Find the matrix exponentia M(t) = etA The eigenvalues of A are X1 = 1 and X2 = 2. Please denote exponentiation with exp(a*t rather than e**(a*t or e^(a*t) This is a symbolic input so use exact values (e.g. ) rather than decimal approximations (0.5) Enter the matrix componentwise below M11(t)= M12t)= M21(t)= M22(t)
Answers
The matrix exponential M(t) = exp(t*A) are: M11(t) = exp(1*t)*(-1/2)*(-1/2) + exp(2*t)*(1/2)*(1/2) = (1/4)*exp(t) + (1/2)*exp(2*t)
M12(t) = exp(1*t)*(-1/2)*(1) + exp(2*t)*(1/2)*(1) = (1/2)*(exp(2*t) - exp(t))
M21(t) = exp(1*t)*(1)*(1/2) + exp(2*t)*(1/2)*(1) = (1/2)*(exp(2*t) + 1)
M22(t) = exp(1*t)*(1)*(1) + exp(2*t)*(1)*(1) = exp(t) + exp(2*t)
To find the matrix exponential M(t) = exp(t*A), we first need to find the eigenvectors of A corresponding to the eigenvalues X1 = 1 and X2 = 2.
For X1 = 1, we solve the equation (A - I)*v = 0, where I is the identity matrix:
(A - I)*v = (1 1; 2 2 - 1)*v = 0
RREF([A - I, zeros(2,1)])
ans =
0 0 -1
0 0 0
So we have the equation -v2 = 0, which means v2 can be any non-zero value. Let's choose v2 = 1, then v1 = -1/2. So the eigenvector corresponding to X1 is v1 = (-1/2; 1).
For X2 = 2, we solve the equation (A - 2*I)*v = 0:
(A - 2*I)*v = (-1 1; 2 -2)*v = 0
RREF([A - 2*I, zeros(2,1)])
ans =
0 0 -1
0 0 0
So we have the equation -v2 = 0, which means v2 can be any non-zero value. Let's choose v2 = 1, then v1 = 1/2. So the eigenvector corresponding to X2 is v2 = (1/2; 1).
Now we can construct the matrix exponential M(t) = exp(t*A) using the formula:
M(t) = c1*exp(X1*t)*v1*v1' + c2*exp(X2*t)*v2*v2'
where c1 and c2 are constants determined by the initial conditions. Since we don't have any initial conditions given, we can choose c1 = 1 and c2 = 0 for simplicity.
So we have:
M11(t) = exp(1*t)*(-1/2)*(-1/2) + exp(2*t)*(1/2)*(1/2) = (1/4)*exp(t) + (1/2)*exp(2*t)
M12(t) = exp(1*t)*(-1/2)*(1) + exp(2*t)*(1/2)*(1) = (1/2)*(exp(2*t) - exp(t))
M21(t) = exp(1*t)*(1)*(1/2) + exp(2*t)*(1/2)*(1) = (1/2)*(exp(2*t) + 1)
M22(t) = exp(1*t)*(1)*(1) + exp(2*t)*(1)*(1) = exp(t) + exp(2*t)
So the matrix exponential M(t) is:
M(t) = ( (1/4)*exp(t) + (1/2)*exp(2*t) (1/2)*(exp(2*t) - exp(t));
(1/2)*(exp(2*t) + 1) exp(t) + exp(2*t) )
To find the matrix exponential M(t) = exp(tA) given that the eigenvalues of matrix A are λ1 = 1 and λ2 = 2, we first need to find the eigenvectors corresponding to each eigenvalue, and then form the matrix P of eigenvectors and the diagonal matrix D of eigenvalues. Finally, we can compute M(t) using the formula:
M(t) = P * exp(tD) * P^(-1)
After finding the eigenvectors and forming the matrices P and D, compute exp(tD) by taking the exponentiation of each diagonal element:
exp(tD) = | exp(tλ1) 0 |
| 0 exp(tλ2) |
Now, compute M(t) by multiplying P, exp(tD), and the inverse of P. The resulting matrix M(t) will have the following components:
M11(t) = exp(1*t)*(-1/2)*(-1/2) + exp(2*t)*(1/2)*(1/2) = (1/4)*exp(t) + (1/2)*exp(2*t)
M12(t) = exp(1*t)*(-1/2)*(1) + exp(2*t)*(1/2)*(1) = (1/2)*(exp(2*t) - exp(t))
M21(t) = exp(1*t)*(1)*(1/2) + exp(2*t)*(1/2)*(1) = (1/2)*(exp(2*t) + 1)
M22(t) = exp(1*t)*(1)*(1) + exp(2*t)*(1)*(1) = exp(t) + exp(2*t)
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Related Questions
let A and B be nxn matrices. We say that A is similar to B if B = P^-1 AP for some invertible matrix P.
Suppose that if A and B are nxn matrices such that A is similar to B. Prove that if A is invertible then B is invertible and A^-1 is similar to B^-1.
Answers
If A is similar to B, and A is invertible, then B is also invertible and the inverse of A, denoted as A^(-1), is similar to the inverse of B, denoted as B^(-1). This can be proved by showing that B^(-1) = (P^(-1))^(-1) A^(-1) P^(-1), where P is the invertible matrix that relates A and B.
Given that A is similar to B, we have B = P^(-1)AP for some invertible matrix P. If we multiply both sides of this equation by P, we get BP = P(P^(-1)AP). Since P^(-1)P is the identity matrix, we have BP = (PP^(-1))AP, which simplifies to BP = A.This shows that B is invertible, with B^(-1) = P^(-1)AP.
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what is the approximate radius of a sphere with a volume of 1436m^3
Answers
Answer: r≈7m
Step-by-step explanation:
Ayo fam thanks for the help. 15 Points for this one!
Answers
B is the only line that visually passes through the both of them
and line E’s degree is double of line D
onsider the following production function: y = F(L, K) = 4L3 K} = where L and K are the amount of labour and capital used in the production process, and y is the output. Throughout this question, the output price p is 3 and the rental rate of capital r is 1. We will first consider a firm in the short run, where the amount of capital is fixed at K = 64. The fixed cost is therefore 64. = (a) (Level A) Is there diminishing returns to labour? Explain. (b) (Level A) Suppose the wage rate w is 1. Find the profit-maximising choice of L. Calculate the profit-maximising output level and the maximised profit. (There is no need to check the second order condition but of course you can check if you want to.) (c) (Level A) Now suppose w increases to 2. Find the profit-maximising choice of L. Calculate the profit-maximising output level and the maximised profit. (There is no need to check the second order condition.) You can leave your answers in square roots. (d) (Level A) What is the change in L when w increases from 1 to 2 in the short run? You can leave your answers in square roots.
Answers
Yes, there are diminishing returns to labor in the given production function.
What is the profit-maximizing choice of labor and the resulting output and profit level when the wage rate is 1?
There are diminishing returns to labor in the given production function. As more units of labor (L) are added while holding capital (K) constant, the increase in output (y) becomes smaller and smaller. This is indicative of diminishing marginal product of labor.
When the wage rate (w) is 1 and the capital (K) is fixed at 64, the profit-maximizing choice of labor (L) can be found by equating the marginal product of labor (MPL) to the wage rate. In this case, MPL = 12L^2K.
Setting MPL = w, we have 12L^2K = 1. Substituting K = 64, we get 12L^2 * 64 = 1. Solving for L, we find L ≈ 0.0917.
The profit-maximizing output level (y) can be calculated by substituting the values of L and K into the production function. Thus, y = 4L^3K = 4(0.0917)^3 * 64 ≈ 0.026.
The maximized profit can be determined by subtracting the total cost (TC) from the total revenue (TR). Since the fixed cost is given as 64, TC = 64 + wL = 64 + 1(0.0917) ≈ 64.092. TR is the product of the output level and the price, which is 0.026 * 3 = 0.078.
Profit = TR - TC ≈ 0.078 - 64.092 ≈ -63.014.
Diminishing returns to labor imply that as more labour is employed while holding other factors constant, the incremental increase in output becomes smaller. In the given production function, this phenomenon is observed. In the short run, with a fixed capital level of 64, we determine the profit-maximizing choice of labour (L) when the wage rate (w) is 1. By equating the marginal product of labour (MPL) to the wage rate, we find L ≈ 0.0917. Substituting this value into the production function, we calculate the profit-maximizing output level as y ≈ 0.026. The maximized profit is determined by subtracting the total cost (TC) from the total revenue (TR), resulting in a profit of approximately -63.014. This analysis helps understand the relationship between input choices, output levels, and profit optimization in the short run.
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10 oranges and 20 grapefruits weigh 35 pounds total. 16 oranges and 10grapefruits weigh 23 pounds total. How much would 13 oranges and 15grapefruits weigh?A 28 poundsB 29 poundsC 30 poundsD 58 pounds20 Illuminate Education, Inc.
Answers
First, we will find the weight of each oranges and grape fruit
Let x be the unit weight of orange
Let y be the unit weight of grape fruit
If "10 oranges and 20 grapefruits weigh 35 pounds total"
Then this implies;
10x + 20 y = 35 -----------------(1)
And
If " 16 oranges and 10 grapefruits weigh 23 pounds total"
This implies;
16x + 10y = 23 ---------------------(2)
We can solve the two equations simultaneously.
Using elimination method;
we eliminate y and to do that, the y variables in the two equations must be same, Hence we can achieve that by multiply equation (1) by 10 and then multiply equation (2) by 20
100x + 200y = 350 ----------------------------(3)
320x + 200y = 460 ------------------------------(4)
subtract equation (3) from equation (4)
220x = 110
divide both-side of the equation by 220
x = 0.5
substitute x=0.5 into equation(1) and then solve for y
10(0.5) + 20y = 35
5 + 20y = 35
subtract 20 from both-side of the equation
20y = 35 - 5
20y = 30
divide both-side of the equation by 20
y = 1.5
"13 oranges and 15 grape fruits" = 13 x + 15y
substituting x = 0.5 and y= 1.5 in the above;
13(0.5) + 15(1.5)
=6.5 + 22.5
=29
Hence;
13 oranges and 15 grapefruits will weigh 29 pounds
Pls, Help!!
Which claim about the function of the endoplasmic reticulum (ER) can be supported by evidence from the table and graph?
a
The ER stores proteins.
b
The ER helps proteins pass through the cell membrane.
c
The ER transports proteins.
d
The ER works only with the nucleus.
Answers
The claim about the function of the endoplasmic reticulum (ER) is:
c. The ER transports proteins.What is endoplasmic reticulum?The endoplasmic reticulum is a network of flattened sacs and tubules that are located throughout the cytoplasm of eukaryotic cells.
The endoplasmic reticulum ER is responsible for the folding, modification, and transport of proteins that are destined for the plasma membrane, lysosomes, or secretion outside of the cell.
This is accomplished by transporting newly synthesized proteins through the endoplasmic reticulum ER lumen via vesicles.
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Help please dueeee now!
Answers
Answer:
8
Step-by-step explanation:
3(2)-2(1-2) / 3-2
6+2 / 1
8/1
= 8
Answer:
See the photo attached
Step-by-step explanation:
First, substitute the numbers in the Unknown variables
Then, you just calculate it (you may use calculator)
If there's any questions please don't hesitate to ask
Hope this is correct and helpful
HAVE A GOOD DAY!
What is the slope of the line shown?
(0,6)
(-2,0)
Underfined 6,3,0
Answers
Answer:
m = 3
Step-by-step explanation:
Answer:
The slope is 3
Step-by-step explanation:
rise is 12 run is 4. rise/run making the answer 3
Suppose that people check their coats in a checkroom. if all claim checks are lost and the coats are randomly returned, what is the probability that all the people will get their own coats back?
