The general solution of the given system is x(t) = c1t(1 1) + c2t(1 -1).
To find the general solution of x′ = (−1 1 −1 −1 ) x, we first need to find the eigenvalues and eigenvectors of the matrix A = (−1 1 −1 −1).
The characteristic polynomial of A is given by det(A - λI) = 0, where I is the 2x2 identity matrix and λ is the eigenvalue:
|−1-λ 1 |
|-1 -λ| = (-1-λ)(-1-λ) - (-1)(1) = λ^2 + 2λ = λ(λ+2) = 0.
So the eigenvalues of A are λ1 = 0 and λ2 = -2.
To find the eigenvectors corresponding to each eigenvalue, we need to solve the equations:
(A - λ1I)x1 = 0 and (A - λ2I)x2 = 0.
For λ1 = 0, we have:
(A - λ1I)x1 =
| -1 1 |
| -1 -1 | x1 = 0.
Solving this system of equations, we get x1 = t(1 1), where t is any scalar.
For λ2 = -2, we have:
(A - λ2I)x2 =
| 1 1 |
| -1 -3 | x2 = 0.
Solving this system of equations, we get x2 = t(1 -1), where t is any scalar.
Thus, the general solution of x′ = (−1 1 −1 −1 ) x can be written as a linear combination of the eigenvectors:
x(t) = c1t(1 1) + c2t(1 -1),
where c1 and c2 are constants that depend on the initial conditions.
for such more question on matrix
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Sami lights up a candle every 10 minutes. Every candle burns for exactly 40 minutes. How many candles are burning exactly 55 minutes after Sami lit up the first candle?
Answer:
4
Step-by-step explanation:
Candle is lit every 10 minutes :
Number of candles lit in 55 minutes:
Starting from 0 minute ; Numbe rod candles lit on 55 minutes = 6
1st candle burns out after 40 minutes
Second burns out after 50 minutes
Third will burn out after 60 minutes
Hence Number of candles still burning :
Number of candles lit - Number of candle burnt out
6 - 2 = 4 candles
Graph the image of △JKL after a reflection over the line y=x
Answer:
K (2,-4)
L (4,-6)
J (2,-9)
Step-by-step explanation:
The required graph of the image of △JKL after a reflection over the line y=x has been attached below.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The triangle △JKL is given in the represented graph, which vertices are as follows :
J (-9, 2)
K (-4, 2)
L (-6, 4)
The image of △JKL after a reflection over the line y = x will be triangle △J'K'L' that vertices are as follows :
K' (2,-4)
L' (4,-6)
J' (2,-9)
Hence, the required graph of the image of △JKL after a reflection over the line y=x has been attached below.
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The Sum Of A Number And Six
Answer:
x+6
Hope this helps! :)
Answer:
The sum of a # and 6 is...
Step-by-step explanation:
It’s at 15??
Plz help ill mark brainlest
Answer:i believe its 3 correct me if im wrong
Step-by-step explanation:
Answer:
either 6/10 or 7/10
Step-by-step explanation:
Can someone please help me ASAP? What are the points? Point: (_, _)
Answer:
Step-by-step explanation:
I believe the point is 2:5
Hope this helps
Please asnwer the picture
b/4 = 3.2 help me plz
Answer:
Step-by-step explanation:
B/4=3.2
B=12.8
Write the converse, inverse and contrapositive of each conditional statement, and tell if the resulting statement is True or false
2. If mA = 100, then is not a right angle.
Converse:
Inverse:
Contrapositive:
Answer:
See below.
Step-by-step explanation:
It's good to recall what these terms mean:
Conditional statement: if p then q
Converse: if q then p
Inverse: if not p then not q
Contrapositive: if not q then not p
Conditional statement:
If m<A = 100, then <A is not a right angle.
p = m<A = 100
q = <A is not a right angle
Converse:
If angle A is not a right angle, then m<A = 100.
False. An angle that is not a right angle can have many measures other than 100 degrees.
Inverse:
If the measure of <A is not 100 degrees, then <A is a right angle.
False. If an angle has a measure of other that 100 degrees, it can have many measures in addition to 90 degrees, so it is not necessarily a right angle.
