The eigenvalues of the given matrix are 4, 2, 0, and 0, with corresponding eigenvectors given by [1, sin(πn/5), sin(2πn/5), sin(3πn/5)] for eigenvalue 4, [1, sin(πn/5), sin(2πn/5), sin(3πn/5)] for eigenvalue 2, [0, cos(πn/5), cos(2πn/5), cos(3πn/5)] for eigenvalue 0 (n ≠ 0), and [0, 1, -2, 1] and [1, 0, 0, 0] for eigenvalue 0 (n = 0).
To find the eigenvalues and eigenvectors, we start by using the sine transform. Let S be the 4x4 sine matrix, i.e., the entry in the i-th row and j-th column of S is given by sin(πij/5). Then, we can write the given matrix as M = 3I + S + S^T, where I is the 4x4 identity matrix.
Next, we find the eigenvalues of S. Since S is a real symmetric matrix, its eigenvalues are real and its eigenvectors are orthogonal. By inspection, we see that the columns of S are orthogonal and have length 2, so the eigenvalues of S are given by λn = 2(1 - cos(πn/5)) for n = 1, 2, 3.
Now, we can find the eigenvalues of M. Since M = 3I + S + S^T, the eigenvalues of M are given by μn = 3 + λn + λm, where λn and λm are the eigenvalues of S. Thus, we have μ1 = 4, μ2 = 2, and μ3 = μ4 = 0.
To find the eigenvectors of M, we need to solve the equations (M - μnI)x = 0 for each eigenvalue μn. For μ1 = 4, we have (M - 4I)x = (S - 2I)(S^T - 2I)x = 0, which has non-trivial solutions of the form [1, sin(πn/5), sin(2πn/5), sin(3πn/5)] for n = 1, 2, 3, 4.
Similarly, for μ2 = 2, we have solutions of the form [1, sin(πn/5), sin(2πn/5), sin(3πn/5)] for n = 1, 2, 3, 4. For μ3 = 0, we have solutions of the form [0, cos(πn/5), cos(2πn/5), cos(3πn/5)] for n ≠ 0. Finally, for μ4 = 0, we have two linearly independent solutions: [0, 1, -2, 1] and [1, 0, 0, 0].
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uhh- well uh i need help and it would be lovely if ya’ll helped ty very much
Answer:
x + 3 = y
Step-by-step explanation:
Hope that helps!
25a² -4b²+28bc-49c² factorize
Step-by-step explanation:
Since both terms are perfect squares, factor using the difference of squares formula,
Step-by-step explanation:
= 25 a²- ( 4b²- 28bc +49c²)
=. 25a²- {( 2b)²- 2(2b)(7c)+ (7)²}
= 25a²- { (2b - 7c)²}
= (5a)²- (2b -7c)²
= { 5a -(2b-7c)} { 5a+ ( 2b-7c)}
= ( 5a - 2b +7c) ( 5a +2b - 7c)
plz mark my answer as brainlist plzzzz.
hope this will be helpful to you .
plz you find it useful plz mark my answer as brainlist.
PLS HELP QUICK !!!!!!!
what is the area of this figure?
Answer:
... what figure?
Step-by-step explanation:
you forgot to add a picture
Answer:
ummmm what...?........
eliminate the parameter in the equations x=5cos(t) -7 and y=5sin(t)+9. how can the rectangular equation be described?
circle
ellipse
parabola
hyperbola
Answer:
the answer is A
Step-by-step explanation:
The parameters represent a circle with a radius of 5 units, centered at (-7,9) and the equation of the circle is (x + 7)² + (y - 9)² = 5².
