The general solution of the given fourth-order linear homogeneous differential equation is given by y(t) = c₁e^(3t) + c₂e^(5t) + c₃e^(-2t)cos(4t) + c₄e^(-2t)sin(4t), where c₁, c₂, c₃, and c₄ are constants.
To find the general solution of the fourth-order linear homogeneous differential equation y⁽⁴⁾ - 4y″ + 2y″ - 12y′ + 45y = 0, we first solve the characteristic equation to obtain the roots. Based on the nature of the roots, we apply the appropriate methods to find the general solution.
The characteristic equation for the given differential equation is r⁴ - 4r³ + 2r² - 12r + 45 = 0. To solve this equation, we can use various methods such as factoring, synthetic division, or the quadratic formula. By finding the roots of the characteristic equation, we obtain the characteristic roots.
Depending on the nature of the roots, we can classify the solutions into different cases. If all roots are distinct, the general solution is of the form y(x) = c₁e^(r₁x) + c₂e^(r₂x) + c₃e^(r₃x) + c₄e^(r₄x), where c₁, c₂, c₃, and c₄ are constants determined by the initial conditions.
If the roots are repeated, we can include additional terms with higher powers of x in the general solution. For example, if we have a repeated root r with multiplicity m, the general solution includes terms of the form cₙxⁿe^(rx), where n ranges from 0 to m-1.
In some cases, complex roots may appear, leading to solutions involving sine and cosine functions. These complex roots appear in conjugate pairs, and the general solution includes terms of the form c₁e^(αx)cos(βx) + c₂e^(αx)sin(βx), where α and β are real numbers.
By finding the roots of the characteristic equation and applying the appropriate methods based on the nature of the roots, we can determine the general solution of the given fourth-order linear homogeneous differential equation.
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Software can generate samples from (almost) exactly Normal distributions.
Here is a random sample of size 5 from the Normal distribution with mean 10 and standard deviation 2:
6.47 7.51 10.10 13.63 9.91
These data match the conditions for a z test better than real data will: the population is very close to Normal and has known standard deviation s = 2, and the population mean is µ = 10.
Test the hypotheses
H0 : µ = 8
Ha : µ ? 8
In Exercise 15.41 (given above), a sample from a Normal population with mean µ = 10 and standard deviation s = 2 failed to reject the null hypothesis H0 : µ = 8 at the a = 0.05 significance level.
Enter the information from this example into the Power of a Test applet.
(Don't forget that the alternative hypothesis is two-sided.)
What is the power of the test against the alternative µ = 10?
The power of the test against the alternative µ = 10 is 1.
Given: A sample from a Normal population with mean µ = 10 and standard deviation s = 2 failed to reject the null hypothesis
H0: µ = 8 at the a = 0.05 significance level.
To find :
The power of the test against the alternative µ = 10.
Step 1: We have
H0 : µ = 8
Ha: µ ≠ 8α
= 0.05
Sample size n = 5
Population Standard deviation s = 2
Population means µ = 10
The alternative hypothesis is two-sided.
Hence α/2 = 0.025.
Using a normal table, the critical values for a two-tailed test at the 0.05 level of significance are -1.96 and +1.96 respectively.
Step 2: We know that
[tex]\[z=\frac{\overline{x}-\mu }{\frac{s}{\sqrt[]{n}}}\][/tex]
where [tex]\[\overline{x}\][/tex] = sample mean,
µ = Population mean,
s = Population Standard deviation and
n = sample size.
By using the given data, z can be calculated as below:
[tex]\[z=\frac{10-8}{\frac{2}{\sqrt[]{5}}}[/tex]
=[tex]4.47[/tex]
The value of z falls in the critical region if it is less than -1.96 or greater than +1.96.
Since 4.47 is greater than +1.96, the null hypothesis is rejected.
Since the null hypothesis is rejected, it is logical to expect that the power of the test will be high.
Hence, the power of the test against the alternative µ = 10 is 1 (100%).
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Cari’s Bakery, Inc., began operations in October. The owner contributed cash of $14,400 and a delivery truck with fair value of $19,200 to the company.
Which of the following describes how these transactions would affect the company’s equity accounts?
A) Increase contributed capital by $33,600
B) Increase earned capital by $33,600
C) Increase contributed capital by $14,400 and earned capital by $19,200
D) Increase earned capital by $14,400 and contributed capital by $19,200
E) None of these are correct.
The transaction would affect the company's equity accounts by increasing contributed capital by $14,400 and earned capital by $19,200. The correct answer is option C.
Equity accounts are a component of the balance sheet that represents the net worth of a business. The equity accounts include contributed capital and earned capital. Contributed capital, also referred to as paid-in capital, is the value of cash or other assets contributed to a company by investors in exchange for shares of ownership in the company. Contributed capital represents the long-term financial interests of owners in the business.
Earned capital is the amount of money that a business earns through its operations. It is also referred to as retained earnings. The difference between a business's assets and liabilities is its equity. It represents the total value of the assets that a company owns after all liabilities have been settled. According to the question, the owner contributed cash of $14,400 and a delivery truck with a fair value of $19,200 to the company. This transaction will increase contributed capital by $14,400 (the cash contribution) and increase earned capital by $19,200 (the delivery truck contribution).Therefore, option C: Increase contributed capital by $14,400 and earned capital by $19,200 is the correct answer.
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Quadratic Functions
Determine the value of y, if x is −9. y=x^2+8
Answer:nn
Step-by-step explanationn o:
Answer:
y = 89
Step-by-step explanation:
x = -9
y = x^2 + 8
y = (-9)^2 + 8
y = 81 + 8
y = 89
The cost to place an ad in a weekly paper is $5.50 per line,i.The print set-up fee is $7.50.
Answer:
whats the question?
Step-by-step explanation:
Which inequality is true if p = 3.4 ?
Answer:
the shape isnt angled thats what it means
Step-by-step explanation:
Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!
Answer: n=4
Step-by-step explanation:
Given
3n-(2+n)=6
Expand Parenthesis (REMEMBER TO CHANGE SIGNS)
3n-2-n=6
Combine like terms
2n-2=6
Add 2 on both sides
2n-2+2=6+2
2n=8
Divide both sides by 2
2n/2=8/2
n=4
Hope this helps!! :)
Please let me know if you have any questions
Answer:
4
Step-by-step explanation:
4 Is the Answer because you have to multiply 4 to all the N's. Which means you have to multiply 4 by 3 which equals 12. Then 2+4=6. Then you would do 12-6=6. There's your answer. Here is the equation if it were like the problem: 12 - (2+4). I'm sure you can figure out the rest. Thanks. If you find any fault in my answer let me know! Have a good day!
Sami cut 6 and three fourth inches off a long roll of paper if the row 36 and one third inches long how long was the original roll of papers
Answer:
43 1 ÷12
Step-by-step explanation:
The computation of the length of the original roll of papers is shown below:
36 1 ÷3 and 6 3 ÷ 4 together
Now convert the above fractions into a number
36 1 ÷ 3 = 109 ÷3
And,
6 3 ÷4 = 27 ÷ 4
Now add these two numbers i.e.
109 ÷3 + 27 ÷ 4
= 436 + 81 ÷ 12
= 517 ÷12
= 43 1 ÷12
Show the enteiws to close $2000 in expense, $5000 in revenue, and
$500 in dividens.
To close the $2,000 in expenses, $5,000 in revenue, and $500 in dividends, we need to transfer these amounts to the appropriate accounts and close the temporary accounts at the end of the accounting period. Here are the journal entries to close these amounts:
Close Expenses:
Date | Account | Debit | Credit
End of Year | Expenses | $2,000 |
| Income Summary | | $2,000
Close Revenue:
Date | Account | Debit | Credit
End of Year | Income Summary | $5,000 |
| Revenue | | $5,000
Close Dividends:
Date | Account | Debit | Credit
End of Year | Retained Earnings | $500 |
| Dividends | | $500
After these closing entries, the balances of the temporary accounts (Expenses, Revenue, and Dividends) will be zero, and their respective amounts will be transferred to the Income Summary and Retained Earnings accounts. The Income Summary account will show the net income (revenue minus expenses) for the period.
Please note that the specific account titles may vary depending on the company's chart of accounts, so make sure to use the appropriate account titles according to your specific chart of accounts.
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OMG PLS HELP WITH THIS IM PANICKING OMG I GOT A F IN MATH MY MOM JUST YELLED AT ME IM CRYING PLS HELP WITH THS- PLSS TELL ME WHAT TO DRAW
Answer:
Step-by-step explanation:
Answer:
13107 employees
A. The picture
B. 10,972 + 2,135 = n
13107 = n
Step-by-step explanation:
10,972 + 2,135 = 13107
What should be drawn is in the photo.
What is the name of the blue dot located inside the curve of the parabola
below?
O A. Focus
B. Center
O C. Directrix
D. Vertex
The blue dot located inside the curve of the parabola is Focus.
What are Parts in Parabola?
The essential feature of a parabola is that all of its points are the same distance from a point called the focus and a line called the directrix. The vertex, axis, latus rectum, and focal length are also key components of a parabola.
The latus rectum, also known as the focal diameter, is the line segment that runs through the focus and parallel to the directrix. The focal diameter's endpoints are located on the curve.
A parabola is the set of all points ( x, y ) in a plane that are the same distance from a fixed line called the directrix and a fixed point not on the directrix (the focus).
A parabola will have three key components: a focus, a directrix, and a vertex. This upward-opening parabola demonstrates that all points,, along the parabola's curve will be the same distance from the focus and the directrix.
Thus, the blue dot located inside the curve of the parabola is Focus.
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Arthur wrote that 15 – 14.7 = 3.
Use the drop-down menus to explain why 3 is incorrect.
the point is supposed to be in front of the three
.3
Answer:
the answer is 0.3
Step-by-step explanation:
I hoped this helped
PLEASE HELP!! I DON'T UNDERSTAND!!!!! I WILL MARK!!!!
Answer:
2
Step-by-step explanation:
first use order of operations.
1/2(4^2)-6
1/2*16-6
then simplify to get:
8-6=2
Answer: 2
Step-by-step explanation:
The question is asking you to substitute the b with 4 and find the solution to the expression.
[tex]\frac{1}{2}b^{2} -6[/tex]
[tex]=\frac{1}{2}(4)^{2} -6[/tex]
[tex]=\frac{1}{2}(16) -6[/tex] (PEMDAS so you do the exponent first)
[tex]=8 -6[/tex] (PEMDAS so you do the multiplication first)
[tex]=2[/tex]
John is 30 years old. He will receive two payments of $2500 each. The first payment will be an unknown number of years in the future. The second payment will be five years after the first payment. At an annual effective interest rate of I=5%, the present value of the two payments is $2606. Determine at what age John will receive the second payment.
Answer:
16 years
Step-by-step explanation:
Let us assume that he would received the first payment after t years
So
The following formula should be used
PV = P ÷ (1 + r)^t + P ÷ (1 + r)^t+5
$2,606 = $2,500 ÷ (1 + 0.05)^t + $2,500 ÷ (1 + 0.05)^t + 5
$2,606 = $2,500 ÷ 1.05^t (1 + 1 ÷ (1.05)^5)
1.05^t = $2,500 ÷ $2,606 (1.7835) = 1.71098
t = ln(1.71098) ÷ ln(1.05)
= 11
Therefore he would be received the second payment after
= 11 + 5
= 16 years
Find the value of x for which / || m
Answer:
Step-by-step explanation:
The integrat (cos(x - 3) dx is transformed into L' (t)dt by applying an appropriate change of variable, then g(t) i g(t) = 1/2 cos (t-3/2) This option g(t) = 1/2 sin(t-3/2)
The integrat (cos(x - 3) dx is transformed into L' (t)dt an g(t) = 1/2 sin(t-3/2) is incorrect. The correct option g(t) = 1/2 cos(t-3/2).
To transform the integral ∫cos(x - 3)dx into L'(t)dt using an appropriate change of variable, the substitution method make the substitution:
t = x - 3
To find dt, differentiate both sides of the equation with respect to x:
dt = dx
substitute these expressions into the integral:
∫cos(x - 3)dx = ∫cos(t)dt
The integral has been transformed into ∫cos(t)dt.
regarding the options for g(t),
Option 1: g(t) = 1/2 cos(t-3/2)
Taking the derivative of g(t) with respect to t,
g'(t) = -(1/2)sin(t - 3/2)
Option 2: g(t) = 1/2 sin(t-3/2)
Taking the derivative of g(t) with respect to t,
g'(t) = (1/2)cos(t - 3/2)
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solve the problem. determine if the lower bound theorem identifies -4 as a lower bound for the real zeros of f(x). f (x) = 3x3 2x2 - 9x 4 select one: a. yes b. no
The correct answer is: a. yes. To determine if the lower bound theorem identifies -4 as a lower bound we need to analyze the behavior of the function as x approaches negative infinity.
The lower bound theorem states that if a polynomial function has a negative leading coefficient (in this case, 3), then any lower bound M must have the property that f(M) is either negative or zero.
Let's evaluate f(-4) to see if it is negative or zero: f(-4) = 3(-4)^3 + 2(-4)^2 - 9(-4) + 4= 3(-64) + 2(16) + 36 + 4= -192 + 32 + 36 + 4= -120. Since f(-4) = -120 is negative, the lower bound theorem identifies -4 as a lower bound for the real zeros of f(x).Therefore, the correct answer is: a. yes
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Drag and drop all methods of showing Triangle Similarity or Triangle Congruence into the appropriate box. SAS, SSS, ASA, AAS, CPOCTAC, HL, AA
Similar Triangle Justifications Congruent Triangle Justifications
Answer:
hi
Step-by-step explanation:
by
Hang was trying to factor 10x^2 + 5x she found that the greatest common factor of these terms was 5x and made an area model what is the width of the area model
Width of Heng's area model is 2x + 1
Step-by-step explanation:
Given:
Greatest common factor is 5x
To Find:
The width = ?
Solution:
let the be the area
And 5x be the length
Then area = length x width
Now rewriting the formula for width, we get
Width =
Substituting the values in the above formula
Width =
Width = 2x + 1
someone help please!! oh and pls don’t put any links
Answer:
10 visits
Step-by-step explanation:
So first let's make an equation, 7.74x + 8.93= 86.33. When you solve for x you get 10.
A rectangular prism with a length of 5 inches a width of 4 inches and a height of 3 inches is how many square inches
Answer:
20
Step-by-step explanation:
length x width = area
4 x 5 = 20
(not 100% sure, but I hope this helps)
During the summer John collected cans to recycle. In August he collected 718 cans bringing his total to 2,275 cans. How many cans did John collect before August?
Answer: 1557 cans
Step-by-step explanation:
Since we are informed that John collected 718 cans in August bringing his total number of cans to 2,275 cans, the number of cans that John collected before August will be:
= Total number of cans collected - Number of cans collected in August
= 2275 - 718
= 1557 cans
What is equivalent to 8?
A:2^3
B:3^-2
C:2^-3
D:3^2
Answer: A:2^3
Step-by-step explanation:
8=2*2*2=(2)^3
i need to find the area and circumference for each circle
Answer:
Step-by-step explanation:
5
How would I put this?
Answer:
10.35
Step-by-step explanation:
63,756 x 60 = 3825360
70 x 5,280 = 369600
3825360 ÷ 369600 = 10.35
The scores on the Wechsler Adult Intelligence Scale are approximately Normal, with 100 and 11. The proportion of adults with scores above 110 is closest to 0.25 b.0.33. c0.14. 4.0.18 Colleges often rely heavily on raising money for an "annual fund" to support operations. Alumni are typically solicited for donations to the annual fund. Studies suggest that the graduate's smal income is a good predicar of the amount of money he or she would be willing to donate, and there is a reasonably strong, positive, linear relationship between these variables. In the stadies described a annual income is an explanatory variable. b the correlation between annual income and the size of the donation is positive. c the size of the donation to the annual fund is the response variable. d. All of the answer options are correct.
The proportion of adults with scores above 110 is 0.1841.
Here, we have,
It should be noted that from the information illustrated, Wechsler Adult Intelligence Scale scores are approximately Normal, with a mean of 100 and a standard deviation of 11.
The formula to use will be:
P(a < Z < b) = P(Z < b) – P(Z < a)
a = lower value
b = higher value
Z = z value
It should be noted that the proportion of adults with scores above 110 will be:
= P(x > 110)
= P(z > 110 - 100/11)
= P(z > 0.90)
= 1 - 0.8159
= 0.1841
Therefore, this illustrates those that has scores of more than 110.
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6(x-2)=-18 what does x=
Answer:
x = -1
Step by step explanation:
Distribute 6
6x-12= -18
Add 12 to both sides
6x= -6
Divide both sides by 6
x= -1
Hope this helps
the Median.)
Find quartile 2 using the data below:
23, 45, 52, 28, 42, 87, 56, 32, 48, 55, 24, 63, 68, 76, 67
Answer:
52
Step-by-step explanation:
if you put the numbers in order from least to greatest you'll see that 52 is in the middle
Pls help, answer righhand I’ll mark brainly and you big smart!
Answer:
A. and C.
Step-by-step explanation:
Just remember that to find the roots, use the equation:
(-b +/- sqrt[b^2 - 4ac])/2a
I would appreciate Brainliest, but no worries.
What is the range of the function f = [0,00) + R, defined by the rule f(t) = -247 (a) (0,1) (c) R (b) (0,11 (d) (0,00)
The range of the function f = [0,00) + R, defined by the rule f(t) = -247 is {-247}. The correct option is d.
The range of a function is the set of all possible outputs or y-values. Here, the function is f(t) = -247 with the domain [0,00), which means that for any value of t between 0 and 00 (excluding 00), the function will always give the same output, -247. This is because the rule for the function is simply -247, and doesn't depend on the input value of t.
The range of the function f is simply {-247}, which is a singleton set containing only one element (-247). In other words, the only possible output or y-value for this function is -247, and there are no other possible values for f(t) for any value of t between 0 and 00 (excluding 00).
Thus, the correct option is d.
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the temperature is -2c if the temputure rises to 15c , what is the new temputure
Answer:
13c
Step-by-step explanation:
-2 + 12 = 13