Contrapositive:
If angle A is a right angle, then m<A is not 100 degrees.
True. Only a right angle has a measure of 90 degrees, so an angle with measure 100 deg cannot be a right angle.
chase bought his dream car ,a chevy corvette, for $58,735. sales tax is 5% where chase lives what is the total price chase paid for the corvette?
Answer:
$61,671.75
Step-by-step explanation:
There is a calculator called "Sales Tax Calculator" and if you put in your Before Tax Price and your Sales Tax Rate you will receive your answer of $61,671 and 75 Cents. ($61,671.75)
1. 3x + 2y - Z-6
a) 3 terms
b) 5 terms
c) 4 terms
d) 6 terms
PLEASE HELP
Answer:
c) 4 terms
Step-by-step explanation:
3x is 1 term ,2y is 1 term,z is 1 term,6 is also 1 term
so in all there are 4 terms
10 - 20 - 20 - 20 -20 2- + 1000
Answer:
928
Step-by-step explanation:
Answer: It would be 1252
Necesito ayuda con el punto 4
Give me the slope for the following points (9, 10)
and (7,2)
The answer is
m = 4
Have a great day!!!
Answer:
4 is the slope
Step-by-step explanation:
We know this by using the slop formula, which is y2-y1/x2-x1
We just plug in the points that we know and solve from there,
Give brainliest please :3
What time is it in Vietnam right now?
Answer:
it's
3:26 pm to be exact!
Step-by-step explanation:
15:26
Friday,19February 2021
I hope it's helpful!
Grace and her brother Sid want to raise money to go to band camp. Their parents have agreed to help them up to $400 by paying them $25 when one of them mows the lawn and $10 for each hour that one of them babysits their younger brother. They will have to do a combination of both chores in order to earn the money.
Select the equation that represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.
Step-by-step explanation:
25m + 10b = 400
not enough info to solve for m or b. but that's the equation you would use.
simplify: 4 (3y +x) please show your work
Answer:
12y+4x
Step-by-step explanation:
Multiply 4*3y and 4*x
Distributive property
Help with math
Find CE.
Answer:
6
Step-by-step explanation:
if DB equal to 6 then look down at CE, it has the same distance as D to B so CE equal to 6.
9514 1404 393
Answer:
CE = 10
Step-by-step explanation:
Assuming BC is parallel to DE, that segment divides the sides proportionally.
CE/CA = BD/BA
CE/25 = 6/15
CE = 25(6/15) . . . . multiply by 25
CE = 10
Which of these rational numbers is also an integer?
1. 2/4
2. 0.24
3. 4/2
4. 2.4
Answer:
Ce clasă ești sa văd daca te pot ajuta
Answer:
3. 4/2
Step-by-step explanation:
Easier way to explain it is the numerator or the top number is higher then the denominator or the bottom number.
Find the value of x:
A. X = 41.0
B. X = 122.0
C. X = 61.0
D. X = 120.5
Step-by-step explanation:
hope this will help you..
Daryl jumped off of a diving board, and dove into a pool. The graph below shows his height relative to the surface of the water over time, where Daryl’s height (y) is measured in meters and time (x) is measured in seconds. Which of the following statements are true? (Please select all options which are true.)
Answer:
B,D,E
Step-by-step explanation:
Not entirely sure
A man is cycling in a place where wind is blowing. He travels 12 km against the direction of the blowing wind. In doing so, he took the same time while going 28 km in the direction of the wind. Find the speed of the wind. ( Hint - When the man is cycling in the direction of the wind, wind speed is added to his speed; otherwise it is subtracted.)
Answer:
The speed of the wind is 4.8 km/hr
Step-by-step explanation:
The parameters of the motion of the man are;
The distance the man travels in the given time while moving against the wind = 12 km
The distance the man travels in the giving time while going with the wind = 28 km
From search online for of a similar question, we have;
The speed with which the man is cycling = 12 km/hr
Let. 't', represent the time the travels each distance, let 'w', represent the speed of the wind and let 'v' represent the speed of the man, we have;
Time, t = Distance, d/(Velocity, v)
The resultant speed of the man when he travels against the wing = v - w
The resultant speed of the man when he goes in the the wing = v + w
Therefore, we have;
12/(v - w) = 28/(v + w)
12·v + 12·w = 28·v - 28·w
12·w + 28·w = 28·v - 12·v = 16·v
40·w = 16·v
∴ w = (16/40) × v = (2/5) × v
The speed with which the man is cycling = 12 km/hr
∴ The speed of the wind, w = (2/5) × v = (2/5) × 12 km/hr = 4.8 km/hr
The speed of the wind = 4.8 km/hr.
What is the equation of the line that represents the horizontal asymptote of the function f(x)=25,000(1+0.025)^(x)?
Answer:
The answer is below
Step-by-step explanation:
The horizontal asymptote of a function f(x) is gotten by finding the limit as x ⇒ ∞ or x ⇒ -∞. If the limit gives you a finite value, then your asymptote is at that point.
[tex]\lim_{x \to \infty} f(x)=A\\\\or\\\\ \lim_{x \to -\infty} f(x)=A\\\\where\ A\ is\ a\ finite\ value.\\\\Given\ that \ f(x) =25000(1+0.025)^x\\\\ \lim_{x \to \infty} f(x)= \lim_{x \to \infty} [25000(1+0.025)^x]= \lim_{x \to \infty} [25000(1.025)^x]\\=25000 \lim_{x \to \infty} [(1.025)^x]=25000(\infty)=\infty\\\\ \lim_{x \to -\infty} f(x)= \lim_{x \to -\infty} [25000(1+0.025)^x]= \lim_{x \to -\infty} [25000(1.025)^x]\\=25000 \lim_{x \to -\infty} [(1.025)^x]=25000(0)=0\\\\[/tex]
[tex]Since\ \lim_{x \to -\infty} f(x)=0\ is\ a\ finite\ value,hence:\\\\Hence\ the\ horizontal\ asymtotes\ is\ at\ y=0[/tex]
Olivia has at most 90$ to spend on clothes she wants to buy a pair of jeans for 22$ and spend the rest on shirts that cost 8$ each what is the greatest number of shirts she can buy
Answer:the greatest number of shirts she can buy = 8
Step-by-step explanation:
Amount of money Olivia has =$90
cost of pair of jeans =$22
such that if she buys the pair of jean, Money left to buy shirts = $90-$22= $68
If 1 Shirt= $8
Number of shirts she can buy with $68 = $68/$8= 8.5= 8 1/2
Therefore the greatest number she can buy = 8 shirts.
explain why the expression 2y-y can be written as why
Answer:
y
Step-by-step explanation:
2y-y=y
Answer: 2y-y can be written as y because 2y means you have 2 y’s and 2y’s minus 1 y is just 1 y
Step-by-step explanation:
URGENT PLEASE HELP ASAP
AHAHAHAHAHAHA SO JM IS EQUAL TO 29⁰ AND YOU NEED TO FIND ANGLE L BUT I DON'T KNOW WHAT IT EQUALS TO
what is the answer to 2 - (-5)
Answer:
7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
learn the table of how these symbols work.
in this case its two minuses which make plus so 2+5=7
What is the slope-intercept equation of the line below?
Answer:
D. y = 2x -3
Step-by-step explanation:
The equation of a line in slope-intercept form is
y = mx + b
We need to find m, the slope, and b, the y-intercept.
We can find those two numbers from the graph.
We look in the graph and see that the y-intercept, b, is -3.
Now we have y = mx - 3.
Now we look for the slope. Start at (0, -2). We need to go vertically and horizontally to the next point that is easy to read. We see that point (1, -1) is on a grid intersection making it easy to read, so we will use that point.
Go up 2 units. That is a rise of positive 2. Now go right 1 unit. That is a run of positive 1.
slope = rise/run = 2/1 = 2
m = 2, so now we have
y = 2x - 3
Answer: D. y = 2x -3
what is the answer to 4 - (-4)
-30-0.6k
what does k equal?
Answer:
K would equal to:
K= 50
Hope that helps! :)
Step-by-step explanation:
How many distinct, real solutions does the following equation have?
x^2=49
A) Two distinct, real solution
B) One distinct, real solution
C) No solutions
Answer:
A) two (they are 7 and -7)
Step-by-step explanation: