Find the general solution with two real valued solutions of the following linear sys- tem: y' = 4 5 -2 6 у Show all your work to get a full credit.
Answers
There are no real eigenvalues we cannot find a general solution with two real-valued solutions for this linear system.
How we find the general solution with two real-valued solutions for the given linear system?we'll first write down the system using the given matrix and the terms you've mentioned.
The system is represented as:
y' = A × y, where A = [4, 5; -2, 6]
Now, let's follow the steps to find the general solution:
Find the eigenvalues (λ) of matrix A. To do this, we need to solve the characteristic equation: det(A - λ × I) = 0, where I is the identity matrix.
| 4-λ, 5 |
| -2, 6-λ | = 0
(4-λ)(6-λ) - (-2)(5) = 0
λ² - 10λ + 24 + 10 = 0
λ² - 10λ + 34 = 0
Find the two real eigenvalues (λ1 and λ2) by solving the quadratic equation:
In this case, there are no real eigenvalues, as the discriminant (b² - 4ac) is negative:
Δ = 10² - 4 × 1 × 34 = 100 - 136 = -36
Learn more about Linear system
brainly.com/question/28977228
#SPJ11
Related Questions
Solve 15=3n+6p, for n
Answers
Answer:
\(n=5-2p\)
Step-by-step explanation:
STEP 1: Rewrite the equation as 3 n + 6 p = 15 .
\(3n+6p=15\)
STEP 2: Subtract 6 p from both sides of the equation.
\(3n=15-6p\)
STEP 3: Divide each term by 3 and simplify.
\(n=5-2p\)
find the equation of the tangent line tangent to the graph of
y = -4x^3 + 7x^2 - 9x + 12
at the given point (1, 6) in slope-intercept form.
Answers
To find the equation of the tangent line to the graph of the given function at the point (1, 6), we need to determine the slope of the tangent line at that point.
We can find the slope by taking the derivative of the function and evaluating it at x = 1.
First, let's find the derivative of the function y = -4x^3 + 7x^2 - 9x + 12. Taking the derivative of each term, we get:
dy/dx = -12x^2 + 14x - 9
Now, substitute x = 1 into the derivative to find the slope at the point (1, 6):
m = -12(1)^2 + 14(1) - 9 = -7
The slope of the tangent line is -7. Now we can use the point-slope form of a line to find the equation of the tangent line:
y - y1 = m(x - x1)
Substituting the values (x1, y1) = (1, 6) and m = -7, we get:
y - 6 = -7(x - 1)
Simplifying the equation gives:
y - 6 = -7x + 7
Finally, rearranging the equation to the slope-intercept form gives:
y = -7x + 13
Therefore, the equation of the tangent line to the graph of the function at the point (1, 6) is y = -7x + 13.
To know more about tangent line click here: brainly.com/question/23416900
#SPJ11
How many feet are in 154 centimeters
Answers
Step-by-step explanation:
154 centimeters =
5.05249344 feet (5 feet ⅝ inch)
A small auditorium has chairs arranged with 12 chairs in the front row, 14 chairs in the middle row, and 16 chairs in the back row. guests randomly choose a chair as they walk in. what is the probability that the first guest will take a chair in the front row?
Answers
The probability that the first guest will take a chair in the front row of the small auditorium is 2/7 or approximately 0.2857.
To find the probability that the first guest will take a chair in the front row, we need to determine the total number of chairs and the number of chairs in the front row.
Given that there are 12 chairs in the front row, 14 chairs in the middle row, and 16 chairs in the back row, the total number of chairs in the auditorium is:
Total chairs = 12 + 14 + 16 = 42
Now, since the first guest can choose any chair, and there are a total of 42 chairs, the probability of the first guest taking a chair in the front row is:
Probability = Number of favorable outcomes / Total number of outcomes
The number of favorable outcomes is the number of chairs in the front row, which is 12. The total number of outcomes is the total number of chairs in the auditorium, which is 42.
Probability = 12 / 42
Simplifying the fraction, we have:
Probability = 2 / 7
Therefore, the probability that the first guest will take a chair in the front row is 2/7 or approximately 0.2857.
Learn more about probability here:
https://brainly.com/question/31828911
#SPJ11
Type a digit that makes this statement true.
20,604,70_
is divisible by 6
Answers
Answer:
2
Step-by-step explanation:
Can someone help me
Answers
The multiplicity οf -2 is 1. The multiplicity οf 1+i and 1-i is alsο 1Since the quadratic factοr 13x²+27x+47 has nο real rοοts, it dοes nοt have any multiplicity fοr real numbers such as -2.
