ (u + v + w) du dv dw = ∫(0,3) ∫(0,3) ∫(0,9-u^2-v^2) (u+v+w) dw dv du
= ∫(0,3) ∫(0,3) (u+v)(w) + (1/3)(w^3) dv du
Hence, By solving this iteratively we get the final answer as 342.
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Find the surface area of the soild.
Answer:
288
Solution
(8x5)x4=160
(8x8)x2=64
160+64=288
what is the slope through the line of (-8, 11) and (-1, -5)
Answer:
-2.29
Step-by-step explanation:
Slope is Y - Y/X - X
- 5 - 11/ - 1 - (- 8)
-16/-1+8
-16/7
-2.29
question a factory manager selected a random sample of parts produced on an old assembly line and a random sample of parts produced on a new assembly line. the difference between the sample proportion of defective parts made on the old assembly line and the sample proportion of defective parts made on the new assembly line (old minus new) was 0.006. under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being the proportion of defective parts made on the old assembly line is greater than that of the new assembly line. the pp-value of the test was 0.018.
Two methods can be used to administer the test.
A different theoryAbsent HypothesisThe justification for each of them is given below.What is hypothesis?Writing down the hypothesis throughout the proposal phase is required. Instead of a hypothesis that develops as a result of looking at the data, this will help to keep the research effort concentrated on the main goal and establish a firmer foundation for evaluating the study's outcomes. For these questions, answer option C is the best choice.Another possibility is that there are more faulty parts produced on the old assembly line than on the new assembly line.The value of the p is equal to 0.018, which is equivalent to 0.06 under the null hypothesis that the proportion of defective components produced on the old assembly line is equal to that produced on the new assembly line.Therefore, We infer that the solution to these questions is option C. The likelihood of noticing a difference of 0.006 is 0.018 if there is no difference in the proportions of all defective parts produced on the two assembly lines.
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Over the last 50 years the average cost of a car has increased by a total of 1,126%. If the average cost of a car today is 30.031, how much was the average cost 50 years ago.
The amount of average cost 50 years ago will be $2,667.05.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Over the last 50 years, the average cost of a car has increased by a total of 1,126%. If the average cost of a car today is 30,031. Then the amount of average cost 50 years ago will be given as,
⇒ $30,031 / 1,126%
⇒ $30,031 / 11.26
⇒ $2,667.05
The amount of average cost 50 years ago will be $2,667.05.
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what is the slope through the line of (6, 3) and (5, -1)
Answer:
slope is 4
Step-by-step explanation:
A random survey of autos parked in the student lot and the staff lot at a large university classified the brands by county of origin, as seen in the accompanying table. Are there differences in the national origins of cars driven by students and staff?
Yes there is difference in the national origins of cars driven by students and staff, and that is 31 cars.
Following is the table showing the data of the survey of auto parked in the student lot and the staff lot, classified the brands by the country of origin. we can see that total number of car of all the given countries, driven by the students is 195. And the total number of car of all the given countries, driven by the staff is 164.
So the difference is 195 - 164 = 31 cars.
--The given question is incomplete, the complete question is
"A random survey of autos parked in the student lot and the staff lot at a large university classified the brands by country of origin, as seen in the accompanying table. Are there any difference in the national origins of cars driven by students and staff?
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a telegraph pole is supported by a wire, the wire is attached to the pole 6m above the ground and to a point on the ground 2.5m from the foot of the pole calculate the total length of the wire needed, if an extra 0.8m is needed for the attachment.
A wire that supports telegraph poles is joined to them at intervals of 6 metres above the ground and 2.5 metres from the pole's foot for a total length of 7.3 metres.
What is the length between two telephone poles?Assume that x is the wire's length. [tex]$x^2=2.5^2+6^2$[/tex] Pythagorean theory [tex]$x^2=6.25+36$[/tex]
[tex]$x^2=6.25+36$\\ $x^2=42.25$[/tex]
As [tex]$x > 0, x=\sqrt{42,2 \sqrt{2}}=6, \sqrt{m}$[/tex]
Total length [tex]$=6.5+2.8=7.3 \mathrm{~m}$[/tex]
There are 50 metres between each telephone pole. Utility poles are made more stable by guy wires. The pole is covered by a ground wire the entire way around. Any power on the pole is safely directed underground by this device. This is a representation of the essential hardware that can differ depending on where you are found on a distribution pole. Typically, lineside telegraph poles are placed 60 to 70 yards apart, a little closer, and ideally within curves.
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Open MINITAB file rateMP.mpj from your email. This data represents information on 700 instructors from the popular website ratemyprofessors.com. All instructors are sampled from the Foothill-De Anza Community College District. Here is a description of the data: College: Foothill or De Anza Smiley: Positive - Neutral Negative Photo: Instructor has a photo Hot: Instructor has a chili pepper Gender: Male or Female Dept: Academic Department (example - Mathematics) Division: Academic Division (example - PSME) Num: Number of Ratings for that faculty member Overall: Average Overall Quality Rating (1-5 scale, lowest to highest) Easiness: Average Easiness Rating (1-5 scale, hardest to easiest) We are going to use Minitab to make some graphs for this data. Specifically, we are going to look at the average easiness rating of Foothill-De Anza Community College instructors, and we will use the 700 instructors as a sample. First, let's ask some questions about this data.
What is the average easiness rating of Foothill-De Anza Community College instructors? What are the distributions of easiness ratings for instructors with a photo, chili pepper, and no chili pepper? Is there a relationship between gender and easiness ratings?
To answer these questions, we first need to open the MINITAB file rateMP.mpj. Upon opening the file, we can see that it contains data on 700 instructors from Foothill-De Anza Community College, including the college they teach at, their gender, the department and division they teach in, the number of ratings they have received, their overall quality rating, and their easiness rating. To answer the first question, we can use the average function on the easiness column to find the overall average easiness rating of Foothill-De Anza Community College instructors. To answer the second question, we can use a bar chart to compare the distributions of easiness ratings for instructors with a photo, chili pepper, and no chili pepper. To answer the third question, we can use a two-way table to examine the relationship between gender and easiness ratings. After creating these graphs and tables, we can then interpret our results.
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the coefficient of determine (r2) gives information on both the direction of the linear relationship between 2 quantitative variables and the tightness of the linear relationship
The lowest possible value of R² is 0 and the highest possible value is 1. Put simply, the better a model is at making predictions, the closer its R² will be to 1.
The coefficient of determination (R²) measures how well a statistical model predicts an outcome. The outcome is represented by the model’s dependent variable.
The lowest possible value of R² is 0 and the highest possible value is 1. Put simply, the better a model is at making predictions, the closer its R² will be to 1.
Suppose that you perform a simple linear regression that predicts students’ exam scores (dependent variable) from their time spent studying (independent variable).
If the R2 is 0, the linear regression model doesn’t allow you to predict exam scores any better than simply estimating that everyone has an average exam score.
If the R2 is between 0 and 1, the model allows you to partially predict exam scores. The model’s estimates are not perfect, but they’re better than simply using the average exam score.
If the R2 is 1, the model allows you to perfectly predict anyone’s exam score.
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The local historical society wants to preserve two buildings. The total age of the buildings is 219 years. If one building is
twice as old as the other, what are the ages of the two buildings?
Both buildings are 219 years old, with the newer one being 73 years old.
What is an expression?A mathematical expression is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.
In light of this, the buildings' combined age is 292 years.
Now,
If the newer structure is x years old, the older structure is 3 times that old.
The buildings here have a combined age of 292 years.
Therefore, we obtain: x + 3x = 292 x 4x = 292 x x = 73
Thus, the more recent structure is 73 years old, or x years old.
The older structure is also three times older.
219 years old is 3 times 73.
As a result, the older building is 219 years old, while the more recent structure is 73 years old.
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Compute the expression shown below.
3
(3.0 × 10-3) ³
Submit your answer in scientific notation.
The result of the given expression in the scientific notation is 2.7 × 10⁻⁸.
What is the scientific notation answer?
Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10⁸.
To compute the expression (3.0 × 10⁻³)³, we can use the following steps.
Multiply 3.0 × 10⁻³ by itself three times.
The expression (3.0 × 10⁻³)³ can be calculated as follows:
(3.0 × 10⁻³)³ = (3.0)³ × (10⁻³)³ = 27 × 10⁻⁹
So the answer in scientific notation is 2.7 × 10⁻⁸.