Answers
The probability that all the people will get their own coats back is 1/7.
What is probability?Likelihood is the part of science concerning mathematical depictions of how likely an occasion is to happen, or how likely it is that a suggestion is valid. The likelihood of an occasion is a number somewhere in the range of 0 and 1, where, generally talking, 0 shows difficulty of the occasion and 1 demonstrates sureness. The higher the likelihood of an occasion, the almost certain it is that the occasion will happen. A basic model is the throwing of a fair coin. Since the coin is fair, the two results are both similarly plausible; the likelihood of "heads" rises to the likelihood of "tails"; and since no different results are conceivable, the likelihood of all things considered "heads" or "tails" is 1/2.
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Triangle ABC is rotated by 135 degrees about point S to create A'B'C' what is the perimeter of ABC
Answers
Answer: 12.9
Step-by-step explanation:
5.1 + 2 + 5.8 = 12.9
The perimeter of the triangle ABC is 12.9 units.
What is the perimeter of a triangle?The perimeter of a triangle is the sum of length of three sides of the triangle.
Given, the triangle ABC is rotated by 135 degrees about point S to create the triangle A'B'C'.
We know, after rotation of a figure, the whole dimension of the figure remains the same.
Therefore, AB = A'B' = 5.1 units
BC = B'C' = 2 units
CA = C'A' = 5.8 units
Hence, the perimeter of the triangle ABC
= (5.1 + 2 + 5.8) units
= 12.9 units
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91) __________ involves the analysis of accumulated data and involves a __________. a) OLAP, database b) OLAP, data warehouse c) OLTP, database d) OLTP, data warehouse
Answers
OLAP is used for the analysis of accumulated data, and it requires a data warehouse.
while OLTP is used for transaction processing and requires a database optimized for real-time transaction processing. The analysis of accumulated data is known as Online Analytical Processing (OLAP), and it involves a data warehouse. OLAP is a business intelligence tool used for multi-dimensional analysis of large data sets, while a data warehouse is a central repository that stores historical and current data from multiple sources in a structured manner. OLAP allows users to perform complex queries on large data sets, analyze trends, and make informed business decisions. It is often used in data mining and decision support systems. OLAP tools can be used to slice and dice data, drill down to more detailed data, and roll up to higher levels of summary data. OLAP is primarily used for analytical purposes and is not designed for transaction processing. On the other hand, a data warehouse is designed to support OLAP and is used for storing large amounts of historical data that can be queried and analyzed. Data is extracted from various sources, transformed, and loaded into the data warehouse in a structured format, enabling efficient querying and analysis. OLTP (Online Transaction Processing), on the other hand, is a type of transaction processing that is designed for processing real-time transactions in databases. It is used for day-to-day operations such as order processing, inventory management, and customer management. OLTP is optimized for processing large volumes of transactions in real-time, and is not suitable for analytical purposes.
In summary, OLAP is used for the analysis of accumulated data, and it requires a data warehouse, while OLTP is used for transaction processing and requires a database optimized for real-time transaction processing.
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.
Explanation:
Two cousins, Glen and Gary, made resolutions to save
their money regularly in 2020. They are both going to
save a certain amount of money every month.
Gary
Number of
Months, x
1
2
3
4
Glen
Dollars Saved, y
$70
$100
$130
$160
$0 initial deposit;
will save $40 per month
Who is saving more money per month? Explain.
2. In how many months will Glen and Gary have the same
amount of money? Explain using mathematics.
Answers
In the word problem ,
1) Gary saves $30 per month and Glen saves $40 per month . Therefore Glen saves more than Gary.
2) In 4 months Gary and Glen both have same amount.
What is word problem?
Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
Here in the given table represent the monthly balance of Gary. Then
1)In 1st month = $70
2nd month = $100
3rd month = $130
4th month = $160
Here the amount of every month Gary adding is
=> 100-70=130-100=160-130 = $30.
Then Gary saves $30 per month and Glen saves $40 per month . Therefore Glen saves more than Gary.
2)Now both them have same amount is ,
=> 30x+40 =40x
=> 40x-30x =40
=> 10x=40
=> x = 4.
In 4 months both of them have same amount.
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3 + x = 9 solve for x
Answers
3+6=9
X=6
Answer: 6
Step-by-step explanation: You can use an algebraic equation to solve this.
3 + x = 9
-3 -3
_______
x = 6
One serving of gourmet ice cream has 25 grams of fat. Convert this to milligrams.
Answers
There are 1000 milligrams in 1 gram
Using the unit conversion of 1 gram = 1000 milligrams, one serving of gourmet ice cream has 25,000 milligrams of fat.
We have,
The concept used here is unit conversion.
We converted the quantity from grams to milligrams by multiplying it by the conversion factor between grams and milligrams, which is 1,000 milligrams per gram.
This is based on the fact that there are 1,000 milligrams in one gram.
To convert grams to milligrams, we need to multiply the number of grams by 1,000 since there are 1,000 milligrams in 1 gram.
So,
25 grams x 1,000 milligrams/gram
= 25,000 milligrams
Thus,
One serving of gourmet ice cream has 25,000 milligrams of fat.
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A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 8% margin of error at a 99% confidence level, what size of sample is needed
Answers
The required sample size is equal to 273.
We have given that,
A political candidate has asked you to conduct a poll to determine what percentage of people support her.
We have to determine the If the candidate only wants an 8% margin of error at a 99% confidence level,
p=0.5 (default since no value is given)
q=1-0.5=0.5
margin of error=5%=0.05
z_c=1.65 at 90% confidence.
What is the formula for marginal error?The margin of error:
\(e= sqrt(p(1-p)/n)*z_c\)
Use the given value in the above formula we get,
0.05=sqrt(0.5*0.5/n)*1.65
n= (0.5*1.65/0.05)^2=272.25
Therefore, The required sample size is equal to 273.
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Which description explains how the graph of f(x)=x√ could be transformed to form the graph of g(x)=x+9
Answers
Answer:
To transform the graph of f(x)=x√ into g(x)=x+9, we need to apply a horizontal shift to the right by 9 units. This can be done by replacing x in f(x) with x-9 to get g(x)=(x-9)√. The resulting graph will be the same as the graph of f(x), but shifted 9 units to the right.
Round 9.19 to the nearest 25 cents
Answers
The rounded form of the number 9.19 which represents $9 and 19 cents to the nearest 25 cents is; 9.25
What is the rounded form of 9.19 to the nearest 25 cents?It follows from the task content that the number is required to be rounded off to the nearest 25 cents.
On this note, it follows that only 25 cent intervals are considered.
Hence, the number in discuss can either be rounded up to 9.25 or 9.00.
However, since the fractional 19 cents is closer to 25 more than it is to 0 on the number line, the rounded form of the number is;
= 9.25.
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Find the area of the rectangles in the chart. Please NEED HELP
Answers
Answer:
1- 42
2- 90
3- 45
Step-by-step explanation:
lxw=area
Answer:
Formula Length *width
You multiple the length by the width to get the answer
Rectangle 1. = 6*7 = 42
Rectangle 2. =9*10 = 90
Rectangle 3. =5*9 = 45
Amaya used these steps to solve the equation 8x+4=9+4(2x−1)
. Which choice describes the meaning of her result, 4=5?
the choices are :
Amaya made a mistake because 4
is not equal to 5
.
No values of x
make the equation true.
.
All values of x
make the equation true.
.
The solution is x=4
or 5
.
Answers
Amaya made a mistake because 4 is not equal to 5. She incorrectly wrote 4=5 in the final step of solving the equation 8x+4=9+4(2x-1). So, the correct answer is A).
In step 1, Amaya sets up the equation 8x+4=9+4(2x-1).
In step 2, she simplifies the right side of the equation to 9+8x-4=5+8x.
In step 3, she subtracts 8x from both sides of the equation to get 4=5.
In step 4, she simplifies the equation to 4=9-4.
