what is the form of the particular solution for the given differential equation? y''-2y'-3y=4 6xe^2x
Answers
The particular solution, y''-2y'-3y=4 6xe^2x, will be in the form of (Ax^2 + Bx + C)e^(2x).
The form of the particular solution for the given differential equation, y'' - 2y' - 3y = 4(6x)e^(2x), can be found using the following steps:
Step 1: Identify the homogeneous solution
The homogeneous equation is y'' - 2y' - 3y = 0. Its characteristic equation is r^2 - 2r - 3 = 0, which factors into (r - 3)(r + 1) = 0. The roots are r1 = 3 and r2 = -1. So, the homogeneous solution is y_h(x) = C1 * e^(3x) + C2 * e^(-x).
Step 2: Determine the form of the particular solution
Since the right-hand side of the given differential equation is 4(6x)e^(2x), the form of the particular solution, y_p(x), will be a linear combination of x * e^(2x) and its derivatives. Therefore, the form of the particular solution will be:
y_p(x) = (Ax^2 + Bx + C)e^(2x), where A, B, and C are constants to be determined.
Step 3: Find the particular solution
To find the particular solution, substitute y_p(x) into the given differential equation and solve for the constants A, B, and C. Then, the particular solution, y_p(x), will be in the form of (Ax^2 + Bx + C)e^(2x).
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Related Questions
g(x)= -16x2 + 64x + 80 where x is the number of seconds after the rocket is launched. The function can also be written in factored form as g(x) = -16 (x + 1)(x - 5). What is the y-intercept of the function? What does it represent?
Answers
Answer:
y=80
Step-by-step explanation:
when solve y-intercept let x=0
y= -16(0)2+64(0)+80
y=0+0+80
y=80
(0;80)
I just need the second part please! It is an exponential function
Answers
Solution:
The volume of the cases in 2001 is given below as
\(=17.8billion\)The percentage increase from 2000 is given below as
\(=4\%\)The exponential function is given below as
\(\begin{gathered} y=ab^t \\ where, \\ b=1+r \\ r=4\% \end{gathered}\)By substituting the values, we will have
\(\begin{gathered} y=ab^{t} \\ 17.8=a(1+\frac{4}{100})^1 \\ 1.04a=17.8 \\ \frac{1.04a}{1.04}=\frac{17.8}{1.04} \\ a=17.12billion \end{gathered}\)Hence,
The final answer is YES, THE EXPONENTIAL MODEL FUNCTION IS APPROPRIATE
Therefore,
The exponential model after y years will be
\(C(y)=17.12(1.04)^y\text{ }billion\text{ }cases\)
Can any one tell me this i have to do this for my tomorrow school
Answers
Answer:
Step-by-step explanation:
5068300- five million, sixty-eight thousand, three hundred
472607- four hundred seventy-two thousand, six hundred seven
51325678- fifty-one million three hundred twenty-five thousand six hundred eighty-seven
On Wednesday a local hamburger shop sold a combined total of 304 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Wednesday?
Will mark if it is an actual correct answer with an actual explanation
Answers
Answer:
It would be 76 hamburgers were sold on Wednesday
Step-by-step explanation:
I divided the total 304 by 4 and got 76. Then when you multiply that out you get a total of 304
What type of variable is the number of auto accidents reported in a given month q?
Answers
Answer:
Discrete
Step-by-step explanation:
Discrete is the type of variable in which the number of auto accidents reported in a given month q
Discrete data is a count that uses integers and has a finite number of potential values. This sort of information can't be broken down into smaller chunks. Discrete data consists of finite, numeric, countable, and non-negative integers with discrete variables.
As we know that the number of auto accidents that can be reported in a month will be always a whole number, therefore, the number of accidents can be represented as 0, 1, 2,..., 1000, etc.
Thus, the type of variable is the number of auto accidents reported in a given month is Discrete.
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PLEASE HELP WILL MARK BRAINLIESTT
Answers
Answer:
Where the question?
Step-by-step explanation:
for each triangle below, determine the lengths of all the sides, determine the type of triangle being shown and then write a conclusion statement
Answers
According to the information we can infer that the lengths of all sides are: Side AB ≈ 5.39 units, Side BC ≈ 2.83 units, Side AC ≈ 4.47 units and the triangle is Scalene.
How to calculate the length of each side?Using the given coordinates, we can calculate the lengths of the sides of the triangle as follows:
Side AB:
a = (2, 1)b = (7, 3)Distance AB = √((7 - 2)² + (3 - 1)²) = √(25 + 4) ≈ √29 ≈ 5.39 unitsSide BC:
b = (7, 3)c = (4, 5)Distance BC = √((4 - 7)² + (5 - 3)²) = √((-3)² + 2²) ≈ √13 ≈ 2.83 unitsSide AC:
a = (2, 1)c = (4, 5)Distance AC = √((4 - 2)² + (5 - 1)²) = √(2² + 4²) ≈ √20 ≈ 4.47 unitsBased on the calculated side lengths, we can determine that all sides have different lengths, making this triangle a scalene triangle.
In conclusion, the triangle with coordinates A(2, 1), B(7, 3), and C(4, 5) is a scalene triangle with side lengths approximately 5.39 units, 2.83 units, and 4.47 units respectively.
What are length, breadth, and height?Length refers to the longest extent or distance of an object, typically measured in a straight line.Breadth represents the width or the measurement of the object from side to side, perpendicular to the length.Height signifies the vertical dimension of an object, measured from the bottom or base to the top.
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line 1 is y=2x line 2 is y=2x-3 how many solutions are there and whats the coordinates.
Answers
Answer:
no solutions
Step-by-step explanation:
y = 2x → (1)
y = 2x - 3 → (2)
since both equations express y in terms of . equate the right sides to find any solutions.
2x - 3 = 2x ( add 3 to both sides )
2x = 2x + 3 ( subtract 2x from both sides )
0 = 3 ← false statement
this indicates there are no solutions
You ask a neighbor to water a sickly plant while you are on vacation. Without water the plant will die with probability 0.85. With water it will die with probability 0.4. You are 88 % certain the neighbor will remember to water the plant.When you are on vacation, find the probability that the plant will die.ANSWER:You come back from the vacation and the plant is dead. What is the probability the neighbor forgot to water it?Answer:
Answers
The probability that the neighbor forgot to water the plant, given that the plant is dead, is approximately 12.6%.
Let's denote the events as follows:
A: The plant dies without water.
B: The plant dies with water.
W: The neighbor waters the plant.
We are given the following probabilities:
P(A) = 0.85 (probability of the plant dying without water)
P(B) = 0.4 (probability of the plant dying with water)
P(W) = 0.88 (probability that the neighbor waters the plant)
We need to calculate the probability that the neighbor forgot to water the plant, given that the plant is dead:
P(W' | A) = (P(W') * P(A | W')) / P(A)
To calculate P(W' | A), we need to find P(W') (probability that the neighbor forgot to water) and P(A | W') (probability that the plant dies without water, given that the neighbor forgot to water).
P(W') = 1 - P(W) = 1 - 0.88 = 0.12
P(A | W') = P(A) = 0.85
Substituting these values into the formula, we get:
P(W' | A) = (0.12 * 0.85) / 0.85 ≈ 0.126
Therefore, the probability that the neighbor forgot to water the plant, given that the plant is dead, is approximately 0.126 or 12.6%.
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when a certain unfair die is rolled, an even number is times as likely to appear as an odd number. the die is rolled twice. what is the probability that the sum of the numbers rolled is even?
Answers
The probability that the sum of the numbers rolled on the dice is even =1/2.
What is referred as probability?A probability is a measure of the magnitude of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages including several from 0% to 100% can be used to describe probabilities.For the given question,
A fair dice is rolled twice.
Six different results are available with a single roll of the dice (1,2,3,4,5,6)
Therefore, if two dice are rolled, there are a total of 36 possible results, or 6².
Sample space for the sum of even = [(1,1), (1,3), (1,5), (2,2), (2, 4),(2,6), (3, 1), (3,3),(3,5),(4,2),(4,4),(4,6), (5, 1), (5,3),(5,5),(6,2),(6,4),(6,6)]
Total sample space for sum of even = 18
For the probability that the sum of the numbers rolled is even is -
probability (sum is even) = 18 / 36 = 1/2
Thus, the probability that the sum of the numbers rolled is even is 1/2.
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0.2 divided by what equals -1
Answers
I hope this helps
Ask if you have any questions
Which expression has a value of 1?
30 + [(9 x 2) + (4 x 3)]
30 ÷ [(9 x 2) + (4 x 3)]
30 - [(9 x 2) + (4 x 3)]
30 x [(9 x 2) - (4 + 3)]
Answers
The expression given is 30 x [(9 x 2) - (4 + 3)]. In order to find which expression has a value of 1, we must simplify the expression. First, we must solve the parentheses by adding 4 and 3 together, which equals 7, and multiplying 9 and 2 together, which equals 18.
So, the expression now becomes 30 x [18 - 7]. Next, we must solve the brackets by subtracting 7 from 18, which equals 11. So, the expression now becomes 30 x 11. Finally, we must multiply 30 and 11 together to get the final answer, which is 330. Therefore, the given expression does not have a value of 1.
Hello! Let's solve the given expression and check if its value is 1.
Expression: 30 x [(9 x 2) - (4 + 3)]
Step 1: Perform operations within the parentheses first.
9 x 2 = 18
4 + 3 = 7
Step 2: Substitute these values back into the expression.
30 x (18 - 7)
Step 3: Perform subtraction inside the parentheses.
30 x (11)
Step 4: Perform the final multiplication.
30 x 11 = 330
The given expression has a value of 330, not 1.
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I need a bit of help
Answers
Substitute r = 2 and s = 3 into the expression:
5r + 7s - 3(r + s) + 4 = 5(2) + 7(3) - 3(2 + 3) + 4
= 10 + 21 - 15 + 4
= 20
Therefore, the value of the expression when r = 2 and s = 3 is 20.
Given:-
\( \texttt{r = 2}\)\( \: \)
\( \texttt{s = 3}\)\( \: \)
Solution:-
\( \texttt{5r+ 7s - 3( 2 + 3 ) + 4}\)\( \: \)
put the given values in the equation
\( \texttt{5( 2 ) + 7 ( 3 ) - 3( 2 + 3 ) + 4.}\)\( \: \)
\( \texttt{10 + 21 - 6 - 9 + 4}\)\( \: \)
\( \texttt{31 - 15 + 4}\)\( \: \)
\( \texttt{16 + 4}\)\( \: \)
\( \texttt{ \red{20}} \: \)\( \: \)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
hope it helps ⸙
what is the answer to -5m=-75
Answers
Answer:
M=15
Step-by-step explanation:
ǟռֆաɛʀ:
40% of 300= 120.
Step-by-step explanation:
Let's the number is 100u (u denotes unit)
Then, 75% of the number is= (75%×100u)=75u
According to question if 75 is added to 75% of the number then it will be (75u+75) and it will be equal to the number itself.
So, 100u=75u+75
Or, 25u=75
Or, 1u=3
then 100u=300
The number is 300
The reason why we perform an analysis of variance for comparing means rather than conducting multiple two-mean comparisons is Multiple choice question. because multiple two-mean comparisons increase the Type I error probability. simply because ANOVA has simpler calculations but otherwise offers no benefit over the multiple t-tests. power is compromised when using t-tests.
Answers
Instead of performing repeated two-mean comparisons, we conduct an analysis of variance to compare means because doing so reduces the likelihood of Type I errors. Here option A is the correct answer.
ANOVA is preferred over multiple two-mean comparisons because it reduces the Type I error probability and offers several benefits over conducting multiple t-tests.
When conducting multiple two-mean comparisons, the likelihood of making a Type I error (i.e., rejecting a true null hypothesis) increases with each comparison made. This is known as the multiple comparison problem, and it can lead to an inflated false positive rate.
In contrast, ANOVA uses a single test to compare multiple means simultaneously, reducing the likelihood of making a Type I error. ANOVA achieves this by partitioning the total variation in the data into different sources of variation and estimating the amount of variation due to random chance.
Additionally, ANOVA offers several benefits over multiple t-tests. One advantage is that it provides a statistical significance test for the overall difference among the groups, not just for pairwise comparisons. ANOVA also allows for the testing of interactions between factors that influence the mean differences. Furthermore, ANOVA calculations can be more efficient than conducting multiple t-tests, especially when the number of groups is large.
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Complete question:
The reason why we perform an analysis of variance for comparing means rather than conducting multiple two-mean comparisons is
A. Because multiple two-mean comparisons increase the Type I error probability.
B. Simply because ANOVA has simpler calculations but otherwise offers no benefit over the multiple t-tests.
C. Power is compromised when using t-tests.
2. Multiply (-4)(-2)(-5). (5 points)
O
-40
O
-8
8
Answers
(8)(-5)=-40
Answer: -60
Step-by-step explanation: -4x-3x-5=-60...
2 mũ x+2 mũ x+2 mũ x+2 mũ x=32
Answers
Answer:
x = 3
Step-by-step explanation:
<=> 2^x + 2^x + 2^x + 2^x = 32
<=> 4x2^x=32
<=> 2^x = 8
<=> x = 3
Which expression is equivalent to
(3²)
Answers
Answer:
3 + 6 = 92 + 1 + 4 + 2 = 918 : 2 = 93 + 3 + 3 = 9Step-by-step explanation:
Which expression is equivalent to
(3²)
3² = 9
3 + 6 = 92 + 1 + 4 + 2 = 918 : 2 = 93 + 3 + 3 = 9f(x) = -x3+ 3x2 - 5 a) List the coordinates of any extrema (if they exist), and classify as a max or min. b) State where the function is increasing and/or decreasing, c) List any inflection points. d)
Answers
(a) This equation has two coordinates: x = 0 and x = 2, 0 at max and 2 at min. (b) function is increasing on these intervals. (c) x = 1 is an inflection point.
To find the extrema of the function, we need to find the critical points by taking the derivative and setting it equal to zero. Differentiating the function, we get f'(x) = -3x + 6x. Setting this equal to zero gives us -3x + 6x = 0. Factoring out x, we have x(-3x + 6) = 0.
This equation has two solutions: x = 0 and x = 2.To determine whether these points are maxima or minima, we can evaluate the second derivative at these points. Taking the second derivative of f(x), we get f''(x) = -6x + 6. Substituting x = 0 and x = 2 into f''(x), we find that f''(0) = 6 and f''(2) = -6. Since f''(0) > 0, it is a minimum, and f''(2) < 0, it is a maximum.
(b) To find where the function is increasing or decreasing, we can examine the sign of the first derivative. Since f'(x) = -3x + 2 + 6x, we can test the intervals between the critical points x = 0 and x = 2. We find that f'(x) > 0 for x < 0 and 0 < x < 2, indicating that the function is increasing on these intervals. Similarly, f'(x) < 0 for 0 < x < 2 and x > 2, indicating that the function is decreasing on these intervals.
(c) To find the inflection points, we need to find where the concavity of the function changes. This occurs when the second derivative changes sign. From earlier, we know that f''(x) = -6x + 6. Setting f''(x) = 0, we find x = 1 as the potential inflection point.
To determine if it is an inflection point, we check the concavity on either side of x = 1. Plugging in values close to 1, we find that f''(0.5) = 3 and f''(1.5) = -3, indicating a change in concavity and confirming that x = 1 is an inflection point.
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One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.28 hour is desired. Past studies suggest that a population standard deviation of hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Answers
Complete question:
One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.28 hours is desired. Past studies suggest that a population standard deviation of 1.5 hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Answer:
111 students
Step-by-step explanation:
Given the following :
Margin of Error (E) = 0.28
Population standard deviation (sd) = 1.5
Recall:
Margin of Error(E) = Z * (sd/√n)
Taking a confidence interval of 95%
The Z value at a 95% confidence interval is 1.96
Plugging our values, we have :
Margin of Error(E) = Z * (sd/√n)
0.28 = 1.96 * (1.5/√n)
0.28 = 2.94 / √n
√n × 0.28 = 2.94
√n = 2.94 / 0.28
√n = 10.5
Square both sides to obtain n
n = 10.5^2
n = 110.25
Which of the following scenarios is the best fit for the graph?
A. The value of a $100 stock grows in value by 10% each year.
B. The batting average of a baseball team increases by 50 points each year.
C. The population of a small town decreases by 10% each year.
D. A class's percent correct on a standardized Algebra I test increases after using a new software program.
Answers
Answer: A
Step-by-step explanation:
The correct option is A.
What is an exponential function?In mathematics, an exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
Given is that a graph,
So, from the graph we can concluded that it is an exponential and positive function,
Therefore, as x increases y also increases.
We know that the exponential function is given by =
y = abˣ
So, when x = 0, y = 100,
100 = a × b⁰
a = 100
When x = 4, y = 150,
150 = 100 × b⁴
b⁴ = 1.5
b = 1.11
y = 100(1.11)ˣ
Change = 110-100 / 100 × 100% = 10%
Therefore, we can say the value of a $100 stock grows in value by 10% each year.
Hence the correct option is A.
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what is the solution to the equation 3x + 15 = 9
Answers
Answer:
3x + 15 = 9
3x = 9 - 15
3x = -6
x = -6/3
x = -2.
help plz- these were given to me and i was told i could only get help on two-
Answers
A recipe calls for 3/4 cup of flour. You want to make 1/2 of the recipe. How much flour do
you need?
Answers
Answer:
(Down below)
Step-by-step explanation:
Okay, we have 1 recipe and for that recipei we only need 3/4 cup of flour. But we only want 1/2 of that recipe. So, all we have to do is
3/4 ÷ 1/2 and we will get our answer.
(You should be able to do this but I will give the answer anway)
6/4
Hope this helps :)
HELP ASAP!!!.
Molly wants to laminate a painting. The painting is a square that has an area of 225 square inches. The laminator charges 0.24 per square inch of lamination. How much will it cost Molly to laminate the entire painting?
Answers
Answer:
$54
Step-by-step explanation:
Since its $0.24 per 1 square inch, you would multiply 0.24 by the total amount of square inches. When we do this, we get 54 as our answer.\
Hope this helps!
Tyrone is converting startfraction 45 over 50 endfraction to a percent. which method should he use to find the percent? divide the numerator and denominator of the fraction by 2. subtract 40 from the numerator and denominator of the fraction. multiply the numerator and the denominator of the fraction by 2. add 50 to the numerator and denominator of the fraction.
Answers
40% first you turn it into a decimal, then u multiply it by 100 to get your percent.
For solving this question we will use the Unitary method
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The term "unitary method" refers to a process where the value of one item is initially determined before determining the values of any other items.
The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.
2/5 = 0.4
0.4 x 100 = 40% first u turn it into a decimal, then u multiply it by 100 to get ur percent
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The full question will be
Tyrone is converting StartFraction 45 Over 50 EndFraction to a percent. Which method should he use to find the percentage?
14.
Jeremy can build a model airplane in 5 hours less time than his brother. Working together they need 6 hours to build the plane. How long would
it take Jeremy to build the model airplane working alone?
Answers
To work together, their combined work rate is the sum of their individual work rates. So we have:
1/x + 1/(x-5) = 1/6
We can solve for x, the number of hours it would take Jeremy's brother to build the model airplane alone:
6(x)(x-5) = x(x-5) + x(6)
Simplifying this expression, we get:
6x^2 - 30x = x^2 - 5x + 6x
5x^2 - 31x = 0
x = 31/5
So it would take Jeremy's brother 6 hours and 12 minutes to build the model airplane alone.
Since we know Jeremy can build it in 5 hours less time, it would take him 31/5 - 5 = 6 1/5 - 5 = 1 1/5 or 1 hour and 12 minutes to build the model airplane working alone.
1. Quadrilateral BGTS has vertices B (-3, 4), G (-1, 3), T (-1, 1), and S (-4, 2). Graph BGTS and its image after a translation along (5,0) and a reflection in the x-axis.
Answers
The image is attached with answer
What is a Quadrilateral ?
A quadrilateral is a polygon with four sides , four angles and four vertices.
It is given in the question that
Quadrilateral BGTS has vertices B (-3, 4), G (-1, 3), T (-1, 1), and S (-4, 2).
A graph has to be drawn of
its image after a translation along (5,0) and a reflection in the x-axis.
The coordinates after translation and reflection is is B (8, -4), G (6, -3), T (6, -1), and S (7, -2).
The image is attached with the answer .
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Item 8 You choose two different movies on a list at random. Out of 15 movies on the list, 9 are action movies. The first movie you choose is an action movie. What is the probability that the second movie is also an action movie? Write your answer as a fraction in simplest form.
Answers
Answer:
4/7
Step-by-step explanation:
Pr = Expected outcome/Total outcome
Since Total movies = 15
Total outcome = 15
If there are 9 actions movies
Pr(selecting the first action movie) = 9/15
Since the total remaining movies will be 14 (no replacement)
If the second movie is taken, Pr(second action movie) = 8/14 = 4/7
|3n – 6| = 6
absolute value equation
Answers
Answer:
\(n=\{0,\: 4\}\)
Step-by-step explanation:
\(|3n-6| = 6\\\therefore 3n - 6 = \pm 6\\\therefore 3n = 6 \pm 6\\\therefore 3n =6+6\:\: or\:\: 3n = 6-6\\\therefore 3n =12\:\: or \:\:3n = 0\\\\\therefore n =\frac{12}{3}\:\: or\:\: n =\frac{0}{3}\\\\\therefore n = 4 \:\: or\:\: n = 0\\\\\therefore n=\{0,\: 4\}\\\)