Answer:
The answer of the function is y=x-5
Find the general solution of the following second order differential equation. y" + 6y' +9y = e^-3x Inx.
General solution of the second order differential equation:
-6Ae^(-3x) / x + 9Bxe^(-3x) * ln(x) - Be^(-3x) / x^2
To find the general solution of the given second-order differential equation: y" + 6y' + 9y = e^(-3x) * ln(x)
We will use the method of undetermined coefficients to find a particular solution and then combine it with the complementary solution to obtain the general solution.
Step 1: Finding the particular solution
Since e^(-3x) * ln(x) is a product of exponential and logarithmic functions, we assume a particular solution in the form of:
yp = (A + Bx) * e^(-3x) * ln(x)
where A and B are constants to be determined.
Step 2: Find the first and second derivatives of yp.
yp' = (Ae^(-3x) * ln(x) - 3(A + Bx)e^(-3x) * ln(x) + (A + Bx) * e^(-3x) / x
yp" = (Ae^(-3x) * ln(x) - 3(A + Bx)e^(-3x) * ln(x) + (A + Bx) * e^(-3x) / x)'
yp" = (-9(A + Bx)e^(-3x) * ln(x) + 3(A + Bx)e^(-3x) * ln(x) - 3(A + Bx)e^(-3x) / x + (A + Bx) * (-e^(-3x) / x^2 + e^(-3x) / x))
Simplifying, we have:
yp" = -9(A + Bx)e^(-3x) * ln(x) - 6(A + Bx)e^(-3x) / x + (A + Bx) * (-e^(-3x) / x^2 + e^(-3x) / x)
Step 3: Substitute yp, yp', and yp" into the original differential equation to find the values of A and B.
yp" + 6yp' + 9yp = e^(-3x) * ln(x)
Substituting the expressions we found for yp and its derivatives:
(-9(A + Bx)e^(-3x) * ln(x) - 6(A + Bx)e^(-3x) / x + (A + Bx) * (-e^(-3x) / x^2 + e^(-3x) / x))
6((Ae^(-3x) * ln(x) - 3(A + Bx)e^(-3x) * ln(x) + (A + Bx) * e^(-3x) / x))
9((A + Bx) * e^(-3x) * ln(x))
= e^(-3x) * ln(x)
Expanding and simplifying, we get:
-9Ae^(-3x) * ln(x) + 3Bxe^(-3x) * ln(x) - 6Ae^(-3x) / x + 6Bxe^(-3x) / x + Ae^(-3x) / x - Be^(-3x) / x^2 + Be^(-3x) / x + 9Ae^(-3x) * ln(x) + 9Bxe^(-3x) * ln(x)
= e^(-3x) * ln(x)
Combining like terms, we have:
-6Ae^(-3x) / x + 9Bxe^(-3x) * ln(x) - Be^(-3x) / x^2
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is the function described by the points in this table linear or nonlinear? x y −3 9 −1 1 0 0 1 1 3 9 responses linear linear nonlinear
The function described by the points in this table is nonlinear.
Based on the given points in the table, we can determine whether the function is linear or nonlinear by examining the relationship between the x and y values.
Let's look at the x and y values:
x y
-3 9
-1 1
0 0
1 1
3 9
If we observe that for every change in x, the corresponding change in y remains constant, then the function is linear. In other words, if the ratio of the change in y to the change in x is constant, the function is linear.
Let's calculate the ratios:
For x = -3 to x = -1:
Change in y = 1 - 9 = -8
Change in x = -1 - (-3) = 2
Ratio = -8/2 = -4
For x = -1 to x = 0:
Change in y = 0 - 1 = -1
Change in x = 0 - (-1) = 1
Ratio = -1/1 = -1
For x = 0 to x = 1:
Change in y = 1 - 0 = 1
Change in x = 1 - 0 = 1
Ratio = 1/1 = 1
For x = 1 to x = 3:
Change in y = 9 - 1 = 8
Change in x = 3 - 1 = 2
Ratio = 8/2 = 4
As we can see, the ratios are not constant. The ratio changes from -4 to -1, then to 1, and finally to 4. Therefore, the function described by the points in this table is nonlinear.
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Peter is making an "X marks the spot" flag for a treasure hunt. The flag is made of a square white flag with sides of 12 centimeters. He will make the "X" by stretching red ribbon diagonally from corner to corner.
Answer:
33.94 cms of ribbon
Step-by-step explanation:
Because you need two diagonals to form the x, therefore the amount of ribbon needed is the sum of the distance of both diagonals.
When crossing the diagonal, a rectangular angle is formed, where the diagonal would be the hypotenuse, we know that the distance of the hypotenuse can be calculated by means of the legs, which we know its value (12):
d ^ 2 = a ^ 2 + b ^ 2
a = b = 12
d ^ 2 = 12 ^ 2 + 12 ^ 2
d ^ 2 = 288
d = 288 ^ (1/2)
d = 16.97
16.97 cm is what it measures, a diagonal, therefore tape is needed:
16.97 * 2 = 33.94
A total of 33.94 cms of ribbon is needed
Answer from jmonterrozar
sara bought x pounds of chocolate covered raisins, which sell for $1.50 a pound, and y pounds of yogurt covered raisins, which sell for $1.20 a pound. sara bought a total of 40 pounds of the two types of raisins for a total of $51.90." help me write a system of equations to model this scenario
Simplify. simplify simplify
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(\dfrac{4}{9})^2}[/tex]
[tex]\mathsf{= \dfrac{4}{9}\times\dfrac{4}{9}}[/tex]
[tex]\mathsf{= \dfrac{4^2}{9^2}}[/tex]
[tex]\mathsf{\dfrac{4\times4}{9\times9}}[/tex]
[tex]\mathsf{4 \times 4 = \bold{16}\leftarrow \underline{Numerator}}[/tex]
[tex]\mathsf{9\times9 = \bf 81}\leftarrow\mathsf{\underline{Denominator}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \boxed{{\bf \dfrac{16}{81}}}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
If sin A=0.7986, then the measure of Đ A, to the nearest degree is?
Answer:
B
Step-by-step explanation:
A will equal the sine inverse (arc sine or sin^-1 ) of 0.3571. Using a calculator, sin^-1(0.3751) = 22.03 degrees (B)
Given that coule.us) - EILE DE M2)]. lajure the linearity rule and & (c) = c. to derive the equation for constate) in ternis of EA), Mj and H2(erive expression for cours, 34%, and 22 are independent random vartolus. f(x)= [ (x for 2 exc4 = 56) o elsewhere for a continuon ona random variable &. (a) Compute. P/2 ex <3). (6) Compute Elx), the mean of t. (8) Given (6) For some other random variable & My (t) = e. Determine the mean Ele) for this other random variable. (5* +32+) P.
(a) The probability that X is less than 3, P(X < 3), is 0.
(b) The mean of X, denoted as E(X), is 71/24, which is approximately 2.9583 when rounded off to four decimal places.
(c) Given Y = e^X, the mean of Y, denoted as E(Y), is approximately 15.75 when rounded off to two decimal places.
(a) It is required to compute P(X<3). Since the range for which f(x) is not equal to 0, is the interval from 2 to 4 for f(x), the probability that X is less than 3 is 0.
Similarly, for X > 4, P(X > 4) = 0.
P(2 ≤ X ≤ 4) = ∫f(x)dx from 2 to 4= ∫ (x/24 - 7/3) dx from 2 to 4= [x^2/(2 × 24) - 7x/3] from 2 to 4= 1/4 - 28/3 + 8/(2 × 24) + 14/3= 71/24= 2.9583(rounded off to four decimal places)
(b) The mean of X can be computed as follows:
E(X) = ∫xf(x)dx from -∞ to ∞= ∫ (x/24 - 7/3) dx from 2 to 4= [x^2/(2 × 24) - 7x/3] from 2 to 4= 1/4 - 28/3 + 8/(2 × 24) + 14/3= 71/24= 2.9583(rounded off to four decimal places)
(c) Y = e^X
The mean of Y can be computed as follows:
E(Y) = E(e^X)= ∫ e^x f(x) dx from -∞ to ∞= ∫ e^x (x/24 - 7/3) dx from 2 to 4= [e^x (x - 31)/(24)] from 2 to 4= (e^4/6 - 31e^4/24 - e^2/6 + 31e^2/24) ≈ 15.75(rounded off to two decimal places).
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approximate the area under the curve graphed below from x = 2 x=2 to x = 5 x=5 using a left endpoint approximation with 3 subdivisions.
The approximate area under the curve from x = 2 to x = 5, using a left endpoint approximation with 3 subdivisions, is 13.5 square units.
To approximate the area under the curve, we divide the interval from x = 2 to x = 5 into three equal subdivisions, each with a width of (5 - 2) / 3 = 1. The left endpoint approximation involves using the leftmost point of each subdivision to approximate the height of the curve.
In this case, we evaluate the function at x = 2, x = 3, and x = 4, and use these values as the heights of the rectangles. The width of each rectangle is 1, so the areas of the rectangles are calculated as follows:
Rectangle 1: Height = f(2) = 2, Area = 1 * 2 = 2 square units.
Rectangle 2: Height = f(3) = 4, Area = 1 * 4 = 4 square units.
Rectangle 3: Height = f(4) = 7, Area = 1 * 7 = 7 square units.
Finally, we add up the areas of the three rectangles to obtain the approximate area under the curve: 2 + 4 + 7 = 13 square units. Therefore, the approximate area under the curve from x = 2 to x = 5 using a left endpoint approximation with 3 subdivisions is 13.5 square units.
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Solve the differential equation (D^2 + 4)y=6 sin2x +3x^2 =
The solution to the differential equation (D^2 + 4)y = 6 sin(2x) + 3x^2 is y = (3/4)x^2 + A sin(2x) + B cos(2x).
To solve the given differential equation (D^2 + 4)y = 6 sin(2x) + 3x^2, where D represents the derivative operator, we can use the method of undetermined coefficients.
First, we find the general solution to the homogeneous equation (D^2 + 4)y = 0. The characteristic equation is r^2 + 4 = 0, which has complex roots ±2i. Therefore, the general solution to the homogeneous equation is y_h = A sin(2x) + B cos(2x), where A and B are constants.Next, we find a particular solution to the non-homogeneous equation. By inspection, we can guess that y_p = (3/4)x^2 is a particular solution.Finally, the general solution to the non-homogeneous equation is the sum of the homogeneous and particular solutions:y = y_h + y_p
y = A sin(2x) + B cos(2x) + (3/4)x^2
Here, A and B are arbitrary constants that can be determined by applying initial or boundary conditions, if given.
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1 point
Finish the similarity statement. (Note: your answer will be the 3 letters of
the other triangle. You must place them in the correct order and use
CAPITAL letters!) APQR-4
R
4 in
6 in
VA
8 in
4 in
3 in
2 in
YOUR ANSWER IS ANGLE BAC
What should be done to both sides of the equation in order to solve y - 4.5 = 12.2?
To solve the equation y - 4.5 = 12.2 we have to add 4.5 on both sides of the equation.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is y - 4.5 = 12.2
y minus four point five equal to twelve point two.
In the equation y is the variable and minus is the operator in the equation.
To solve the equation we have to isolate the variable y.
To isolate the variable y we have to add 4.5 on both sides of the equation
y-4.5+4.5=12.2+4.5
y=16.7
Hence, to solve the equation y - 4.5 = 12.2 we have to add 4.5 on both sides of the equation.
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PLEASE HELP ILL GIVE BRAINLIEST
WHATS THE PERCENT CHANGE SHOW WORK
Answer:
34.55556%
Step-by-step explanation:
Regan cycles 78 miles in 6 hours. His average speed for the first 30 miles is 15 miles per hour. Work out Regan's average speed for the last 48 miles.
Answer:
12 mph
Step-by-step explanation:
Given that:
Total distance traveled = 78 miles
Time taken, t = 6 hours
Average speed for first 30 miles = 15 mph
Time taken = distance / speed
Time taken = 30 / 15
Time taken = 2 hours
Average speed for last 48 miles = x
Time taken to travel last 48 miles = (6 - 2) = 4 hours
Average speed for last 48 miles :
Distance traveled / time taken
48 miles / 4 hours
= 12 mph
Which of the following represents y < 2x - 3?
help a girl out please
Answer:
A
Step-by-step explanation:
the y intercept (where x is 0) should be -3 because of y<3x-3
Which set of numbers is infinite?
A) integers between -4 and 7
B) whole numbers between 1 and 17
C) natural numbers between 5 and 10
D) irrational numbers between 10 and 30
Answer:
D). irrational numbers between 10 and 30
The water used by the 12 students during the experiment was poured from a beaker after the water was poured 1/4 gallon of water was left in the beaker What was the total number of fluid ounces of water in the beaker before the water was poured by the 12 students
Answer:
128 fluid ounces
Step-by-step explanation:
We were told that:
During the experiment was poured from a beaker after the water was poured 1/4 gallon of water was left in the beaker
Hence, this means that the total gallon of water in the beaker is 1 gallon
Convert 1 gallon to fluid ounces
1 gallon =128 fluid ounces
Therefore, the total number of fluid ounces of water in the beaker before the water was poured by the 12 students is 128 fluid ounces.
a manufacturer knows that their items have a normally distributed lifespan, with a mean of 4.4 years, and standard deviation of 1.2 years.the 7% of items with the shortest lifespan will last less than how many years?
Using the standard deviation, mean, and z-score, the 7% of items with the shortest lifespan will last less than approximately 1.59 years.
What is 7th percentile of items with the shortest lifespan?To find the number of years that the 7% of items with the shortest lifespan will last, we need to determine the z-score corresponding to the 7th percentile of the normal distribution.
Step 1: Convert the given percentile to a z-score using the standard normal distribution table or a statistical calculator. The 7th percentile corresponds to a z-score of approximately -1.405.
Step 2: Use the formula for z-score to find the corresponding value in terms of years:
x = μ + z * σ
where x is the value we are looking for, μ is the mean, z is the z-score, and σ is the standard deviation.
Plugging in the values:
x = 4.4 + (-1.405) * 1.2
x = 1.59 years
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Find the product.
-7(-a 2)(-5)
Answer:
3
5
(
−
2
)
Step-by-step explanation:
Simplify then multiple the numbers
2. Dibuja la mesa de tu casa, denota los puntos evidentes y nombra los siguientes elementos u objetos geométricos.
a) Tres planos.
b) Dos rectas de planos distintos.
c) Dos ángulos de un plano y dos de otro.
d) Dos rayos. e) Dos semirrectas.
Answer:
a) The floor of the room, each edge and the top of the table.
b) The edge of one side and one leg of the table.
c) The angle formed between the sides of the table and the angle between the legs of the table and its edges.
d) The vertices of the top of the table.
e) These are same lines.
Step-by-step explanation:
An angle is the amplitude between the two lines. Plane is an object which consists of two dimensions and infinite points. The segment is a fragmented line. A ray is a line which a starting point and a direction.
A) Tres planos que surgen a partir de la mesa de mi casa son la superficie de la mesa, la superficie del suelo sobre el cual se apoya la mesa, y la superficie de la pared sobre la cual reposa la mesa.
B) Dos rectas de planos distintos pueden ser el borde de la mesa, por una parte, y la pared, por el otro.
C) Dos ángulos de un plano y dos de otro son el vértice de la mesa y el ángulo formado entre el borde de la misma y un vaso, por un lado, y el ángulo formado por una baldosa y la pata de la mesa y el ángulo recto formado por las líneas de una baldosa, por la otra.
D) Dos rayas pueden ser la línea a ras del suelo y la línea a ras de la mesa.
E) Dos semirrectas pueden ser ambas patas de la mesa.
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Does anyone know how to work this out step by step?
Answer:
[tex]2x^{3} +10[/tex]
Step-by-step explanation:
[tex]x*2x*x+10=2x^{3} +10[/tex]
2.46 strong association but no correlation. here is a data set that illustrates an important point about correlation: corr x 25 35 45 55 65 y 10 30 50 30 10 (a) make a scatterplot of y versus x. (b) describe the relationship between y and x. is it weak or strong? is it linear? (c) find the correlation between y and x. (d) what important point about correlation does this exercise illustrate?
a. In the picture we can see that the scatterplot is given for the data in the given table.
b. It is not linear as we can see from scatterplot.
c. The correlation between y and x is 0.
d. when r = 0 there is no relationship between x and y.
Given that,
The data is given in the table.
We know that,
a. We have to make a scatterplot of y versus x.
In the picture we can see that the scatterplot is given for the data in the given table.
b. We have to describe the relationship between y and x.
When x increases y increases upto certain point after that y start to decrease but x is increases only
Therefore, it is not linear as we can see from scatterplot.
c. We have to find the correlation between y and x.
The formula for the correlation coefficient is
r = [tex]\frac{n\times \sum XY-\sum X \times\sum Y}{\sqrt{[n\sum X^2 - (\sum X)^2][n\sum Y^2 - (\sum Y)^2]} }[/tex]
Now we find summation of all X, Y and XY, [tex]X^2[/tex] and [tex]Y^2[/tex]
X Y XY [tex]X^2[/tex] [tex]Y^2[/tex]
25 10 250 625 100
35 30 1050 1225 900
45 50 2250 2025 2500
55 30 1650 3025 900
65 10 650 4225 100
Now, ∑X = 225
∑Y = 130
∑XY = 5850
∑[tex]X^2[/tex] = 11125
∑[tex]Y^2[/tex] = 4500
Now, Substitute the values in the formula
r = [tex]\frac{5\times 5850-225 \times130}{\sqrt{[5\times 11125 - (225)^2][5\times 4500 - (130)^2]} }[/tex]
r = 0
Therefore, The correlation between y and x is 0.
d. We have to find what important point about correlation does this exercise illustrate.
Therefore, when r = 0 there is no relationship between x and y.
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Solve for x. Please help me I am confused.
Answer:
72
Step-by-step explanation:
Multiply all the numbers, and you get the answer
Identify the location of the point (6, -2). A. P B. Q C. R D. S
Answer:
Step-by-step explanation:
Does the equation 3(2x−1)+5=6(x+1) have one, none, or an infinite amount of solutions?
Answer: No solutions
Step-by-step explanation: If you solve the problem all the way, you get 0 = 4 which is not valid so there is simply no solution
The given equation 3(2x−1)+5=6(x+1) has no solution. Option B is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given equation ⇒
⇒= 3(2x−1)+5=6(x+1)
Simplify the above expression,
⇒ 6x - 3 + 5 = 6x + 1
⇒ 2 ≠ 1
Thus, the given equation has no solution.
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Use the binomial distribution to determine the probability that 10 rolls of a fair die will show exactly seven fours. Express your answer as a decimal rounded to 4 decimal places.
The probability of getting exactly seven fours in ten rolls of a fair die is approximately 0.0574.
To determine the probability of exactly seven fours in 10 rolls of a fair die, we can use the binomial distribution formula:
P(X = k) = (nCk) * p^k * (1-p)^(n-k)
Where:
P(X = k) is the probability of getting exactly k successes (in this case, rolling a four) in n trials (in this case, rolling a die 10 times),
nCk is the number of combinations of n items taken k at a time,
p is the probability of success on a single trial (rolling a four), and
(1-p) is the probability of failure on a single trial (not rolling a four).
In this case, n = 10, k = 7, p = 1/6 (since there is a 1/6 chance of rolling a four on a fair die), and (1-p) = 5/6.
Plugging these values into the formula:
P(X = 7) = (10C7) * (1/6)^7 * (5/6)^(10-7)
Calculating the combinations:
(10C7) = 10! / (7! * (10-7)!) = 10! / (7! * 3!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
Substituting the values:
P(X = 7) = 120 * (1/6)^7 * (5/6)^(10-7)
Calculating the probability:
P(X = 7) = 120 * (1/6)^7 * (5/6)^3 ≈ 0.0595
Therefore, the probability that exactly seven fours will appear in 10 rolls of a fair die is approximately 0.0595 (rounded to 4 decimal places).
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A rectangular prism has a volume of 900 cubic units. The prism has a length of 25 units and a width of 12 units. Which equation could be used to find h, the height of the prism?
Answer:
52 cubic units
Step-by-step explanation:
got it right on edg
Answer:
37h 900
Step-by-step explanation:
what value of x makes the equation -2/3x + 3 1/3x - 1/2 = -1/3x + 5 1/2 true?
A) 2
B) 1/2
C) -2
D) -1/2
Answer:
2
Step-by-step explanation:
Identify the values of A, B, and C
5x2 + x - 18 = - 9x + 3x2
A=2, B=10, C=-18
A=2, B=9, C=-18
A=5, B=1, C=-18
A=8, B=-8, C=-18
Answer:
A=2, B=10, C=-18
The answer is the first one.
Step-by-step explanation:
[tex]5x^{2} -3x^{2} +x+9x-18=0[/tex]
[tex]2x^{2} +10x-18=0[/tex]
Formula: [tex]f(x)=ax^{2} +bx+c[/tex]
What is the slope and y-intercept of 9x - 3y = 15?
NO FILES PEOPLE!
slope is 3
y-intercept is 0,-5
The error of rejecting the null hypothesis, when it is actually true is: alpha beta Type Il error Type I error
The error of rejecting the null hypothesis when it is actually true is known as a Type I error or alpha error. It represents the incorrect rejection of a null hypothesis that is true in reality.
Type I errors are associated with the significance level (alpha) chosen for a statistical test and occur when the test incorrectly concludes that there is a significant effect or relationship when there isn't one.
In hypothesis testing, the null hypothesis represents the assumption of no effect or no relationship between variables. The alternative hypothesis, on the other hand, suggests the presence of an effect or relationship. The significance level (alpha) is the threshold set by the researcher to determine the probability of rejecting the null hypothesis.
A Type I error occurs when the null hypothesis is true, but the statistical test incorrectly rejects it, leading to a false conclusion of a significant effect or relationship. This error is also known as a false positive. The probability of making a Type I error is denoted by alpha.
Type I errors are considered undesirable because they lead to incorrect conclusions and may result in wasted resources or inappropriate actions based on flawed evidence.
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