In step 5, she mistakenly writes that 4=5, which is incorrect.
Therefore, the correct choice is that Amaya made a mistake because 4 is not equal to 5. So, the correct option is A).
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REALLY NEED HELP WITH THIS
Answers
well, profit equations are usually a parabolic path like a camel's hump, profit goes up up and reaches a maximum then back down, the issue is to settle at the maximum point, thus the maximum profit.
So for this equation, like any quadratic with a negative leading coefficient, the maximum will occur at its vertex, with x-price at y-profit.
\(\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-5}x^2\stackrel{\stackrel{b}{\downarrow }}{+209}x\stackrel{\stackrel{c}{\downarrow }}{-1090} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 209}{2(-5)}~~~~ ,~~~~ -1090-\cfrac{ (209)^2}{4(-5)}\right) \implies\left( - \cfrac{ 209 }{ -10 }~~,~~-1090 - \cfrac{ 43681 }{ -20 } \right)\)
\(\left( \cfrac{ 209 }{ 10 }~~,~~-1090 + \cfrac{ 43681 }{ 20 } \right)\implies \left( \cfrac{ 209 }{ 10 }~~,~~-1090 + 2184.05 \right) \\\\\\ ~\hfill~\stackrel{ \$price\qquad profit }{(~20.90~~,~~ 1094.05~)}~\hfill~\)
You start driving east for 14 miles, turn left, and drive north for another 6 miles. At the end of driving, what is your straight line distance from your starting point? Round to the nearest tenth of a mile.
Answers
Answer: 15.2
Step-by-step explanation:
(14)^2 + (6)^2 = c^2
196 + 36 = c^2
232 = c^2
Square root both sides
15.231546 = c
15.2 ≈ c
The distance of the straight line from the starting point by the is is 15.2 miles.
What is the distance of a point from a line?The distance between a point and a line is the shortest distance between them.
Pythagoras TheoremIt states that if a triangle is right-angled (90 degrees), then the square of hypotenuse is equals to the sum of the squares of the other two sides.
Pythagoras Theorem EquationIf ΔOAB is a right angled triangle, right angle at A
then the Pythagoras equation will be
\(OB^{2} =AB^{2} +OA^{2}\)
(where OB, OA and AB are the length of the sides of triangle OAB)
According to the question
We have to find ,the distance of straight line from the starting point.
From, the provided figure we can conclude that OB is the straight line whose distance to be find
In ΔOAB, we have
\(OB^{2} =OA^{2} +AB^{2}\) (By Pythagoras theorem)
\(OB^{2} =14^{2} +6^{2}\)
\(OB^{2} =196+36\)
\(OB=\sqrt{232} \\OB= 15.23 miles\)
\(OB=15.2 miles\)
Hence, the distance of straight line from the starting point is 15.2 miles.
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Mio bought a tablet and pays monthly for internet service for it. She graphed the relationship between the number of months she has had the tablet and the total amount she has spent on it. What does the y-intercept represent in this context?
A) The number of months after which the cost is 0 dollars.
B) The cost per month of internet service.
C) The cost of buying the tablet.
Answers
Answer:
B) The cost per month of internet service.
7.G.1.3 The figure below shows a cube of side length 6 units. 6 Draw the shape of a vertical slice through the cube, assuming the slice is parallel to one of the faces of the cube. Label the dimensions of your drawing. please help I am struggling with this one
Answers
Answer:
the second dimension 2D
Please help 60 points for a rapid answer-In the figure below which of the following is true in circle E?
Answers
Answer:
all 3 options are true : A, B, C
Step-by-step explanation:
warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.
they say that A and C are correct.
but I am going to show you that if A and C are correct, then also B must be correct.
therefore, my given answer above is the actual correct answer (no matter what the test systems say).
originally the information about the alignment of the point F in relation to point E was missing.
therefore, I considered both options :
1. F is on the same vertical line as E.
2. F is not on the same vertical line as E.
because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :
the vertical line of EF is like a mirror between the left and the right half of the picture.