Deducing the figure from the parameters:The given equations are:
x = 5cos(t) - 7, and
y = 5sin(t) + 9
if we rearrange the above equations we get:
(x + 7) = 5cos(t), and
(y - 9) = 5sin(t)
Taking square of both equation we get:
(x + 7)² = 25cos²(t), and
(y - 9)² = 25sin²(t)
Now, adding the equations we get:
(x + 7)² + (y - 9)² = 25cos²(t) + 25sin²(t)
(x + 7)² + (y - 9)² = 25
(x + 7)² + (y - 9)² = 5²
This is an equation of a circle with a radius of 5 units and the center at (-7,9)
since, the equation of a circle with radius R units and centered at (a,b) is given by:
(x -a)² + (y - b)² = R²
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In Vicky's rose garden, 2 of the rose bushes are blooming and the other 17 rose bushes are not blooming. What is the ratio of the number of bushes that are blooming to the total number of bushes?
Answer:
2 : 19
Step-by-step explanation:
We know 2 of the bushes are blooming (this is the left number in my answer) but the other 17 are not. Neither of these is the total number of bushes. To find that, we need to add these together to get 2 + 17 = 19.
This means 2 out of 19 rose bushes are blooming.
Hope this helps! Have a great day!
Plzzzzz help need fast if cannn plzzz
Answer:
D) 2.1
Step-by-step explanation:
HOPE IT HELPS YOU
YOU CAN MARK ME AS BRAINIEST IF YOU WANT
Answer: 2.1 I think please don’t be mad if I’m wrong
Step-by-step explanation:
Suppose that the height H of a Ferris wheel can be modeled by the function H(A=-16cos(pi t/45)+24 where t is the time in seconds. What is the maximum height of a cabin? Use 3.14 for pi
Answer:
Step-by-step explanation:
Range of cosine is -1 to 1
Range of height is 8 to 40
giving brainliest to whoever answers correctly, help please!!!
Answer:
Kyle is correct, the quadrilaterals are not similarStep-by-step explanation:
Measure the corresponding sides and verify if the ratios are same or not.
Corresponding sides:
AB and LM, BC and MN, CD and NO, AD and LOThe measures, using coorinates and the distance formula:
AB = √(2-1)² + (4-3)² = √2LM = √(16-14)² + (4-6)² = √8 = 2√2BC = √(5-2)²+(5-4)² = √10MN = √(23-16)²+(2-4)² = √53We can see the ratios of the two pairs are not same:
AB/LM = 1/2BC/MN = √10/531/2 ≠ √10/53We can state that Kyle is correct
Find the solution of the system of equations.
6x+y=30
−2x−5y=18
Answer:
Step-by-step explanation:
6x + y = 30
-6x - 15y = 54
-14y = 84
y = -6
6x - 6 = 30
6x = 36
x = 6
(6, -6)
Anthony went shopping for a new pair of sneakers. Sales tax where he lives is 4%. The price of the pair of sneakers is $37. Find the total price including tax. Round to the nearest cent
Answer:
$38.48
If this helps, make sure to rate it 5 stars and give me brainliest and a thanks!
Elan took his cat and dog to the vet, his cat weighed 482 pounds, and his dog weighed 158 pounds, how much pounds did his dog weigh?
Five Saturnians are shown below. Bruce is frowning and has the same antennae as Eve. Abby and Cindy are both smiling but only one has three eyes. Dave, Eve, and Cindy all have the same number of eyes. Eve is pictured directly to the left of Dave. Which Saturnian is smiling and has curved antennae.
Answer:
! will edit once i get a response !
Step-by-step explanation:
do you have a picture? if so, please upload it
Helppppppppppppppppppp
Answer:
1.base
2.Quitiont
3.subtract
4.product
5 multiply the exopnent.
The ratio of the interior angles of a triangle is 1 : 3 : 5. What are the angle measures? Write the angle measures from least to greatest.
Answer:
angles
1x
3x
5x
1x +3x +5x = 180 (ASP)
9x = 180
x= 180÷9
x= 20
1x= 20
3x= 60
5x=100
angles are 20°, 60°, 100°
Step-by-step explanation:
hope it helps u
Marsha went shopping at Best Buy and spent $75.25. If the sales tax was 8.75%, how much was her total bill?