Determining the multiplicity οf zerοs οf a pοlynοmial functiοn.The given functiοn is f(x) = 13x³ + 14x² + 12x + 8x + 6x + 8.
Tο find the multiplicity οf each zerο, we need tο first factοrize the pοlynοmial. We can use synthetic divisiοn tο factοrize the pοlynοmial and find its zerοs:
-2 | 13 14 12 8 6 8
| -26 24 -72 128 -268
+----------------------------
13 -12 36 -64 134 -260
1+i | 13 14 12 8 6 8
| 13 27i 27+13i 35-7i 41-13i
+-----------------------------------
13 27+14i 27-13i 43-7i 47-13i 0
1-i | 13 14 12 8 6 8
| 13 -27i 27-13i 35+7i 41+13i
+-----------------------------------
13 27-14i 27+13i 43+7i 47+13i 0
Hence, the factοrizatiοn οf the given pοlynοmial is:
f(x) = (x+2)(x-1-i)(x-1+i)(13x²+27x+47)
The zerοs οf the pοlynοmial are -2, 1+i, and 1-i.
The multiplicity οf -2 is 1 because it appears as a linear factοr (x+2) in the factοrizatiοn.
The multiplicity οf 1+i and 1-i is alsο 1 each because they appear as linear factοrs (x-1-i) and (x-1+i) in the factοrizatiοn.
Since the quadratic factοr 13x²+27x+47 has nο real rοοts, it dοes nοt have any multiplicity fοr real numbers such as -2.
To know more about roots and multiplicity, visit:
brainly.com/question/29770367
#SPJ1
A rainwater was 2/3 full of water. After 60 liters of water were used from the barrel, it was 5/12 full. How much water does the barrel hold when full?
Answers
Answer: 240 liters
=======================================================
Work Shown:
x = capacity of barrel in liters
This value of x is some positive real number. It represents the most amount of water the barrel can hold.
The problem states that the barrel is 2/3 full to start with. This means, we start off with (2/3)x liters of water. Then we subtract off 60 of them to get to 5/12 full, meaning we have (5/12)x liters left.
We can form this equation
(2/3)x - 60 = (5/12)x
Multiply both sides by 12 to clear out the fractions
(2/3)x - 60 = (5/12)x
12*( (2/3)x - 60 ) = 12*(5/12)x
12*(2/3)x - 12*60 = 12*(5/12)x
8x - 720 = 5x
From here we solve for x
8x - 5x = 720
3x = 720
x = 720/3
x = 240
The barrel's full capacity is 240 liters
--------------------------
Check:
2/3 of 240 = (2/3)*240 = 160
The barrel starts off with 160 liters of water inside.
We then use 60 of them to be left with 160-60 = 100 liters
Note how 100/240 = (5*20)/(12*20) = 5/12, showing that 100 liters out of 240 total reduces to the fraction 5/12. In other words, when we say "5/12 full" we mean 100 liters full. This helps confirm we have the right answer.
Mike put sports books on 13 of a bookshelf.
He put history books on 14 of a bookshelf.
What fraction of the bookshelf did NOT have sports books on it?
Enter your answer in the boxes.
Answers
The fraction of the bookshelf that did NOT have sports books on it is 14/27.
To find the fraction of the bookshelf that did NOT have sports books on it, we need to find the total number of bookshelves that had books on them. Since Mike put sports books on 13 of a bookshelf and history books on 14 of a bookshelf, we can add these two values to get the total number of bookshelves:
Total number of bookshelves = 13 + 14
Total number of bookshelves = 27
Therefore, there are 27 bookshelves in total, and the fraction of the bookshelf that did NOT have sports books on it is equal to the number of bookshelves that had history books on them divided by the total number of bookshelves:
Fraction of bookshelf with history books = 14/27
To find the fraction of the bookshelf that did NOT have sports books on it, we need to subtract the fraction of bookshelf with sports books from 1:
Fraction of bookshelf without sports books = 1 - Fraction of bookshelf with sports books
Fraction of bookshelf without sports books = 1 - 13/27
Fraction of bookshelf without sports books = 14/27
Therefore, the fraction of the bookshelf that did NOT have sports books on it is 14/27.
To learn more about fraction click here
brainly.com/question/10354322
#SPJ11
Simplify. Write the expression using only positive exponents. m^−2⋅n^3
Answers
Step-by-step explanation:
n³/m²
remember, x^-n = 1/(x^n)
best answer gets brainliest
Answers
Answer:
D
Step-by-step explanation:
8n = 32
32/8n
n=4
Conroy Creations has been hired to create invitations to the Spring Gala. The
invitations are to be created using a 6 inch by 4 inch sheet of paper folded
horizontally. Inside the invitation includes a large image in the center so that
when the card is opened it illustrates a reflection over the fold of the card.
Which figure below could be used as the center of the invitation
Answers
Answer:
D
Step-by-step explanation:
The given sheet of paper is folded horizontally, thus a pattern with respect to the fold is formed inside the paper. This pattern would in the form of two lines crossing each other at right angles.
To illustrate a reflection over the fold of the card, the pattern in option D could be used as the center of the invitation.
Therefore, the correct option is D.
Consider the two triangles. Triangles A B C and T R S are shown. Sides A C and T S are congruent. Sides T B and R S are congruent. If RT is greater than BA, which statement is true? By the converse of the hinge theorem, mAngleC = mAngleS. By the hinge theorem,TS > AC. By the converse of the hinge theorem, mAngleS > mAngleC. By the hinge theorem, BA = RT.
Answers
Answer:
its c
Step-by-step explanation:
By the converse of the hinge theorem, mAngleS > mAngleC.
By the converse of the H. theorem, the statement that is true about the triangles is mAngleS > mAngleC.
What is converse of the H. theorem?The Converse H. Theorem explains that if two different triangles have two of their sides to be congruent to each other, having third side of the first triangle longer to the third side of the second triangle.
Then it can be deduced that the first triangle will have its included angle larger compare to the second triangle.
Hence, since Sides A C and T S are congruent and RT is greater than BA, then base on the defined theorem, mAngleS > mAngleC.
Learn more about H. theorem at:
https://brainly.com/question/15227724
#SPJ9
A square board was attached to a wall. The board was divided by four squares and each square was colored either black or white. How many possible combinations of such coloring are there, if we cannot rotate the given board? PLEASE HELP QUICK! IM NEW AND I NEED ANSWERES! I HOPE BRAINLY DEOS NOT FAIL ME!
Answers
Answer:
24 combinations
Step-by-step explanation:
For this problem, you use factorials. Factorials are when you multiply every number below it except zero. So like the factorial of 3 or 3! is 3*2*1 is 6.
Factorials are used to figure out how many combinations there are of something. So for you, we have 4 different quadrants so we write that as 4! (! is the sign for factorials.)
By the way, welcome to brainly.
Let f(x) = [infinity] xn n2 n = 1. find the intervals of convergence for f. (enter your answers using interval notation. ) find the intervals of convergence for f '. find the intervals of convergence for f ''
Answers
Best guess for the function is
\(\displaystyle f(x) = \sum_{n=1}^\infty \frac{x^n}{n^2}\)
By the ratio test, the series converges for
\(\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{(n+1)^2} \cdot \frac{n^2}{x^n}\right| = |x| \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = |x| < 1\)
When \(x=1\), \(f(x)\) is a convergent \(p\)-series.
When \(x=-1\), \(f(x)\) is a convergent alternating series.
So, the interval of convergence for \(f(x)\) is the closed interval \(\boxed{-1 \le x \le 1}\).
The derivative of \(f\) is the series
\(\displaystyle f'(x) = \sum_{n=1}^\infty \frac{nx^{n-1}}{n^2} = \frac1x \sum_{n=1}^\infty \frac{x^n}n\)
which also converges for \(|x|<1\) by the ratio test:
\(\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{n+1} \cdot \frac n{x^n}\right| = |x| \lim_{n\to\infty} \frac{n}{n+1} = |x| < 1\)
When \(x=1\), \(f'(x)\) becomes the divergent harmonic series.
When \(x=-1\), \(f'(x)\) is a convergent alternating series.
The interval of convergence for \(f'(x)\) is then the closed-open interval \(\boxed{-1 \le x < 1}\).
Differentiating \(f\) once more gives the series
\(\displaystyle f''(x) = \sum_{n=1}^\infty \frac{n(n-1)x^{n-2}}{n^2} = \frac1{x^2} \sum_{n=1}^\infty \frac{(n-1)x^n}{n} = \frac1{x^2} \left(\sum_{n=1}^\infty x^n - \sum_{n=1}^\infty \frac{x^n}n\right)\)
The first series is geometric and converges for \(|x|<1\), endpoints not included.
The second series is \(f'(x)\), which we know converges for \(-1\le x<1\).
Putting these intervals together, we see that \(f''(x)\) converges only on the open interval \(\boxed{-1 < x < 1}\).