Therefore, the answer in scientific notation is 2.7 × 10⁻⁸.
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Can some help? I will give brainliest!
Answer: the answer I don’t know
Step-by-step explanation:
PLS help ASAP anything will help me
Answer:
1. x/0=7
2.x+1=2
3. x=7
Step-by-step explanation:
1. you can't divide by zero so it's undefined
2. x=1
3. when you graph this on a graph, the line goes on forever, as long as it satisfies the equation x+1.
A regular hexagon is composited of 6 equilateral Triangles.
X is 6.7cm.
What is the vertical height of the hexagon?
X
According to the question of equilateral triangles, 6.7√3 cm is the vertical height of the hexagon.
What is equilateral triangles?An equilateral triangle is a triangle with all three sides having the same length and all three angles measuring 60 degrees. It is one of the three basic shapes in geometry and is considered to be the most symmetrical triangle. The sides of an equilateral triangle are always congruent, meaning all three sides have the same length. The sides of an equilateral triangle are also always perpendicular, meaning all three angles are equal to 60 degrees. The area of an equilateral triangle can be calculated using the formula A = (1/2)bh, where b is the length of the base and h is the length of the height.
The vertical height of the hexagon can be calculated using the Pythagorean Theorem. The length of each side of the equilateral triangle is x/2 and the height of the triangle is x√3/2.
The total vertical height of the hexagon is therefore 6 x x√3/2, which is equal to 6.7√3 cm.
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What’s the difference between 13/4 and 1/2
Answer:
11\4
Step-by-step explanation:
the lcm of 4 and 2 is 4. divide 4 by each denominator. your answer multiplied by the numerator. then you find the difference between the two numbers
if TU=10 and UV=10, , what is TV
Answer:
TV = 20
Step-by-step explanation:
TV is given by the formula
TV =TU + UV
From the question
TU = 10
AND
UV = 10
Therefore
TV= 10 + 10
TV = 20.
2. Evan runs a t-shirt business. He sells shirts for $10. After selling 10 shirts, Evan has $70. Assume x represents the number of shirts sold, and y represents the profit, use this information to fill in the blanks in the statement: How much money did Evan have before he sold any shirts?
A) -$30
B) $30
C) $100
D) $0
Answer:
D
Step-by-step explanation:
The statement says that Evan sells shirts for $10 and after selling 10 shirts, he has $70. We know that the profit is the revenue (the amount of money earned) minus the costs. In this case, the revenue is the amount of money Evan earns from selling shirts and the costs are the amount of money Evan has spent on producing and buying the shirts. We can use this information to set up the equation y = 10x - c where y is the profit, x is the number of shirts sold, and c is the costs.
Given that Evan has $70 after selling 10 shirts, we can substitute 10 for x and 70 for y into the equation to get:
70 = 10(10) - c
Solving for c we get:
c = -30
This means that the costs were $30. To find out how much money Evan had before he sold any shirts we need to subtract the costs from the initial amount. Evan had $0 before he sold any shirts, so the answer is D) $0.
find $a$ if $a$ and $b$ are integers such that $x^2 - x - 1$ is a factor of $ax^{17} bx^{16} 1$.
a must be equal to zero for the given equation to be true.
The given polynomial can be written in the form [tex]$(x-1)(x+1) = 0$[/tex]. This expression can be equated to zero to solve for $x$. By equating it to zero and solving, we can find that [tex]$x = 1$[/tex] and [tex]$x = -1$[/tex]. We can substitute each of these values into the given equation and solve for $a$.
Forx = 1:
[tex]$a(1)^{17}b(1)^{16}1 = 0$ \\ $a\cdot 1 \cdot b \cdot 1 \cdot 1 = 0$\\$a \cdot b = 0$[/tex]
Therefore, $a$ must be equal to zero for the given equation to be true.
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The variables x and y are proportional.Use the vaules to find the constant aof proportonality.Then write the equation that relates x and y. When y = 20, x=12.
PLEASE HELP
The equation that relates x and y is: x = 3y/ 5
What is direct proportion?A direct proportion is a variation in which two given variables are related to one another in such a way that as the value of one increases, the values of the other also increases.
Thus, given that x and y are proportional, we have;
x [tex]\alpha[/tex] y
x = ky
But x = 12, and y = 20. Then;
12 = k*20
k = 12/ 20
= 3/5
So that,
substituting the value of k, to have
x = 3/5 * y
= 3y/ 5
x = 3y/ 5
Therefore, the equation that relates x and y is: x = 3y/ 5
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Please hurry
The distance between two cities is listed
as 2,462 miles. Which number represents
the best approximation of this distance
in miles?
alsvej
2.4 × 10²
K
2.4 x 10³
L
2.5 × 10²
M 2.5 × 10³
N 2.6 × 10³
Answer:
M
Step-by-step explanation:
2,462 rounded is 2,500
2.5 × 10^3= 2,500
The answer is 2.5 × 10³ Because its = 2500
During 2022, Frank Stewart purchased 220 shares of common stock issued by Red Hot Food Processing for $3100 including commission. Later in the same year, Frank sold the shares for $3200 after commission. Calculate the following. (Round all answers to two decimal places.)
1: profit of his stock transaction
2: Percentage return on investment:
The computation of the profit and percentage return on Frank Stewart's stock transaction is as follows:
1) Profit = $1002) Percentage return = $3.23%.What are profits and percentage returns?Profits represent the gain generated from an investment or business activity.
The percentage returns are the profits expressed as a percentage of the investment.
The percentage returns are also known as the return on investment (ROI).
Total investment in the common stock of Red Hot Food Processing = $3,100
The sales proceeds after commission = $3,200
Profit = $100 ($3,200 - $3,100)
Percentage return = 3.23% ($100/$3,100 x 100)
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Given the two rectangles below. Find the area of the shaded region.
Answer:
The area of the shaded region is 36.
Step-by-step explanation:
First, let's find the area of the rectangle as a whole, which will be 5*10 = 50. How did we get 50? The right side is 5 (from 2+3), and the top is 10 (3+7). Multiplying those numbers together will give you the area.
Now, the problem asks to find the shaded region. Let's solve for the area of the non-shaded region: (7*2) = 14.
Now, we can subtract the whole rectangle area minus the non-shaded region to find the shaded region:
50 - 14 = 36
A poll of 1,000 randomly selected registered voters was taken and 680 responded that they favor candidate X for mayor (p 1 = 0.6800). Just before the election, another poll of 900 registered voters was taken and 598 individuals responded that they favor candidate X (p 2 = 0.6644). A 90% two-proportion z confidence interval for the true difference between p 1 and p 2was found to be (-0.0199, 0.0510). What is the meaning of the interval in the context of the problem?
a)There has been no change in support for the candidate.
b)There has been a substantial drop in support for the candidate.
c)There has been a substantial gain in support for the candidate.
d)It is probable for the candidate to get most of the votes because the confidence interval includes zero.
e)It is not probable for the candidate to get most of the votes because support has dropped below 50%.
The meaning of the interval is "there has been no change in support for the candidate". Thus, option (a) is correct.
The 90% two-proportion z-confidence interval (-0.0199, 0.0510) represents the likely range of the genuine difference between the two polls in support of candidate X.
Because the interval comprises 0, the difference in support between the two polls is unlikely to be statistically significant. In other words, there is no compelling evidence that there has been a significant shift in support for the candidate.
Options b), c), d), and e) imply a substantial change in support for the candidate, either positive or negative.
Thus, option (a) is correct.
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From the observation deck of a skyscraper, Morgan measures a 67∘ angle of depression to a ship in the harbor below. If the observation deck is 955 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
405.37
Step-by-step explanation:
tan(67) = 955/ X
(tan(67) )(X), (955) (X)
X tan(67) = 955
X tan(67)/ tan(67) = 955/ tan(67)
X= 405.37
List the values of x at which f has a local minimum. Select the correct
choice below and fill in any answer boxes within your choice.
The correct choice is b. There are no local maxima. The intervals where the function is increasing. Since the square of any real integer is always positive, the function 3x² will always be growing right since it will never be less than 6 right.
