Answer:
Step-by-step explanation:
Given that:
The equation of the damped vibrating spring is y" + by' +2y = 0
(a) To convert this 2nd order equation to a system of two first-order equations;
let y₁ = y
y'₁ = y' = y₂
So;
y'₂ = y"₁ = -2y₁ -by₂
Thus; the system of the two first-order equation is:
y₁' = y₂
y₂' = -2y₁ - by₂
(b)
The eigenvalue of the system in terms of b is:
[tex]\left|\begin{array}{cc}- \lambda &1&-2\ & -b- \lambda \end{array}\right|=0[/tex]
[tex]-\lambda(-b - \lambda) + 2 = 0 \ \\ \\\lambda^2 +\lambda b + 2 = 0[/tex]
[tex]\lambda = \dfrac{-b \pm \sqrt{b^2 - 8}}{2}[/tex]
[tex]\lambda_1 = \dfrac{-b + \sqrt{b^2 -8}}{2} ; \ \lambda _2 = \dfrac{-b - \sqrt{b^2 -8}}{2}[/tex]
(c)
Suppose [tex]b > 2\sqrt{2}[/tex], then λ₂ < 0 and λ₁ < 0. Thus, the node is stable at equilibrium.
(d)
From λ² + λb + 2 = 0
If b = 3; we get
[tex]\lambda^2 + 3\lambda + 2 = 0 \\ \\ (\lambda + 1) ( \lambda + 2 ) = 0\\ \\ \lambda = -1 \ or \ \lambda = -2 \\ \\[/tex]
Now, the eigenvector relating to λ = -1 be:
[tex]v = \left[\begin{array}{ccc}+1&1\\-2&-2\\\end{array}\right] \left[\begin{array}{c}v_1\\v_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]
[tex]\sim v = \left[\begin{array}{ccc}1&1\\0&0\\\end{array}\right] \left[\begin{array}{c}v_1\\v_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]
Let v₂ = 1, v₁ = -1
[tex]v = \left[\begin{array}{c}-1\\1\\\end{array}\right][/tex]
Let Eigenvector relating to λ = -2 be:
[tex]m = \left[\begin{array}{ccc}2&1\\-2&-1\\\end{array}\right] \left[\begin{array}{c}m_1\\m_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]
[tex]\sim v = \left[\begin{array}{ccc}2&1\\0&0\\\end{array}\right] \left[\begin{array}{c}m_1\\m_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]
Let m₂ = 1, m₁ = -1/2
[tex]m = \left[\begin{array}{c}-1/2 \\1\\\end{array}\right][/tex]
∴
[tex]\left[\begin{array}{c}y_1\\y_2\\\end{array}\right]= C_1 e^{-t} \left[\begin{array}{c}-1\\1\\\end{array}\right] + C_2e^{-2t} \left[\begin{array}{c}-1/2\\1\\\end{array}\right][/tex]
So as t → ∞
[tex]\mathbf{ \left[\begin{array}{c}y_1\\y_2\\\end{array}\right]= \left[\begin{array}{c}0\\0\\\end{array}\right] \ \ so \ stable \ at \ node \ \infty }[/tex]
The ratio of boys to girls in the class is 2 to 8, what percent of the class is boys?
Answer:a) 20%
Step-by-step explanation: 2× 100/ 8+2
Answer:
20%
Step-by-step explanation:
girls are 80% just so you know
solve the equation
[ 3 2 5 5 ] [ x1 x2] + [ 1 2 ] = [ 2 -3 ]
Answer:
x1=3 x2=-4
Step-by-step explanation
The value of the x₁ = 3.2, and x₂ = -3.8 if the linear equation in two variables is 3x₁ + 2x₂ = 2, and 5x₁ + 5x₂ = -3.1
What is the matrix?It is defined as the group of numerical data, functions, and complex numbers in a specific way such that the representation array looks like a square, rectangle shape.
The determinant in arithmetic is a real number that is a variable of the rows and columns of a square matrix. It lets specifying a few aspects of the matrix and the linear map that the matrix provides.
It is given that:
[tex]\left[\begin{array}{ccc}3&2\\5&5\\\end{array}\right] \left[\begin{array}{ccc}x_1\\x_2\\\end{array} \right] = \left[\begin{array}{ccc}2\\-3\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}3x_1+2x_2\\5x_1+5x_2\\\end{array}\right] = \left[\begin{array}{ccc}2\\-3\\\end{array}\right][/tex]
On comparing:
3x₁ + 2x₂ = 2
5x₁ + 5x₂ = -3
The above two equations represent linear equations in two variables:
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
After solving with substituion method:
x₁ = 3.2
x₂ = -3.8
Thus, the value of the x₁ = 3.2, and x₂ = -3.8 if the linear equation in two variables is 3x₁ + 2x₂ = 2, and 5x₁ + 5x₂ = -3.
Learn more about the matrix here:
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If f(x)= tan^-1(2x), find lim x->2 (f(x)-f(2))/x-2
A. 2/17
B.1/17
C.-2/15
D. -1/15
Answer:
The value of the limit is 12.
Step-by-step explanation:
Small typing mistake, the limit is of h tending to 0.
Then
Calling the limit L
h is the common term in the numerator, then
Simplifying by h
Since h tends to 0.
Pls help ASAP Explain why this mapping is or is not a function.
A. This is a function because every input maps to only one output
B. This is a function because every output maps only the input
C. This is not a function because more than on input maps to an output
D. This is not a function because more than one output maps the input
Answer:
correct answer is a
Step-by-step explanation:
its a function as long as every input has one output, 1 output can have any number of inputs
i choose d mb i got it wrong
Can someone please help me I tryed already
Answer:look at the picture below
Step-by-step explanation:
given f(x)=x(x-3)+4 what is the derivative of f at a?
[tex]f(x) = {x}^{2} - 3x + 4 \\ \frac{d}{dx} ( {x}^{2} - 3x + 4) \\ g(x) = 2x - 3[/tex]
Let g(x) = f'(x)
Substitute a in x, therefore the answer is.
[tex]g(a) = 2a - 3[/tex]
— Note that it'd be better to use f'(a) or y' instead. For this one, I let g(x) equal the derivative of f(x) —
find the gof of g[5X+2]^3-4
Answer:
what is value of f in given function
PART B The Connecticut Speeding inequality In many places in Connecticut, the speed limit on interstate highways is still 55 miles per hour. The formula used for calculating speeding fines on interstate highways in Connecticut is shown below. Judges in Connecticut have the ability to lower fines to any amount above $0, but fines may not exceed $350.
[tex]f(s) \leqslant 10(s - 55) + 40[/tex]
Maximum fine: $350 Again, frepresents the amount of the fine in dollars and s represents the recorded speed of the car in miles per hour.
1.Write a realistic domain and range for the conneticut speeding inequality as compund inequaleties. Explain your choice.
Search that question on brainless and you’ll for sure find yourself an answer.
Edwin Edwards and Karen Davis owned EEE, Inc., which owned three convenience stores, all of which sold gasoline. Reid Ellis delivered to the three convenience stores $26,675.02 worth of gasoline for which he was not paid. Ellis proved that Edwards and Davis owned the business, ran it, and in fact personally ordered the gasoline. He claimed that they were personally liable for the debt owed him by EEE, Inc. Decide. [Ellis v.
Edwards, 348 S.E.2d 764 (Ga. App.)]
Question Completion:
Note: This is a Law question, not Mathematics.
Answer:
Decision:
Edwards and Davis are not personally liable for the debts of EEE, Inc.
Step-by-step explanation:
That Edwin Edwards and Karen Davis owned EEE Inc. does not force them to be personally liable for the debts of EEE Inc. EEE Inc. is a separate legal entity. There is the legal separation of ownership and the liabilities of Edwards and Davis are limited to the capital they contributed or undertook to contribute to the corporation. The corporate veil is only lifted when it is ascertained that EEE Inc. was not run as a legal entity separate from the owners. We can also conclude that there is no evidence of abuse of the corporate form of EEE Inc. with comingling of assets or for the purpose of promoting fraud or injustice or evasion of tort or contractual responsibility on the part of Edwards and Davis. Therefore, Edwin Edwards and Karen Davis are not personally liable for the debts of EEE Inc. as claimed by Reid Ellis.
Please helppppppppppppp me
Answer:
with what?
Step-by-step explanation:
It is known that the mean cholesterol level for all Americans is 190. Construct the relevant hypothesis test to show that only children have an average higher cholesterol level than the national average. We tested 100 children and find out the mean is 198. You can use your own confidence level. (All Americans Standard Deviation is 15)
Answer:
95% of confidence intervals are
(197.706 , 198.294)
Step-by-step explanation:
Explanation:-
Given sample size 'n'=100
Mean of the sample x⁻ = 198
The standard deviation of the Americans =15
95% of confidence intervals are determined by
[tex](x^{-} - Z_{\alpha } \frac{S.D}{\sqrt{n} } , x^{-} +Z_{\alpha } \frac{S.D}{\sqrt{n} })[/tex]
Level of significance = 0.05
Z₀.₀₅ = 1.96
= [tex](198 - 1.96 \frac{15}{\sqrt{100} } , 198 +1.96\frac{15}{\sqrt{100} })[/tex]
= ( 198 -0.294 ,198 +0.294)
= (197.706 , 198.294)
95% of confidence intervals are
(197.706 , 198.294)
Any help please thank you I appreciate it
Answer:
x=33
Step-by-step explanation:
The angles have to add up to 180, so you get:
2x - 18 + 4x = 180
6x = 180 + 18
x = 198/6
x = 33
PLEASE HELP!! AND SHOW WORK PLEASE!!
Answer:
keeping an eye on graph
Step-by-step explanation:
its answer will be
total price for 12.5 pound of rice=$32.5
Can some one help me I will give the brainliest
Answer:
b,0,1
Step-by-step explanation:
as a graded class activity, your teacher asks your class to reflect a triangle across the y-axis and then across the x-axis. Your classmate gets upset because he reversed the order of these reflections and thinks he will have to start over. What can you say to your classmate to help him?
Answer:
Both processes will yield same results and he need not worry
Step-by-step explanation:
Let us firstly check if we will have same results on both steps
y before x
Let us have the point (x,y) on the triangle
y reflection
(-x,y)
then x reflection
(-x,-y)
Let us now get the order in which my friend followed
x reflection
(x, -y)
y reflection
(-x,-y)
we can see that both processes have same results and thus, my friend need not worry
Answer:
The order of these two reflections
does not
matter. The resulting image
is
the same for a reflection in the y-axis followed by a reflection in the x-axis as for a reflection in the x-axis followed by a reflection in the y-axis.
Step-by-step explanation:
What is the probability of the outcome being an A?
Answer:
The probability of the outcome being an A is 1/2.
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] probability of the outcome being an A, option D.
---------------------------------------------
A probability is the number of desired outcomes divided by the number of total outcomes.
The spinner is divided into 8 regions, thus, there are 8 total outcomes.4 of those regions are A, so there are 4 desired outcomes.---------------------------------------------
The probability of the outcome being an A is:
[tex]p = \frac{4}{8} = \frac{1}{2}[/tex]
Thus:
[tex]\frac{1}{2}[/tex] probability of the outcome being an A, option D.
A similar problem is found at https://brainly.com/question/16069806
answer this correctly pls and u get brainliest and 50 points
Answer:
32 degrees
Step-by-step explanation:
One straight line equals 180 degrees
if one angle from one side is 148, then 180-148=32
dont mind this question
Answer:
hello, there.
Step-by-step explanation:
General kanobi
When reaching mile marker 7 on a trail, Natalie uses her GPS to find that her current elevation is 6350 feet. If she follows the trail until its end at mile marker 12, her elevation will be 8720 feet. What is the average change in elevation of Natalie’s position from mile marker 7 to mile marker 12, in feet per mile marker?
Find the difference in elevations:
8720 - 6350 = 2370 feet.
Difference in mile markers: 12-7 = 5
Average change = feet / markers
2370/5 = 474
The answer is 474 feet
micheal clean 45 cars in 5 days. How many cars does Micheal clean per day
Answer:
9
Step-by-step explanation:
I divided 45 by 5 and got 9
Answer:
9
Step-by-step explanation:
45 divided by 5 means, split 45 into 5 groups. Which should get you 9 cars per day.
Suppose that the radius of a circle increases at a constant rate of 0.25 cm/sec. When the radius of this circle is 16 cm, the area of the circle increases at a rate of
Answer:
8πcm²/sec
Step-by-step explanation:
The radius of the circle increases at a rate of dr/dt = 0.25cm/sec
The radius of the circle r = 16cm
The area of the circle increases at a rate of dA/dt = ?
Area of a circle = πr²
We take the derivative with respect to t
dA/dt = 2πrdr/dt
dA/dt = 2 π (16)(0.25)
dA/dt = 8πcm²/sec
Thank you!!!
Answer:
8pi cm^2/sec
Step-by-step explanation:
took the unit test, also give other person brainliest, their answer was REALLY good.
Find the mean, the median, and all modes for the data in the given frequency distribution. (Round your answers to one decimal place. If there is more than one mode, enter your answer as a comma-separated list. If an answer does not exist, enter DNE.)
Points Scored by Lynn Points scored in a basketball game Frequency
2 10
3 9
9 10
11 7
12 3
15 4
16 3
Answer: Mean = 7.8
Median = 9
Mode = 2,9
Step-by-step explanation: Mean is the average value of a data set. Mean from a frequency table is calculated as:
[tex]E(X)=\frac{2(10)+3(9)+9(10)+11(7)+12(3)+15(4)+16(3)}{10+9+10+7+3+4+3}[/tex]
E(X) = 7.8
Mean for the given frequency distribtuion is 7.8.
Median is the central term of a set of numbers. Median in a frequency table is calculated as:
1) Find total number, n:
n = 10 + 9 + 10 + 7 + 3 + 4 + 3 = 46
2) Find position, using: [tex]\frac{n+1}{2}[/tex]
[tex]\frac{n+1}{2}=\frac{47}{2}[/tex] = 23.5
Median is in the 23.5th position.
3) Find the position by adding frequencies: for this frequency distribution, 23.5th position is 9
Median for this frequency distribution is 9.
Mode is the number or value associated with the highest frequency.
In this frequency distribution, 2 and 9 points happen 10 times. So, mode is 2 and 9.
Mode for this distribution is 2 and 9.
Following are the calculation of mean, median, and modes:
Given value:
[tex]\bold{x \ \ \ \ \ \ f} \\\\ 2\ \ \ \ \ 10 \\3\ \ \ \ \ 9\\9 \ \ \ \ \ 10\\11\ \ \ \ \ 7\\12 \ \ \ \ \ 3\\15 \ \ \ \ \ 4\\16 \ \ \ \ \ 3\\[/tex]
To find:
mean, median, and modes=?
Solution:
[tex]\bold{x \ \ \ \ \ \ f \ \ \ \ \ \ cf \ \ \ \ \ \ fx} \\\\2\ \ \ \ \ 10 \ \ \ \ \ 10 \ \ \ \ \ 20 \\3\ \ \ \ \ 9 \ \ \ \ \ 19 \ \ \ \ \ 27 \\9 \ \ \ \ \ 10\ \ \ \ \ 29 \ \ \ \ \ 90 \\11\ \ \ \ \ 7\ \ \ \ \ 36 \ \ \ \ 77 \\12 \ \ \ \ \ 3\ \ \ \ \ 39 \ \ \ \ 36\\15 \ \ \ \ \ 4\ \ \ \ \ 43 \ \ \ \ 60\\16 \ \ \ \ \ 3\ \ \ \ \ 46 \ \ \ \ 48 \\[/tex]
[tex]\Sigma f = 46 \ \ \ \ \ \ \ \ \ \ \Sigma fx= 358[/tex]
Calculating the Mean:
[tex]Mean=\frac{\Sigma fx}{\Sigma f}[/tex]
[tex]=\frac{358}{46}\\\\= 7.78[/tex]
Calculating the Median:
[tex]n= \Sigma f= 46[/tex]
[tex]Median=\frac{ (\frac{n}{2})^{th} +(\frac{n}{2} +1)^{th}}{ 2}[/tex]
[tex]=\frac{ (\frac{46}{2})^{th} +(\frac{46}{2} +1)^{th}}{ 2}\\\\=\frac{ (23)^{th} +(24)^{th}}{ 2}\\\\=\frac{ 3 +3}{ 2}\\\\=\frac{ 6}{ 2}\\\\=3[/tex]
Calculating the Mode:
Mode is the value of 'x' with the highest frequency is 10 for x= 2 and x=9 therefore, the mode is "2,9".
Learn more:
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- 5х – 3х
What do you get from these like terms?
Helppppppppppppppppppppp!!!!!!!!
Because of some theory with angles on same sides of a line between parallel lines, take 180 and subtract the ones you have. 180-107=73 degrees= m angle B
180-46=134 degrees - m angle A
i need help with #1 10 points
Answer:
No it is not proportional
Step-by-step explanation:
You cant multiply each of the inputs by a constant number to get the output.
There is only 2 of them that you can, but the other 2 no. And you want he whole table so you need all of the inputs not just some. So no, its not proportional.
Hope this helped!
15 divided by 6 2/3 =
A. 100
B. 2/14
C. 100 1/4
D. 2 3/4
Relationships between x and y
Answer:
they love each other
Step-by-step explanation:
...........
I need help with this :(
♀️♀️♀️♀️♀️♀️♀️♀️
Answer:
The sum of the areas of square N and square L is equal to the area of square K
Two more than 4 times a number is the number less 7. What is the number?
12 x 12 / 12 x 12 x 12 x 12 - 777 + 21 x 12 x 12 / 12 = ?
Answer:
116,031 about
Step-by-step explanation:
Answer:
20,211
Step-by-step explanation:
Use the correct order of operations, and do one step at a time.
12 x 12/12 x 12 x 12 x 12 - 777 + 21 x 12 x 12/12 =
= 144/12 x 12 x 12 x 12 - 777 + 252 x 12/12
= 12 x 12 x 12 x 12 - 777 + 3024/12
= 144 x 12 x 12 - 777 + 252
= 1728 x 12 - 777 + 252
= 20,736 - 777 + 252
= 19,959 + 252
= 20,211