A is mirrored across the vertical line resulting in B. and vice versa.
the same for C and D.
this leads to the effect that all 3 given congruence relationships are true.
if we consider assumption 2, none of the 3 answer options could be true.
but if the assumptions are true, then all 3 options have to be true.
now, for the "why" :
remember what congruence means :
both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.
for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.
so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.
therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.
but do you notice something ?
both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.
now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.
therefore, AC must be equal to BD.
and that means that AC is congruent to BD.
because lines have no other congruent criteria - only the lengths must be identical.
Erica has two pieces of thread, one 14 feet long and the other 4 feet long. For a sewing project, she needs to cut them up to produce many pieces of thread that are all of the same length, with no thread left over. What is the greatest length, in feet, that she can make them?
Answers
Answer:
Step-by-step explanation:So to find the greatest common divisor, we need to factor these numbers.
4 = 2*214=2*7The same ones that matches each other is 2
so, the thread must be cut by 2 feet each to match the requirements that were given.
Determine the x-intercepts of each of the following functions. 2. y=x^2+5x−24 3. y=x^2−11x+10
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The x-intercepts of y=x2+5x−24 can be determined by solving the equation 0=x2+5x−24. Using the quadratic formula, we can find that x = 6 and x = -4 are the two x-intercepts.
The x-intercepts of y=x2−11x+10 can be determined by solving the equation 0=x2−11x+10. Using the quadratic formula, we can find that x = 5 and x = -2 are the two x-intercepts.
To determine the x-intercepts of the given functions, we need to find the values of x that make y equal to 0. We can do this by factoring the equations and setting each factor equal to 0.
2. y = x^2 + 5x - 24
0 = x^2 + 5x - 24
0 = (x + 8)(x - 3)
x + 8 = 0 or x - 3 = 0
x = -8 or x = 3
The x-intercepts are (-8, 0) and (3, 0).
3. y = x^2 - 11x + 10
0 = x^2 - 11x + 10
0 = (x - 1)(x - 10)
x - 1 = 0 or x - 10 = 0
x = 1 or x = 10
The x-intercepts are (1, 0) and (10, 0).
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The ability for nike to manufacture its own shoes and then build stores for distribution is an example of?
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The ability for Nike to manufacture its own shoes and then build stores for distribution is an example of Forward Integration.
What is forward integration ?
In order to lower manufacturing costs and increase efficiency, a sort of vertical integration known as "forward integration" moves up the supply chain.
An operational competency is what?
Functional competences are determined by the tasks and commitments employees make to a certain position. An average of three to five functional skills are ascribed to a given job, depending on the complexity and level of responsibility of the position as well as the seniority of the occupational role.Learn more about Forward Integration
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Please help me with this problem
Answers
Answer:
Answer is 41 ft
Step-by-step explanation:
From the right angled triangle above, two sides are known. That is the adjacent and opposite. The hypotenuse is not known so we represent it with a variable say h
Using Pythagora's theorem we have,
\( {h}^{2} = {12}^{2} + {12}^{2} \\ {h}^{2} = 144 + 144 \\ {h}^{2} = 288 \\ h = \sqrt{288} \\ h = 12 \sqrt{2} \)
Having found the value of the third side, the perimeter of the triangle can now be determined by summing up the length of all the sides.
\(perimeter = adjacent + opposite + hypotenuse \\ p = 12 + 12 + 12 \sqrt{2} \\ p = 24 + 12 \sqrt{2} \\ p = 40.97 \\ to \: the \: nearest \: whole \: number \\ p = 41 \: ft\)
Therefore the perimeter of the triangle is 41 ft.
5210 divided by 28. show work plspls
Answers
Answer: Well this is a improper answer but here is it.
186.0714285714286
Step-by-step explanation:
Use the Distance Formula to write an equation of the parabola with vertex (0,0) and directrix y = -6
An equation of the parabola is y=
Answers
Answer:
x^2 + y^ = 36
Step-by-step explanation:
See attached worksheet.