What is mean by local maxima? Local maxima refers to the highest point on a graph in a particular neighborhood. It is the highest value of a function in a region of its domain, which lies immediately before and after a lower value. It is a point where the slope of the graph is zero, or the point at which the graph changes direction from increasing to decreasing. Local maxima can be used to identify regions of increased activity or intensity in a graph, or they can be used to determine the rate of change of a function over a range of values. Local maxima are also known as local peaks or local extrema.To learn more about local maxima refer to:
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i got it nevermind!!!! dont need help
The Vales of x in the equations are : 1) 3 (2) 1 (3) 5 (4) 14 (5) 10 respectively
How to solve an equation?A linear equation in one variable is that in which the highest power of its variable is 1
The given equations and their solutions are
2x +1 = 7
By collecting like terms we have
2x = 3
x = 3
2) The given equation is 4x +7 = 11
By collecting like terms we have
4x = 4
Making x the subject we have
x = 1
3) 2x -3 = 7
By collecting like terms we have
2x = 10
Making x the subject we have
x = 5
4) 1/2 x - 3 = 7
By collecting like terms we have
1/2x = 7
x= 14
5) The given equation is 3x - 11 = 19
By collecting like terms we have
3x= 30
Therefore x= 10
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approximately where does the particle achieve its greatest possible acceleration on the interval 0 to b?
The greatest positive acceleration occurs at the midpoint of the interval, when the particle is changing velocity most rapidly.
What is velocity?
Velocity is a measure of the rate of change of an object's position over a period of time. It is a vector quantity, which means it has both magnitude (or size) and direction. Velocity is usually expressed in terms of distance traveled per unit of time, such as meters per second (m/s). Velocity can be determined by dividing the distance traveled by the time taken. For example, if an object travels 20 meters in 5 seconds, its velocity would be 4 m/s. Velocity can also be calculated by taking the derivative of the object's position with respect to time.
The particle will achieve its greatest positive acceleration at the midpoint of the interval, at t = b/2.
This is because the acceleration is greatest when the velocity is changing most rapidly.
At the beginning of the interval, the particle has zero velocity, so it has no acceleration.
At the end of the interval, the particle has reached its maximum velocity, and the rate of change of velocity is zero, so it has no acceleration. Therefore, the greatest positive acceleration occurs at the midpoint of the interval, when the particle is changing velocity most rapidly.
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The Palestinian ministry of sports has four basketball games on a particular night. The ministry wants to assign four teams of officials to the four games in a way that will minimize the total distance traveled by the officials. The supply is always one team of officials and the demand is for only one team of officials at each game. The distances in km for each team of officials to each game location are shown in the following table: officials 1 2 3 a 90 10 100 b 50 40 40 c 60 170 90 A) Formulate this problem as Assignment Model (the objective function and constraint equations for the demand and supply). b) Use QM to solve the Model.
The optimal solution is to assign team 1 to game A, team 2 to game C, and team 3 to game B. The total distance traveled by the officials is 200km.
A) Objective Function:
Minimize Z = 90x1A + 10x1B + 100x1C + 50x2A + 40x2B + 40x2C + 60x3A + 170x3B + 90x3C
Constraints:
x1A + x1B + x1C = 1
x2A + x2B + x2C = 1
x3A + x3B + x3C = 1
x1A, x1B, x1C, x2A, x2B, x2C, x3A, x3B, x3C ≥ 0
B) The optimal solution is as follows:
x1A = 1
x1B = 0
x1C = 0
x2A = 0
x2B = 0
x2C = 1
x3A = 0
x3B = 1
x3C = 0
Z = 200 km
1. Create the objective function
Z = 90x1A + 10x1B + 100x1C + 50x2A + 40x2B + 40x2C + 60x3A + 170x3B + 90x3C
2. Set the constraints
x1A + x1B + x1C = 1
x2A + x2B + x2C = 1
x3A + x3B + x3C = 1
x1A, x1B, x1C, x2A, x2B, x2C, x3A, x3B, x3C ≥ 0
3. Solve the linear programming problem
Using QM, the optimal solution is:
x1A = 1
x1B = 0
x1C = 0
x2A = 0
x2B = 0
x2C = 1
x3A = 0
x3B = 1
x3C = 0
4. Calculate the total distance
Z = 90x1A + 10x1B
The optimal solution is to assign team 1 to game A, team 2 to game C, and team 3 to game B. The total distance traveled by the officials is 200km.
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