Answer:
The answer is 81.834375
Step-by-step explanation:
Hope this helps
Answer:
$81.83
Step-by-step explanation:
Amount spent: £75.25
Sales tax: 8.75%
1% of 75.25 = 0.7525
0.7525 x 8.75 = 6.584375
75.25 + 6.584375 = 81.834375
As this question involves money it needs to be rounded to 2 decimal places:
$81.83
Find the inverse of each function. f (x) = 2x − 4
Mrs. Trotta drives a total of 378 miles over 6 days. She drives the same amount of miles each day. How many miles does Mrs. Trotta drive each day?
Answer:
63 miles per day
Step-by-step explanation:
The miles she drove: 378
Number of days: 6
Solve:
378/6= 63
Check your math:
63*6=378
Hope this helps!
Five friends share 6 snacks equally.
How many fruit snacks will each friend get?
Answer:
A
Step-by-step explanation:
Math has me dead. Looks simple but it really isnt that easy.
Answer:
I am pretty sure the answer is A. I really hope this helps
Step-by-step explanation:
I dont have time to explain it im sorry my next class starts in 3 mins
Answer:A
Step-by-step explanation:
Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
2, 11, 20, ...
Answer:
arithmetic, 9, 1.8181818181818
Step-by-step explanation:
it is arithmetic, because it is adding by 9 every time.
I don't know what they mean by simplist form, but thats what 20/11 equals.
Answer:
yes yes wainth inde Windows
secA-tanA/secA+tanA=cos^2A/(1+sin^2A) could somebody prove this pls......
9514 1404 393
Answer:
it cannot be proven
Explanation:
You cannot prove what isn't true.
We know you know how to use parentheses, so we take the left-side expression at face value. The left-side and right-side functions are different, so cannot be proved to be the same, except at specific angles.
y=-1/2-16K+10 in vertex form
Step-by-step explanation:
Let's solve for k.
y=
−1
2
−16k+10
Step 1: Flip the equation.
−16k+
19
2
=y
Step 2: Add (-19)/2 to both sides.
−16k+
19
2
+
−19
2
=y+
−19
2
−16k=y+
−19
2
Step 3: Divide both sides by -16.
−16k
−16
=
y+
−19
2
−16
k=
−1
16
y+
19
32
Answer:
k=
−1
16
y+
19
32
Question
Identify the transformation that was applied to this letter.
y
R
B
A. Reflection over the x-axis
B. Rotation about the origin
C. Reflection over the yaxis
D. Translation
Answer: Your answer would be A :)
Step-by-step explanation:
Answer:A
Step-by-step explanation:
I took the quiz apeex
Jason buys a Play Station 5 from Amazon for $500 and wants to sell it at a 50% markup. How much does Jason want to sell the PS5 for?
4. Use SUBSTITUTION to solve the system. x= y + 5 2y + x = -4
Answer:
if I I just want free point so I am
I NEED HELP PLS ASAP
ab=
round to the nearest hundredth
a=10t+0 find the y intercept
Answer:
0
Step-by-step explanation:
The y intercept is the constant in this equation, as in the only number unaccompanied or affected by a variable. In this case, assuming y is a and x is t, the y intercept is 0. You can test this by plugging in y=10x+0 into a graphing calculator. The y intercept is where x equals 0, and so if you plug in 0 for x, the result (in this case 0) is the y intercept. Hope this helps, brainliest is always appreciated and have an amazing day!
Please can someone help thanks :)
Answer:
x=124
Step-by-step explanation:
Raon has a pitcher that holds three and seven-hundredths liters of orange juice.
If he divides the juice equally into ten glasses, how many liters of juice will be in each glass?
Choose all the correct answers
0.307
3 x 1 x 7 x 1/100
3 x 1/10 + 7 1/1000
3 x 100 + 7 x 1/ 1000
3.07
3 x 1/10 + 7 x 1/100
Answer:
A
Step-by-step explanation: