The differential equation
[tex]y^{(4)}-n^2y'' = g(x)[/tex]
has characteristic equation
r ⁴ - n ² r ² = r ² (r ² - n ²) = r ² (r - n) (r + n) = 0
with roots r = 0 (multiplicity 2), r = -1, and r = 1, so the characteristic solution is
[tex]y_c=C_1+C_2x+C_3e^{-nx}+C_4e^{nx}[/tex]
For the non-homogeneous equation, reduce the order by substituting u(x) = y''(x), so that u''(x) is the 4th derivative of y, and
[tex]u''-n^2u = g(x)[/tex]
Solve for u by using the method of variation of parameters. Note that the characteristic equation now only admits the two exponential solutions found earlier; I denote them by u₁ and u₂. Now we look for a particular solution of the form
[tex]u_p = u_1z_1 + u_2z_2[/tex]
where
[tex]\displaystyle z_1(x) = -\int\frac{u_2(x)g(x)}{W(u_1(x),u_2(x))}\,\mathrm dx[/tex]
[tex]\displaystyle z_2(x) = \int\frac{u_1(x)g(x)}{W(u_1(x),u_2(x))}\,\mathrm dx[/tex]
where W (u₁, u₂) is the Wronskian of u₁ and u₂. We have
[tex]W(u_1(x),u_2(x)) = \begin{vmatrix}e^{-nx}&e^{nx}\\-ne^{-nx}&ne^{nx}\end{vmatrix} = 2n[/tex]
and so
[tex]\displaystyle z_1(x) = -\frac1{2n}\int e^{nx}g(x)\,\mathrm dx[/tex]
[tex]\displaystyle z_2(x) = \frac1{2n}\int e^{-nx}g(x)\,\mathrm dx[/tex]
So we have
[tex]\displaystyle u_p = -\frac1{2n}e^{-nx}\int_0^x e^{n\xi}g(\xi)\,\mathrm d\xi + \frac1{2n}e^{nx}\int_0^xe^{-n\xi}g(\xi)\,\mathrm d\xi[/tex]
and hence
[tex]u(x)=C_1e^{-nx}+C_2e^{nx}+u_p(x)[/tex]
Finally, integrate both sides twice to solve for y :
[tex]\displaystyle y(x)=C_1+C_2x+C_3e^{-nx}+C_4e^{nx}+\int_0^x\int_0^\omega u_p(\xi)\,\mathrm d\xi\,\mathrm d\omega[/tex]
seven times a number decreased by the number is -48 . Find the number.
Answer:
a = -8
Step-by-step explanation:
Let the required number be "a".
Given that, seven times a number minus the number is -48
7 × a - a = -48
7a - a = -48
6a = -48
a = (- 48) / 6
a = -8
Graph the compound inequality on the number line. x > 7 or x < -4
OSEAMENTE no se la respuesta
Find the distance between the two points (1.5,2.7) and (3.5,4.3) given in polar coordinates and using radians.
Answer:
2.56
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√(3.5 - 1.5)² + (4.3 - 2.7)²
√(2)² + (1.6)²
√(4) + (2.56)
√6.56
= 2.56
A general contractor is constructing a building that requires a concrete foundation that is to be 20 feet by 22 feet and 24 inches thick. If the local home supply store sells concrete for $ 110 per cubic yard, what will be the cost of the concrete for the foundation?
Express your answer rounded up to the next whole dollar.
Answer:
$38427
Step-by-step explanation:
Surface Area Formula: A=2(wl+hl+hw) where l=length w=width h=height
A=2((20(22))+(22(2))+(20(2)) = 1048ft^2
3 ft = 1yds -> 1048 ft = 349 1/3 yds
349 1/3(110)= 38426.66666
$38427
Answer: $2,613,600
Step-by-step explanation:
Concept:
Here, we need to know the idea of unit conversion and a rectangular prism.
When there are multiple units occurring in the same question, then we should convert all the units into one by different conversion factors.
A rectangular prism is a three-dimensional figure that has 6 sides that are rectangles.
1 foot = 12 inches
1 yard = 3 feet
V (rectangular prism) = w · l · h
Solve:
24 inches = 24 / 12 = 2 feet
$110 per cubic yard = 110 × 3³ = $2970 per cubic feet
V = w · l · h
V = (20) (22) (2)
V = 880 feet³
880 × 2970 = $2,613,600
Hope this helps!! :)
Please let me know if you have any questions
The graph shows the solution of the following system of equations. y=-5/3x+3 y=1/3x-3 What is the solution? A. (-3,2) B. (3,2) C. (-3,-2) D. (3,-2)
Answer:
(3,-2)
Step-by-step explanation:
-5/3x + 3 = 1/3x - 3
-5/3x = 1/3x - 6
-2x = -6
x = 3
y = -5/3(3) + 3
y = -5 + 3
y = -2
Question 24 of 58
Four classmates collect data by conducting a poll. They
ask students chosen at random how many books they
have to read for English class.
• Kevin interviews 25 students.
• Mary interviews 92 students.
• Sydney interviews 24 students.
• Caleb interviews 31 students.
Whose results are probably the most trustworthy?
O A. Mary's
OB. Sydney's
C. Kevin's
D. Caleb's
SUBMIT
7,25 x (y+5,6)=58 vậy y =
Answer:
y=2,4
Step-by-step explanation:
7,25x( y+5,6)=58
7,25y+ 40,6=58
7,25y=58-40,6
y=17,4:7,25
y=2,4
x
the mubrer
2. The first term in a sequence is 3.
The rule for the sequence is to multiply by 3 then add 2
Write the next 3 terms in the sequence
Answer:
3, 11, 35.
Step-by-step explanation:
The first 3 terms of the sequence can de written as:
n, 3n + 2, 3(3n + 2) + 2
So when n = 3 the first 3 terms are
3, 3(3) + 2, 3(3(3) + 2)) + 2
= 3 , 9 + 2, 33 + 2
= 3, 11, 35.
In how many distinct ways can the letters of the word MAMAS be arranged?
Answer:
120 ways
Step-by-step explanation:
There are 5 letters.
5! = 5*4*3*2*1
= 20*6
= 120
Answer:
The answer is 30. You cant repeat letters. Ther are 5 letters, the M and A are repeat letters so 5-2=3 5!/3! = 30
Step-by-step explanation:
Translations _______ side lengths of the figure.
A. change
B. alter
C. preserve
D. all of these
Answer:
C. preserve
Step-by-step explanation:
When you translate something in geometry, you're simply moving it around. You don't distort it in any way. If you translate a segment, it remains a segment, and its length doesn't change. Similarly, if you translate an angle, the measure of the angle doesn't change.
Slope 0; through (-5, -1)
with steps please.
Step-by-step explanation:
0 slope means it has in x.
so the equation is y=-1, because that is the coord for the points'y axsis
7. Find the missing side. Round to the nearest tenth
Hi there!
[tex]\large\boxed{x \approx 19.6}[/tex]
We can use right triangle trigonometry to solve.
We are given the angle's adjacent side and are trying to solve for the hypotenuse, so:
Use cosine: cos Ф = A / H
Thus:
cos 30° = 17 / H
Simplify:
0.866 = 17 / H
Isolate for H:
H · 0.866 = 17
H = 17 / 0.866
H = 19.63 ≈ 19.6
Answer:
x = 19.6
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos 30 = 17/x
x cos 30 = 17
x = 17/cos 30
x=19.62990
To the nearest tenth
x = 19.6
An just finished taking statistics, and wants to do a survey on the average salary of Spring 2019 HCC graduates. She calculates that the standard error of the mean is $128.13 after she surveyed a group of students who reported an annual income of $43,650 and she knows the population standard deviation is $2,050, how many students were randomly sampled by An?
Answer:
The appropriate answer is "256".
Step-by-step explanation:
Given:
Standard error,
SE = 128.13
Standard deviation,
[tex]\sigma[/tex] = $2050
As we know,
⇒ [tex]SE = \frac{\sigma}{\sqrt{n} }[/tex]
or,
⇒ [tex]\sqrt{n}= \frac{\sigma}{SE}[/tex]
By substituting the values, we get
[tex]=\frac{2050}{128.13}[/tex]
[tex]=\frac{205000}{12813}[/tex]
[tex]n = (\frac{205000}{12813} )^2[/tex]
[tex]=255.98[/tex]
or,
[tex]=256[/tex]
Alice wants to estimate the percentage of people who plan
on voting yes for the upcoming school levy. She surveys
380 individuals and finds that 260 plan on voting yes.
Identify the values needed to calculate a confidence interval
at the 90% confidence level. Then find the confidence interval.
zo10 z0.05 zo.025 zo01 z0.005
1.282 1.645 1.960 2.326 2.576
Use the table of common z-scores above.
Answer:
"[tex]0.6450 < p < 0.723[/tex]" is the right solution.
Step-by-step explanation:
Given:
n = 380
x = 260
Point estimate,
[tex]\hat p = \frac{x}{n}[/tex]
[tex]=\frac{260}{380}[/tex]
[tex]=0.6842[/tex]
Critical value,
[tex]Zc = 1.645[/tex]
Standard error will be:
[tex]S.E = \sqrt{\frac{0.6842(1-0.6842)}{380} }[/tex]
[tex]=0.0238[/tex]
Margin of error will be:
[tex]E = Zc\times S.E[/tex]
[tex]=1.645\times 0.0238[/tex]
[tex]=0.0392[/tex]
hence,
Confidence level will be:
= [tex]\hat p \pm E[/tex]
= [tex]0.6842 \pm 0.0392[/tex]
= [tex]0.6450 < p < 0.723[/tex]
write an absolute value equations to satsify the given solution set shown on a number line -1/2 1/2 and a
Plz help fast
9514 1404 393
Answer:
|x| = 1/2
Step-by-step explanation:
Perhaps the simplest equation is ...
|x| = 1/2
__
You could get more elaborate:
|2x| = 1
3 -|6x| = 0
What is the remainder when (2x^3 + 4x^2 – 32x + 18) = (x + 3)?
Answer:
X= -5.3 & Y= -2.34
X= 0.49 & Y= 3.49
X= 2.85 & Y=5.85
Step-by-step explanation:
To find the intersection you would need to graph it and locate where both lines will intersect.
Five trucks are to be transported on a ship. Each one weighs 3200 kg and comes
with 8 tyres which weigh 125 kg each. what is the total weight
Total No of trucks: 5
Weight of trucks: 3200Kg
Total weight of trucks: 3200×5
= 16000kg
Total no of tyres = 5 ×8
= 40
Weight of each tyre = 125kg
Total weight of tyres = 125 × 40
= 5000Kg
The total weight of trucks and tyres: 16000 + 5000
= 21000Kg
Answered by Gauthmath must click thanks and mark brainliest
Select the correct answer. Shape 1 and shape 2 are plotted on a coordinate plane. Which statement about the shapes is true? A. Shape 1 and shape 2 are not congruent. B. A translation will prove that shape 2 is congruent to shape 1. C. A rotation and a translation will prove that shape 2 is congruent to shape 1. D. A reflection, a rotation, and a translation will prove that shape 2 is congruent to shape 1.
Answer:
Since I cant say which answer due to no graph, I'll tell you How to do so.
Step-by-step explanation:
if it is A, then the there is at least one angle or line length that is not the same. To find the area of a grided shape, use the traingle theorm of a^2+b^2=c^2.
if it is B, that meants moving the shape to the other will result in a perfect fit. Be sure to find if all side lengths are the same as that means that the shape IS congrouent, as equal side length means equal angles. However, it will not be this choice if the shape is mirrored to the other
A rotation and tranlastion means it is flipped either upside down or up and moved to the shape.
D, a reflection, which means its the opposite. Like a mirrored shape. Then you move it.
A meat packaging plant uses a machine that packages chicken livers in six pound portions. A sample of 91 packages of chicken livers has a standard deviation of 0.47. Construct the 98% confidence interval to estimate the standard deviation of the weights of the packages prepared by the machine. Round your answers to two decimal places.
Lower endpoint______ Upper endpoint__
Answer:
it simple as look
Step-by-step explanation:
He y I a m r a v I t ha n k S
Wowowowowowowowowk
answer this now please :)
9514 1404 393
Answer:
E. 384 cu ft
Step-by-step explanation:
The sum of length and width is half the perimeter, so the width is ...
(40/2) -12 = 8 . . . feet
The depth is half that, so is 8/2 = 4 feet.
The volume is ...
V = LWH = (12 ft)(8 ft)(4 ft) = 384 ft³
Determine a scalar c so that the angle between a = i + cj and b = i + j is 45°.
Answer:
c=0
Step-by-step explanation:
ATQ a.b=|a||b|sin(45)
1+c=sqrt(1+c^2)*sqrt(2)*1/sqrt(2)
1+c=sqrt(1+c^2)
(1+c)^2=(1+c^2)
2c=0, c=0
The required simplified value of c is zero for which the angle between a and b is 45°.
What is a vector?Vector is defined as the quantities that have both magnitude and direction are called a vector quantity and the nature of the quantity is called a vector.
Here,
scaler product is given as,
a . b = |a|.|b|cos45
(i + cj). (i + j) = √[1² + c²] . √[1²+1²] × 1/√2
1 + c = √1 + c²
Squaring both sides
(1 + c)² = 1 + c²
1 + c² + 2c =1 + c²
2c = 0
c = 0
Thus, the required simplified value of c is zero for which the angle between a and b is 45°.
Learn more about vectors here,
https://brainly.com/question/13322477
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please help with math
Answer:
98
Step-by-step explanation:
2, 10, 18, 26, 34, 42, 50... 98
Hope this helps. Have a great day!
write the first 10 multiplies of 6 and 8 pairs of numbers and find this LCM
↪[tex] \huge\rm{answer: } \: \boxed{ \purple{24 }}[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
M(6)= {0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 ...}
M(8) = {0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80...}
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
I hope you understood!✏
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
[tex] \huge\boxed{ \boxed{ \rm{Hope \: this \: helps }}}[/tex]
Answer:
6=0,6,12,18,24,30,36,42,48,54,60
8=0,8,16,24,32,40,48,56,64,72,80
HCF=24,48
LCM=0,6,12,18,,30,36,42,48,54,60,8,16,24,32,40,,56,64,72,80
The least-squares regression equation
y = 3 + 1.16x can be used to predict the height of a plant (in centimeters) after x weeks. Suppose the height of a plant was 9.2 centimeters after 5 weeks.
Calculate and interpret the residual for this plant after 5 weeks.
The residual is
✔ 0.4
, which means that the predicted height of the plant is
✔ 0.4 centimeters less
than the actual height of the plant of
✔ 9.2
centimeters.
Answer:
✔ 0.4
✔ 0.4 centimeters less
✔ 9.2
1.16(5) + 3 = 8.8
9.2 - 8.8 = .4
ED2021
The residual is 0.4
What is regression?
'Regression takes a group of random variables, thought to be predicting Y, and tries to find a mathematical relationship between them. This relationship is typically in the form of a straight line (linear regression) that best approximates all the individual data points.'
According to the given problem,
y = 3 + 1.16x
After 5 weeks, x = 5,
⇒ y = 3 + 1.16(5)
⇒ y = 3 + 5.8
⇒ y = 8.8
Now subtracting y from actual height of plant,
⇒ 9.2 - 8.8
= 0.4
Hence, we can conclude the residual to be 0.4.