əz 22. Suppose z= z(x, y) is implicitly determined by ln(x+y+z) = x+2y+3z. Then dy (z.y.a)=(-1,5,-3)
Answers
the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).
n the given problem, we have an implicit equation ln(x+y+z) = x+2y+3z that defines z as a function of x and y. We are given the values dy = (-1, 5, -3).
To find the derivative dy/dx, we can use the total derivative formula and apply it to the implicit equation. The total derivative is given by dy/dx = - (∂F/∂x)/(∂F/∂y), where F = ln(x+y+z) - x - 2y - 3z.
Differentiating F partially with respect to x and y, we have (∂F/∂x) = 1/(x+y+z) - 1 and (∂F/∂y) = 1/(x+y+z) - 2.
Plugging in the given values of dy = (-1, 5, -3), we can calculate dy/dx = - (∂F/∂x)/(∂F/∂y) = -(-1)/(5-2) = 1/3.
Therefore, the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).
Learn more about equation here: brainly.com/question/29657983
#SPJ11
How many packages of diapers (d) can you buy with $40 if one package costs $8?
Answers
Answer:
5
Step-by-step explanation:
because 8+8+8+8+8=40 or 8*5
and theres 8 five times
Maple has 4 identical loaves of bread that weigh a total of 6.6 pounds. How much does 1 loaf of bread weigh?
Answers
Answer:
1.65
Step-by-step explanation:
Divide 6.6 by 4
An isosceles trapezoid has a perimeter of 43 kilometers. Its shorter base measures 1 kilometer and its longer base measures 4 kilometers. The two remaining sides have the same length; what is that length?
Answers
Answer: The length of each of the two equal sides is 19 km
Step-by-step explanation:. Subtract the giver lengths of the bases: 4+1= 5
43 - 5 = 38.
The trapezoid is iscosceles, so the remaining two sides are equal.
Divide. 38/2 = 19
I hope this helps you!
Need Help Now Do not Wait need help with all will give 20 points!!!!!!!!!!!!!!
Answers
Step-by-step explanation:
the equation of the line simplify your answer type using integers are fraction indication points are the graph this is that what is the answer is
1) If x= 4.2 and y = 5, what is the value of the expression
below? *
13 points
х+бу
69.2
15.2
72
34.2.
Un
Answers
Answer:
Step-by-step explanation:
y-x=0.7
y=x+0.7, so lets plug in that into the expressions instead of y
1)
(y-x)=
x+0.7-x=
x+0.7+(-x)=
x+(-x)+0.7=
x-x+0.7=
0.7
2)
(x-(x+0.7))/((x+0.7)-x)=
(x-x+0.7)/(x+0.7-x)=
(x-x+0.7)/(x+0.7+(-x))=
(x-x+0.7)/(x+0.7+(-x))=
(x-x+0.7)/(x+(-x)+0.7)=
(x-x+0.7)/(x-x+0.7)=
0.7/0.7=
1
0.67 divided by 10 help someone
Answers
Answer:
0.067
Step-by-step explanation:
We just move 0.67's decimal point to the right by one since we are dividing by 10.
0.67 / 10 = 0.067
Sure hope this helps you :)
Give (✿◕‿◕✿)
Write 13 /2 as a mixed number. Give your answer in its simplest form.
Answers
Answer:
6·¹₂ 6¹/₂
Step-by-step explanation:
by dividing 13 by 2, we get the quotient 6, remainder 1 and divisor as 2.
as we know, to write a mixed fraction, we follow Q^R/D, so we get 6¹/₂.
Kevin made cookies and brownies for the bake sale at school. He made 12 more cookies than brownies. He sold cookies for $1.50 and brownies for $2. He sold all of his food and made a total of $123. How many of each item did he sell? *
Answers
Answer:
He made 42 cookies and 30 brownies.
Step-by-step explanation:
Let c = number of cookies
Let b = number of brownies
"He made 12 more cookies than brownies."
The number of cookies is 12 more than the number of brownies.
c = b + 12
"He sold cookies for $1.50 and brownies for $2."
The money he made from selling cookies was 1.5c.
The money he made from selling brownies was 2b.
The total sales were $123
1.5c + 2b = 123
We have a system of equations.
c = b + 12
1.5c + 2b = 123
Substitute c of the second equation with b + 12
1.5(b + 12) + 2b = 123
1.5b + 18 + 2b = 123
3.5b = 105
b = 30
c = b + 12
c = 30 + 12
c = 42
He made 42 cookies and 30 brownies.
Is it true that If A is invertible and if r ≠0, then (rA)^−1=rA^−1.
Answers
The statement is true. Therefore, we have shown that \((rA)^{(-1)} = A^{(-1)}/r,\)which implies that \((rA)^{(-1)} = r^{(-1)}\times A^{(-1)\). Hence, \((rA)^{(-1) }= rA^{(-1)\), since r is nonzero.
To prove this, we can start with the definition of the inverse of a matrix:
If A is an invertible matrix, then its inverse, denoted as \(A^{(-1),\) is the unique matrix such that \(A\times A^{(-1)} = A^{(-1)} \times A = I\), where I is the identity matrix.
Now, let's consider the matrix rA, where r is a nonzero scalar. We want to find its inverse, denoted as \((rA)^{(-1)\).
We can start by multiplying both sides of the equation \(A\times A^{(-1)} = I\) by r:
\(rA\times A^{(-1)} = rI\)
Next, we can multiply both sides of this equation by A from the left:
\(rA\times A^{(-1)}A = rIA\\rAI = rA = rA(A\times A^{(-1)})\)
Now, we can use the associative property of matrix multiplication to rearrange the right-hand side of this equation:
\(rA\times(AA^(-1)) = (rAA)\times A^{(-1)}\\rA\times I = (rA)\times A^{(-1)}\\rA = (rA)\times A^{(-1)}\)
Finally, we can multiply both sides of this equation by \((rA)^{(-1)\) from the left to obtain:
\((rA)^{(-1)}rA = (rA)^{(-1)}(rA)\times A^{(-1)}\\I = A^{(-1)}\)
for such more question on invertible
https://brainly.com/question/31043586
#SPJ11
The table represents a function,
X F(x)
-6 3
-2 1
0 4
3 -2
what is f(-2)?
A) -3
B)-1
C)1
D)3
Answers
Answer:
c
Step-by-step explanation:
the answer is c. because it is the corresponding value to minus two
Find the value of the expression 4a^4 − 2b^2 + 40 when a = 2 and b = 7
Answers
Answer:6
Step-by-step explanation:
4(2)^4 − 2(7)^2 + 40
4(16)-2(7)^2+40
64-2(49)+40
64-98+40
-34+40
6
Answer:
6
Step-by-step explanation:
4a^4 - 2b^2 + 40
Put a = 2 and b = 7
4(2)^4 - 2(7)^2 + 40
Solve the powers first.
4(16) - 2(49) + 40
Multiply.
64 - 98 + 40
Add and subtract.
= 6
i need a bit of help with this bc i’m literally not smart. no work needed, just an answer. i’ll give brainliest.
Answers
Answer:
1. y= -2
Step-by-step explanation:
i hope this helps :)
Answer:
option (3)
Step-by-step explanation:
The equation of a vertical line parallel to the y- axis is
x = c
where c is the value of the x- coordinates the line passes through.
The line passes through (- 2, - 5 ) and (- 2, - 4) with x- coordinates - 2 , then
x = - 2 ← equation of line
You are going to the gas station with your mom. The cost of a car wash is $5.00. The cost per gallon of gas $3.10 per gallon. Write a linear equation to represent the total cost of a trip to the gas station.
Answers
9514 1404 393
Answer:
c = 5.00w +3.10g
Step-by-step explanation:
Let w represent the number of car washes purchased, g represent the number of gallons of gas purchased, and c represent the total cost of the trip.
cost = (cost of car washes) + (cost of gas)
c = 5.00w + 3.10g
complete the following statements of congruence zyx
Answers
Answer:
cba
Step-by-step explanation:
yes correct answer x yimes h yomes z
An acting school claims that 71% of its graduates land major acting roles within one year of graduation. A random sample of 50 graduates was surveyed, and 30 of them had landed major roles within one year of graduation. Let p hat = the proportion of the sample who had landed major roles within one year of graduation.
The probability that 60% or fewer graduates land a major acting role within one year of graduating from this school is 0.043. Does this result provide convincing evidence against the school’s claim?
A. Yes, it is expected that at least 60 graduates from this school will land a major role within one year of graduation.
B. Yes, the probability of seeing the sample result is so far from what is expected that the probability of it occurring by chance alone is very unlikely (0.043 < 0.05).
C. No, the difference between the sample proportion and the parameter is 11%, which is greater than 5%.
D. No, the difference between the sample result and what is expected is not extreme enough. The probability of it occurring by chance alone is not unlikely (0.043 < 0.05).
Answers
Answer:
B
Step-by-step explanation:
EDGE2021!! since the actual probability is smaller than .05, we have evidence against the acting school claiming that 71% of its graduates land major acting roles within one year of graduation.