The particular solution of the differential equation (1) is given by
yp = (x raised to power of 2 - x)e raised to power x
The general solution of the differential equation (1) is given by
y = c1x + c2e raised to power of x + (x raised to power of 2 - x)e^x
where c1 and c2 are arbitrary constants.
The complementary equation of the differential equation (1) is given by
(x−1)y′′−xy′+y=0
The general solution of the complementary equation is given by
y = c1x + c2e^x
where c1 and c2 are arbitrary constants.
To find a particular solution of the differential equation (1), we can use the method of variation of parameters. In this method, we assume that the particular solution is of the form
yp = u(x)x + v(x)e^x
where u(x) and v(x) are functions to be determined.
Substituting this expression into the differential equation (1), we get
(x−1)u′′(x)x + (x−1)u′(x)e^x - xu′(x)x - xu′(x)e^x + u(x)x + v(x)e^x = (x−1)^2e^x
Simplifying this equation, we get
(x−1)u′′ + (x−1)u′ - xu′ + u + v = (x−1)^2e^x
Matching the coefficients of the different powers of x on both sides of the equation, we get the following system of equations:
u′′ = 2e^x
u′ = x - 2
u = x^2 - x
v = 0
Solving this system of equations, we get
u(x) = x^2 - x
v(x) = 0
Substituting these expressions into the expression for yp, we get the following particular solution:
yp = (x^2 - x)e^x
The general solution of the differential equation (1) is given by the sum of the general solution of the complementary equation and the particular solution, which is given by
y = c1x + c2e^x + (x^2 - x)e^x
where c1 and c2 are arbitrary constants.
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What is a volume of this composite solid?
Shape a = 6 x 4 x 3 = 72
Shape b = 4 x 4 x 4 = 64
72 + 64 = 136
A
Answer:
A
Step-by-step explanation:
Let F(x) = xet^2 dt for x ∈ [0, 1]. Find F''(x) for x
∈ (0, 1).
4. Let F(x) = Só xetdt for x € [0,1]. Find F"(x) for x € (0,1). (Al- = ) though not necessary, it may be helpful to think of the Taylor series for the exponential function.)
To find the second derivative of F(x) = [tex]\int\limits^0_x {e^t}^{2} } } \, dx[/tex] dt for x ∈ (0, 1), we can use the fundamental theorem of calculus and apply the chain rule twice. The second derivative is given by F''(x) = [tex]2e^{x^{2} } (1+2x^{2} )[/tex]
To find F''(x), we differentiate F'(x) first. Using the fundamental theorem of calculus, we have F'(x) = [tex]e^{x^{2} }[/tex]. Applying the chain rule, we obtain d/dx([tex]e^{x^{2} }[/tex]) = [tex]2xe^{x^{2} }[/tex].
Now, to find F''(x), we differentiate F'(x) with respect to x. Applying the chain rule again, we have d/dx([tex]2xe^{x^{2} }[/tex]) = [tex]2e^{x^{2} }[/tex] + [tex]4x^{2} e^{x^{2} }[/tex]. Simplifying this expression, we get F''(x) = 2[tex]e^{x^{2} }[/tex](1 + [tex]2e^{x^{2} }[/tex]).
Therefore, the second derivative of F(x) is given by F''(x) = 2[tex]e^{x^{2} }[/tex](1 + 2[tex]{x^{2} }[/tex]) for x ∈ (0, 1). This result shows that the second derivative is always positive for x ∈ (0, 1), indicating that the function is concave up within that interval.
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What is the answer to this problem? 23% of 219
Answer:
50.37
Step-by-step explanation:
Answer: 50.37
Step-by-step explanation:
Bart designed a logo using circles of different sizes. The diameters of three of the circles are
shown. Which measurement is closest to the area of the largest circle in square centimeters?
A 20.7 cm2
B 136.8 cm2
C 34.2 cm2
D 65.1 cm
Answer:
B 136.8 cm²
Step-by-step explanation:
Add the diameters of the three smaller circles to find the diameter of the largest circle.
D = 3 cm + 2.5 cm + 1.1 cm = 6.6 cm
area = πr²
area = 3.14 × (6.6 cm)²
area = 136.8 cm²
Help me with this answer please
The point that is NOT 5 units away from the point (1,4) is (4,0).
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Answer:
Step-by-step explanation:
h
Can someone match all of these definitions to all five words for me? I’m very confused but I’ll mark brainlist if you do at least 4! Please and thanks
Solution: Any value for a variable that makes the equation true.
Reciprocal: Focuses on the use of multiplication and division
Coefficient: A number that is multiplied by a variable in an algebraic expression is a coefficient
Term: A term of an algebraic expression is a number, variable, or product of numbers and variables
Base: The base of a power is the factor that is multiplied repeatedly in the power.
Hope this helps, and have a great day!
Answer:
Solution: any value for a variable that makes an equation true
Reciprocal: focuses on use of multiplication and division
Coefficient: A number being multiplied by a variable in an algebraic expression
Base: the base of a power is a factor that is multiplied repeatedly in power
u got the term definition right
Step-by-step explanation:
Please please please help me with this pleasseee!!!
[tex]\Large\boxed{\tt Answer:~A:~y=-3x+5}[/tex]
All we have to do in order to find the equation that is equivalent to 6x + 2y = 10 is to solve for y.
Step 1: Keep y on one side of the equation and move the rest to the other.
[tex]\tt 6x + 2y = 10\\2y = -6x + 10[/tex]
Step 2: Divide all terms by 2 to isolate y.
[tex]\tt 2y \div 2=y\\-6x \div 2 = -3x\\10 \div 2 =5\\\\y=-3x+5[/tex]
Find the cost of cat food for a 29-day supply, a 30-day supply, and a 31-day supply
Answer:
not a complete question..
Step-by-step explanation:
There were about 1.16 million Hispanic-owned businesses in 1999 and 1.53 million in 2003. Find an exponential model for this data in which t = 0 corresponds to 1999 and the number of businesses is measured in millions.
The exponential model for the data on Hispanic-owned businesses is N(t) =[tex]1.16 e^{(0.084t)[/tex], where t represents the number of years since 1999 and N(t) is the number of businesses in millions.
To find an exponential model for the data, we need to fit it into the general form of an exponential function: N(t) = ae^(kt).
Let's assign t = 0 to correspond to the year 1999 and N(t) represents the number of businesses in millions. We are given two data points: (t=0, N=1.16) and (t=4, N=1.53).
Plugging in the first data point, we have:
1.16 = ae^(k*0) => 1.16 = a.
Next, plugging in the second data point, we get:
1.53 = ae^(4k).
Now, we can substitute a = 1.16 into the second equation:
1.53 = 1.16 e^(4k).
Dividing both sides of the equation by 1.16:
1.32 = e^(4k).
Taking the natural logarithm (ln) of both sides:
ln(1.32) = 4k.
Solving for k:
k = ln(1.32)/4.
Now, we have the values of a = 1.16 and k = ln(1.32)/4. Therefore, the exponential model for the data is:
N(t) = 1.16 * e^((ln(1.32)/4) * t), where t represents the number of years since 1999, and N(t) is the number of businesses in millions.
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PLEASE HELP ME I WILL MARK BRAINLIEST
Answer:the answer is solid B
Step-by-step explanation:
Oh your on edmentum I hate it there is so much work but I can help I'm a math master I'm top 3 smartest at math in my whole school.
Please help me on this question if you would want brianleist!! Tank yah!! ^^
Answer:
x axis
Step-by-step explanation:
1. The angle of depression from the top of the
school to the base of the flag pole in front of
the school is 50°. If the flag pole is 35 feet from
the base of the school, find the height of the
school.
Answer:
41.7feet
Step-by-step explanation:
From the question we are given the following
angle of depression = 50°
Distance of the pole from the base of the feet = 35feet (Adjacent)
Required
height of the school (opposite)
Using the SOH CAH TOA identity
Tan theta = opp/adj
Tan 50 = H/35
H = 35tan 50
H = 35(1.1918)
H = 41.7feet
Hence the height of the school is 41.7feet
plz tell about congruent and similar triangles
Similar: If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.
____________________________________________________________
Congruent: SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal. If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.
Find the slope: numbers are: (1,-3) and (-5,-4)
[tex]\frac{-3 - (-4)}{1 - (-5)}[/tex]
= [tex]\frac{-3 + 4}{1 + 5}[/tex]
= 1/6
Answer: the slope is 1/6How many meters are equal to 3,736 centimeters? Use how the placement of the decimal point changes when dividing by a power of 10 to help you.
Answer:
37.36 meters are equal to 3,736 centimeters.
Step-by-step explanation:
We have that 1 meter is equal to 100 centimeters, so if we want to convert 3,736 cm to m we need to divide by 100:
[tex] x = 3,736 cm*\frac{1 m}{100 cm} = 3,736 cm*\frac{1 m}{10^{2} cm} [/tex]
When we divide a number by a power of 10, we move the decimal point to the left as many places as the power indicates.
Since we are dividing by 10², we need to move the decimal point two places to the left, as follows:
[tex] x = 3,736 cm*\frac{1 m}{10^{2} cm} = 37.36 m [/tex]
Hence, 37.36 meters are equal to 3,736 centimeters.
I hope it helps you!
what is the volume of the right triangle prism shown
Answer:
42cm3
Step-by-step explanation:
v = 0.5× b × h × l
= 0.5 × 4 × 3 × 7
= 42cm3
In macroeconomics, the economy can best be understood through the use of
money.
models.
pricing.
debates.
Answer:
models
Step-by-step explanation:
Answer: B.) Models
Edge
A bathtub holds 525,000 mL of water. How many liters is this? O A 52.5 L B 525 L o c. 5.250 L O D. 52,500 L
Answer:
B. 525 L
Step-by-step explanation:
PLEASE HELP FAST!!! I WILL GIVE BRAINLIEST!!!
Answer:
38 ft ^2
Step-by-step explanation:
8x 3 = 24
1/2(4)(3) = 6
1/2(4)(4) = 8
24+6+8 = 38ft^2
1) Which of the following can cause OLS estimators to be biased? Which of the following do not cause the usual OLS t statistics to be invalid (that is, to have t distributions under H0)? (6 points)
Omitting an important independent variable
Multicollinearity
Heteroskedasticity
Including irrelevant variable
The error term non-normally distributed
The following can cause OLS estimators to be biased: Omitting an important independent variable.
Multicollinearity. Heteroskedasticity, Including an irrelevant variable.
The following does not cause the usual OLS t statistics to be invalid (that is, to have t distributions under H0): The error term non-normally distributed
OLS (ordinary least squares) estimates are typically unbiased when calculated.
However, the following problems may cause OLS estimates to be biased:
Omitting an important independent variable: When an important independent variable is omitted from the regression equation, the OLS estimate of the effect of one variable on the dependent variable is biased.
In particular, the estimate of the effect of the variable that is omitted is influenced by the remaining variables' presence in the equation.
Multicollinearity: When the independent variables in a multiple regression model are strongly related, multicollinearity exists.
When there is multicollinearity in a model, the estimated slope coefficients are frequently biased, making them difficult to interpret.
In this scenario, small changes in the data may cause substantial changes in the estimated coefficients.
As a result, the usual tests of hypothesis may fail to produce reliable inferences.
Heteroskedasticity: In the population, heteroskedasticity exists when the variance of the error term is not constant across observations.
Heteroskedasticity can induce OLS estimates' variance to be biased, even if the estimates are unbiased themselves.
When there is heteroskedasticity, the OLS estimates are no longer BLUE (best linear unbiased estimator).
Including irrelevant variable: When an irrelevant variable is included in a regression equation, the OLS estimates of the other variables' effects are biased, and the estimates' standard errors are larger than necessary.
The error term non-normally distributed: When the error term in a regression equation is non-normally distributed, the distribution of the OLS estimates is also non-normal.
However, this does not affect the distribution of the t statistics under H0.
The reason for this is that, even if the error term is non-normally distributed, the sample mean converges to the population mean, according to the central limit theorem.
Furthermore, the standard error of the mean is unaffected by the distribution of the error term, as long as the sample size is large enough.
As a result, the t statistics can be trusted to be asymptotically normally distributed under H0.
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A 12-sided solid has faces numbered 1 to 12. The table shows the results of rolling the solid 200 times. Find the experimental probability of rolling a number less than 3 .
Answer:
The experimental probability of rolling anumber less than 3 is 3/20
Step-by-step explanation:
16+14=30
30/200
=3/20
Answer:
7/50
Step-by-step explanation:
Which expression is equivalent to 10(−45x+3)−2x?
−8x+3
−10x+3
−10x+30
−30x+30
Answer:
-10x+30
Step-by-step explanation:
just got it right on edg 2021 :)
None of these are correct
use mathmatecial induction to prove that for each non negative odd integer n: 24 / (2²³1 +1+1) (n²₁)
Mathematical induction can be used to prove that for every non-negative odd integer n, the expression [tex]24 / (2^{(3n+1)}+1+1) * (n^2+1)[/tex] holds true.
To prove the statement using mathematical induction, we need to follow two steps: the base case and the induction step.
First, we verify if the statement holds true for the base case, which is typically the smallest value of n. In this case, let's consider n = 0. Plugging in n = 0 into the expression, we get [tex]24 / (2^{(3*0+1)}+1+1) * (0^2+1)[/tex]. Simplifying, we have 24 / (2+1+1) * 1, which equals 24 / 4 * 1, resulting in 6. Therefore, the statement holds true for n = 0.
Next, we assume that the statement is true for some arbitrary odd integer k, and we will prove that it holds true for k+2. Assume that [tex]24 / (2^{(3k+1)}+1+1) * (k^2+1)[/tex] holds true.
Now, we substitute k+2 into the expression and aim to show that it holds true for k+2 as well. We have [tex]24 / (2^{(3(k+2)+1)}+1+1) * ((k+2)^2+1)[/tex]. Simplifying the expression, we get [tex]24 / (2^{(3k+7)}+1+1) * (k^2 + 4k + 5)[/tex].
We can manipulate the equation further to demonstrate that it is equal to the assumed expression for k. By performing algebraic manipulations and simplifications, we can equate the expressions and conclude that the statement holds true for k+2.
Since we have verified the base case and shown that the statement holds true for k+2 when it holds true for k, we can conclude that the statement is true for every non-negative odd integer n.
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A person borrows a certain amount of money. He has to pay the debt in equal installments once every month, for 10 years. The first installment was paid on 2016-01-01. Find the date on which he has to pay the final installment.
Answer: January 1, 2025
Step-by-step explanation:
The debt is due to be paid back in 10 years.
If the first payment was in 2016, the last payment should therefore be:
= 2016 + 9 years
= 2025
We used 9 years because 2016 was the first year of payment so the remaining years would be 9 years.
As the first payment was on January 1, 2016, the last payment would have to be on the same date in 2025 which is:
= January 1, 2025
PLEASE SHOW YOUR WORK!!!!!!!!
A basket of beads contains: 8 red beads, 6 yellow beads, and 6 green beads. A bead will be drawn from the basket and replaced 60 times. What is the reasonable prediction for the number of times a green bead is drawn
I WILL MARK BRAINLIEST!!
Answer:
18 times a green bead is drawn
Step-by-step explanation:
There are 20 beads in the basket. The probability of picking a green bead is 6/20 = 3/10. That means that a green bead would be picked 3/10 of the time.
So, 3/10(60) = 18 times a green bead is drawn
In a recent year, a research organization found that 228 of the 350 respondents who reported earning less than $30,000 per year said they were social networking users. At the other end of the income scale, 290 of the 472 respondents reporting earnings of $75,000 or more were social networking users. Let any difference refer to subtracting high-income values from low-income values. Complete parts a through d below. Assume that any necessary assumptions and conditions are satisfied. a) Find the proportions of each income group who are social networking users. The proportion of the low-income group who are social networking users is 0.6514 The proportion of the high-income group who are social networking users is 0.6144 (Round to four decimal places as needed.)
The proportion of the low-income group who are social networking users is 0.6514.
The proportion of the high-income group who are social networking users is 0.6144.
We have the following information from the question:
A research organization found that 228 of the 350 respondents who reported earning less than $30,000 per year said they were social networking users.
Another income scale, 290 of the 472 respondents reporting earnings of $75,000 or more were social networking users.
We have to find proportions of each income group who are social networking users.
Low-income group:
228 users / 350 respondents = 0.6514
The proportion of the low-income group who are social networking users is 0.6514.
High-income group:
290 users / 472 respondents = 0.6144
The proportion of the high-income group who are social networking users is 0.6144.
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What is the fraction that is equal to 0.534
Answer:
267/500
Step-by-step explanation:
0.534 = 534 / 1000
Simplify to 267/500
Step-by-step explanation:
537/1000
this is the correct answer
Which of the following factors does not affect the mortgage payment? No A. Interest rates
B. The down payment
C. The borrower's credit score
D. The neighborhood the home is located in
Answer:
The neighborhood the home is located in
The factors which does not affect the mortgage payment is the neighborhood the home is located in.
The correct option is D.
We are aware of this;
A mortgage is a loan when the borrower's property is used as security. The mortgage payment is determined by the cost of the property, the interest rate, the down payment, the length of the loan, taxes, and various insurances like homeowners insurance, among other factors.
Hence, It's not depend on ''The neighborhood the home is located in.''
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Two numbers sum to 312 and have a difference of 210. What are the two numbers?
Answer:
51 and 261
Step-by-step explanation:
Let the numbers be x and y
x + y =312
x - y =210
2y=102
y=51
x=312-51=261