Learn more about regression here: https://brainly.com/question/7656407
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Do number three plz triangle theorem
Answer:
AA
Step-by-step explanation:
We know that all three angles are similar as shown by the markings
I would use AA, or the Angle Angle theorem
Find the measure of TU
A. 8
B. 12
C. 14
D. 11
Answer:
D. 11
Step-by-step explanation:
First apply the secant-secant theorem to find the value of x.
Thus,
VU(TU + VU) = VW(BW + VW) (secant-secant theorem)
Substitute
(7)(x + 4 + 7) = (9)(-2 + x + 9)
7(x + 11) = 9(7 + x)
7x + 77 = 63 + 9x
Collect like terms
7x - 9x = 63 - 77
-2x = -14
Divide both sides by -2
x = 7
✔️Find TU
TU = x + 4
Substitute get value of x
TU = 7 + 4 = 11
Answer:
11
Step-by-step explanation:
The mean length of time, per week, that students at a certain school spend on their homework is 24.3 hours, with a standard deviation of 1.4 hours. Assuming the distribution of study times is normal, what percent of students study between 22.9 and 25.7 hours
Answer:
Approximately 68% of students study between 22.9 and 25.7 hours.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 24.3 hours, standard deviation of 1.4 hours.
What percent of students study between 22.9 and 25.7 hours?
22.9 = 24.3 - 1.4
25.7 = 24.3 + 1.4
Within 1 standard deviation of the mean, so:
Approximately 68% of students study between 22.9 and 25.7 hours.
What is the slope of the line that passes through the points (9, -1) and (4, -11)?
Write your answer in simplest form.
Answer:
2
Step-by-step explanation:
We have two points so we can find the slope
m = ( y2-y1)/(x2-x1)
= ( -11 - -1)/( 4 -9)
= (-11+1)/( 4-9)
-10/ -5
= 2
Quantitative noninvasive techniques are needed for routinely assessing symptoms of peripheral neuropathies, such as carpal tunnel syndrome (CTS). An article reported on a test that involved sensing a tiny gap in an otherwise smooth surface by probing with a finger; this functionally resembles many work-related tactile activities, such as detecting scratches or surface defects. When finger probing was not allowed, the sample average gap detection threshold for m = 8 normal subjects was 1.71 mm, and the sample standard deviation was .53; for n = 10 CTS subjects, the sample mean and sample standard deviation were 2.53 and .87, respectively.
Required:
a. Does this data suggest that the true average gap detection threshold for CTS subjects exceeds that for normal subjects?
b. State and test the relevant hypotheses using a significance level of 0.01.
Answer:
Hence, data does not suggest the true average gap detection threshold for CTS subjects exceeds that for normal subjects.
Step-by-step explanation:
H0 : μ1 = μ2
H1 : μ1 < μ2
Given :
m = 8 ; x1 = 1.71 ; s1 = 0.53
n = 10 ; x2 = 2.53 ; s2 = 0.87
The test statistic :
(x1 - x2) / √(s1²/m + s2²/n)
(1.71 - 2.53) / √(0.53²/8 + 0.87²/10)
-0.82 / √0.1108025
Test statistic = - 0.82 / 0.3328700
Test statistic = - 2.463
The degree of freedom using the conservative approach :
Smaller of (10 - 1) or (8 - 1)
df = 7
TCritical value(0.01, 7) = 2.998
Decision region :
Reject H0 if |Test statistic| > |critical value|
Since, 2.463 < 2.998 ; WE fail to reject H0 ; Hence result is not significant at α = 0.01
Multiply:
2 × (–21) × 7
A)
294
B)
–273
C)
–7
D)
–294
Answer:
[tex]2\times \left(-21\right)\times \:7[/tex]
PEMDAS order of operations:
[tex]2\times \left(-21\right)=-2\times \:21=-42[/tex]
[tex]=-42\times \:7[/tex]
[tex]=-294[/tex]
D) -294 is your answer
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