2. Use the predictor-corrector method to solve dy/dx= x² + y²; y(1) = 0 for y(2) with h = 0.01. Repeat for h = 0.05 and then give an estimate of the accuracy of the result of the first calculation.
Answers
The predictor-corrector method is used to solve the given initial value problem with step sizes h = 0.01 and h = 0.05. The accuracy of the result can be estimated by comparing the values of y(2) obtained with both step sizes.
To solve the given initial value problem using the predictor-corrector method, we first need to choose a step size h. Let's start with h = 0.01.
Using the predictor-corrector method, we perform the following steps:
Step 1: Initialization
Set x₀ = 1, y₀ = 0 (initial conditions)
Set h = 0.01
Step 2: Predictor Step
Using the Euler's method, calculate the predicted value of y at the next step:
y_p = y₀ + h * (x₀² + y₀²)
Step 3: Corrector Step
Using the corrected value of y at the next step:
y₁ = y₀ + (h/2) * ((x₀ + h)² + (y₀ + y_p)²)
Step 4: Repeat the process
Repeat steps 2 and 3 until x reaches the desired value, which is 2 in this case.
Performing the above steps iteratively, we calculate the values of y for each step until x = 2.
Now, let's repeat the same process for h = 0.05.
After obtaining the solutions for both h = 0.01 and h = 0.05, we can estimate the accuracy of the result by comparing the values of y(2) obtained with both step sizes. The smaller the difference between the results obtained with different step sizes, the higher the accuracy of the approximation.
By comparing the results, we can assess the convergence and accuracy of the predictor-corrector method for this specific problem and determine the estimated accuracy of the first calculation.
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Related Questions
when severe autocorrelation is indicated after a regression model has been estimated, which underlying regression assumption is violated?
Answers
The fundamental regression assumption that the error terms are independent of one another is broken when substantial autocorrelation is shown following the estimation of a regression model. Here option C is the correct answer.
The two error factors must be somewhat co-correlated in order for there to be autocorrelation. Having it indicates that the correlation between the two error factors is not equal to zero. It goes against the fundamental tenet of the traditional linear regression approach.
Autocorrelation measures the relationship between a variable's current value and its historical values. A perfect positive correlation is represented by an autocorrelation of 1, whereas a perfect negative correlation is represented by an autocorrelation of 1.
An explanation of how one or more independent variables relate to the target variable, response variable, or dependent variable that the regression model predicts.
Complete question:
When severe autocorrelation is indicated after a regression model has been estimated, which underlying regression assumption is violated? A - The dispersion of population data points around the population regression line remains constant everywhere along the line
B - The population of values is normally distributed about the population regression line.
C - Heteroscedasticity
D - The error terms are independent of each other.
E - A linear relationship exists between X and Y in the population
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Solve for x in the diagram below.
Answers
Hi there!
\(\large\boxed{x = 35}\)
The angles shown are linear pairs, meaning they sum up to 180°. Therefore:
180 = 3x + 75
Subtract 75 from both sides:
180 - 75 = 3x
105 = 3x
Divide both sides by 3:
105/3 = 3x/3
x =35°
sangho uploaded a video to a website where viewers can vote that they like or dislike a video. each video begins with a score of 0, and the score increases by 1 for each like vote and decreases by 1 for each dislike vote. at one point sangho saw that his video had a score of 90, and that $65\%$ of the votes cast on his video were like votes. how many votes had been cast on sangho's video at that point?
Answers
Let's assume the total number of votes cast on Sangho's video is 'x'. Given that $65%$ of the votes were like votes, we can determine the number of like votes as $0.65x$.
Since the score increases by 1 for each like vote and decreases by 1 for each dislike vote, the total score can be expressed as:
Score = Number of like votes - Number of dislike votes
Given that the score is 90, we can write the equation:
90 = (Number of like votes) - (Number of dislike votes)
Substituting the number of like votes with $0.65x$, we have:
90 = 0.65x - (x - 0.65x)
Simplifying the equation, we get:
90 = 0.65x - x + 0.65x
90 = 1.3x - x
90 = 0.3x
Dividing both sides by 0.3, we find: x = 90 / 0.3 = 300
Therefore, at the point when Sangho's video had a score of 90 and $65%$ of the votes were like votes, a total of 300 votes had been cast on his video.
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In a fishing community of 9400 people, the number of women exceeds the number of men by 1500. Find the ratio of men to women in the community
Answers
w=women
m+1500=w
m+1500+m=9400
2m+1500=9400
2m=9400-1500
2m=7900
m=7900/2
m=3950
w=3950+1500
w=5450
y= 2x y=3x-10 how do you do this equation
Answers
The solution of the system of equations is x = 10 and y = 20.
What is a quadratic equation?A quadratic equation is a second-order polynomial equation in one variable x ax2 + bx c=0. with ≠ 0. Since this is a quadratic polynomial equation, the Fundamental Theorem of Algebra ensures that it has at least one solution. The solution can be real or complex
To solve an equation, you must find the value of x that makes both equations true at the same time. Once you find the value of x, you can substitute it into both equations to find the corresponding value of y.
One way to do this is to set the two expressions for y equal to each other, since both are equal to y:
2x = 3x - 10
Subtracting 2x from both sides, we get:
-x = -10
Dividing both sides by -1 gives:
x = 10
Now that we know that x = 10, we can substitute it into both equations to find the corresponding value of y. Let's use the first equation:
y = 2x = 2(10) = 20
Therefore, the solution of the system of equations is x = 10 and y = 20.
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On a test that has a normal distribution, a score of 54 falls two standard deviations
above the mean, and a score of 42 falls one standard deviation below the mean.
Determine the mean of this test.
Answers
Let μ be the mean of the distribution and let σ be its standard deviation.
We know that 54 falls two standard deviations above the mean, this can be express as:
\(\mu+2\sigma=54\)We also know that 42 falls one standard deviation below the mean, this can be express as:
\(\mu-\sigma=42\)Hence, we have the system of equations:
\(\begin{gathered} \mu+2\sigma=54 \\ \mu-\sigma=42 \end{gathered}\)To find the mean we solve the second equation for the standard deviation:
\(\sigma=\mu-42\)Now we plug this value in the first equation:
\(\begin{gathered} \mu+2(\mu-42)=54 \\ \mu+2\mu-84=54 \\ 3\mu=138 \\ \mu=\frac{138}{3} \\ \mu=46 \end{gathered}\)Therefore, the mean of the distribution is 46
Let Y1, ..., Y100 be independent Uniform(0, 2) random variables.a) Compute P[2Y< 1.9]b) Compute P[Y(n) < 1.9]
Answers
Any given Y(n) among the set of Y1, Y2, ..., Y100, the probability of Y(n) being less than 1.9 is 0.475.
a) To compute P[2Y < 1.9], where Y is a Uniform(0, 2) random variable, we need to find the probability that twice the value of Y is less than 1.9. The Uniform(0, 2) distribution has a constant probability density function of 1/2 within the interval (0, 2). Since Y is uniformly distributed, the probability that Y takes any specific value within (0, 2) is equal.
To calculate the probability, we need to find the proportion of the interval (0, 2) where 2Y is less than 1.9. Dividing 1.9 by 2 gives us 0.95, and we need to find the proportion of the interval (0, 2) that lies to the left of 0.95. This proportion can be calculated as (0.95 - 0) / 2 = 0.475. Therefore, P[2Y < 1.9] is equal to 0.475.
b) P[Y(n) < 1.9] refers to the probability that a specific random variable, denoted as Y(n), is less than 1.9. Since Y(n) is part of the set of independent Uniform(0, 2) random variables, the probability calculation is the same as in part a). Each Y(n) follows the same distribution, and we can find the proportion of the interval (0, 2) where Y(n) is less than 1.9.
Using the same calculation as before, we determine that P[Y(n) < 1.9] is equal to 0.475. Therefore, for any given Y(n) among the set of Y1, Y2, ..., Y100, the probability of Y(n) being less than 1.9 is 0.475.
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Question of the day
Fill in the table of values below for the equation y=x+3
Х
у
Answers
x | y
———-
0 | 3
1 | 4
Slope: 1
Y-intercept: 3
Answer:
yuuurrrppp
Step-by-step explanation:
53 points!!! find x. do not round your answer. 5cm 6cm 12cm x
Answers
Answer:
16.6
Step-by-step explanation:
By the property of intersecting secants.5(5+x) = 6(6+12)-> 25 + 5x = 6*18-> 5x = 108 - 25-> 5x = 83-> x = 83/5-> x = 16.6what are the two integers
Answers
Answer:
3 and 4
Step-by-step explanation:
2^3 = 8
2^4=16
14 lies in between them
What is ""house flipping?""
a. the process of transferring ownership of a house from one person to another.
b. the process of buying a house with the intention of selling it for a profit after only a short time.
c. the process of two people exchanging the titles to their properties.
d. the process of a house’s market price rapidly fluctuating. please select the best answer from the choices provided a b c d
Answers
house flipping is the buying of a house for a low price with the intention of reselling it for a profit after a short period of time.
Buyers that acquire distressed houses, patch them up, and then resell them for a profit are included. These properties are often found through foreclosures, bank short sales, or property auctions.
To be successful at real estate flipping, you must be able to manage your money properly and invest in inexpensive homes. These are generally properties that need a lot of attention.
Following that, you'll need to spend on modifications that will boost the resale value of the house and draw the attention of a possible buyer. When the improvements are finished, you must list and advertise the home.
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Which equation has no solution?
A.
B.
C.
D.
Answers
Answer:
C.
Step-by-step explanation:
The equation will have no solution if it reduces to the form ...
1 = 0
Other possible forms are ...
0 = 0 . . . . infinite solutions
y + c = 0 . . . . one solution
___
The given equations can be reduced to one of these forms by subtracting the right-side expression from both sides.
A. 2.3y +2 +3.1y -(4.3y +1.6 +1.1y +0.4) = 0 ⇒ 0 = 0 (infinite solutions)
B. 32x +25 -21x - 10x = 0 ⇒ x +25 = 0 (one solution)
C. 5/8x +2.5 -(3/8x +1.5 +1/4x) = 0 ⇒ 1 = 0 (no solutions)
D. 1/3 +1/7y -3/7y = 0 ⇒ y -7/6= 0 (one solution)
PLEASE HELP ITS URGENT I INCLUDED THE PROBLEM IN IMAGE I WROTE IT DOWN!!!
Answers
1.) To solve the inequality \(g/20 ≤ 5\) for \(g\), we can multiply both sides by \(20\) to get rid of the fraction. This gives us\(g ≤ 100\). So the solution to the inequality is \(g ≤ 100\)\(.\)
The solution of the expression is,
⇒ d < 0
Since,
A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The expression is,
⇒ 3 + d < 3 - d
Now, We can simplify as;
⇒ 3 + d < 3 - d
⇒ 3 + d + d < 3
⇒ 3 + 2d < 3
⇒ 2d < 0
⇒ d < 0
Thus, The solution of the expression is,
⇒ d < 0
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\( Y(s)=\frac{2 s-3}{(s-1)^{2}+5} \) \( Y(s)=\frac{3 s+2}{s^{2}+4 s+29} \)
Answers
The required function is \(e^t*cos(\sqrt5t)\)t. In other words, the Laplace transform of \(Y(s) = \frac{2s-3}{(s-1)^2+5}\) is \(e^t*cos(\sqrt5t)\).
The Laplace transform of the function \(Y(s) = (2s-3)/((s-1)^2+5)\) can be found by applying the properties of the Laplace transform.
The Laplace transform is a mathematical operation that transforms a function of time into a function of complex frequency s. It is commonly used in engineering and physics to solve differential equations and analyze dynamic systems.
To find the Laplace transform of a function, we use the definition of the Laplace transform and various properties such as linearity, translation, and frequency shifting. These properties allow us to simplify the expression and apply known transforms from the Laplace transform table.
In the given function \(Y(s) = \frac{2s-3}{(s-1)^2+5}\), we can recognize that the denominator\((s-1)^2+5\) matches the form of a known Laplace transform.
The Laplace transform of \(e^{at}*cos(bt)\) is \(\frac{s-a}{(s-a)^2+b^2}\), which is similar to the given function.
By comparing the given function with the Laplace transform property, we can conclude that the Laplace transforms of Y(s) is \(e^t*cos(\sqrt5t)\).
Therefore, the required function is \(e^t*cos(\sqrt5t)\)t. In other words, the Laplace transform of \(Y(s) = \frac{2s-3}{(s-1)^2+5}\) is \(e^t*cos(\sqrt5t)\).
Question: Find the Laplace transform of \(Y(s) = \frac{2s-3}{(s-1)^2+5}\).
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for f(x) = -4x -9 evaluate for f(6.5)
Answers
Answer:
f=−35
Step-by-step explanation:
1.Simplify 4×6.5 to 26
f=-26-9
2. Simplify -26-9 to -35
f=-35
Help, I need to answer this question
Answers
Answer:
Step-by-step explanation:
factors of 8
Answer:
F- of a 8* i think
Step-by-step explanation:
in parallelogram RSTU, what is SU?
Answers
Answer:
RSTU is a parallelogram and SU is a diagonal of the parallelogram. Quantity I : Value of x Quantity II : Value of y
Step-by-step explanation:
y= -x + 1 and y= 2/3x - 4 What is the solution to the system of equations?
Answers
Answer:
x=3 /
steps: (For x)
Turn the equation into --> -x+1 = 2/3x-4
Next is the multiply the equation by 3 to make isolating x easier so it becomes --> -3x+3=2x-12
Now arrange the terms to where variables are on a side and constants are on a side
it should look like --> -3×-2x=-12-3
Now combine like terms --> -5x=-15
finally just divide by -5 on both sides
x=3
For y:
substitute X for either of the equations
y=2/3 x 3-4
y=-2
The solution is (3,-2)
What is the solution to the equation -4(2x+3) = 2x+6-(8x+2)?
O x = -10
O x=-8
5
Ox= -2
4
O x = 7
Answers
Step-by-step explanation:
-4(2x+3) = 2x+6-(8x+2)
-8x-12 = 2x + 6 -8x -2
cut off -8x two sides of the equation
-12 = 2x + 6 -2
-12 -4 = 2x
-16 = 2x
2x = -16
x = -8
The solution to the equation is \(x = -5\)
The equation of the function is given as:
\(-4(2x + 3) = 2x + 6 - (8x + 2)\)
Open the brackets
\(-8x - 6 = 2x + 6 - 8x - 2\)
Evaluate the like terms
\(- 6 = 2x + 6 - 2\)
Collect like terms
\(2x = -6 - 6 + 2\)
Evaluate the like terms
\(2x = -10\)
Divide through by 2
\(x = -5\)
Hence, the solution to the equation is \(x = -5\)
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A hypothesis can be differentiated from a theory because it is...
a. a specific prediction arising from the theory. c. it talks about how one specific variable affects d. all of the above.
Answers
A hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. The statement that is true is, a hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. A hypothesis is a suggested explanation of a phenomenon or observed data that is testable.
Hypotheses are more detailed, and are written to explain precisely what you think is going to occur in your research and the reason for that prediction. A hypothesis will be rejected if it does not fit the data, whereas a theory will be modified to fit the data.
A hypothesis is more like a forecast, and a theory is more like a law that explains how certain events operate. Thus, we can conclude that a hypothesis is a specific prediction arising from the theory.
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(i need a fast answer) On a coordinate plane, point G is at (2, 8), point H is at (10, 10), point I is at (10, 0), and point J is at (6, negative 4). Which side has a length of 10 units?
HG
GJ
HI
IJ
Answers
Answer:The guy above me is correct you can give him brainlest.
Have a great day!
9. For which equation is the solution 6? (1 point)
Ox+6=10
04x=24
Ox-6=12
04=24
Answers
Answer:
04x=24
Step-by-step explanation:
04x=24
divide both sides by 4 to let x stand alone
04x÷4=24÷4
x=6
what is the average rate of change of y with respect to x over the interval [1, 5] for the function y = 4x 2?
Answers
The average rate of change of y with respect to x over the interval [1, 5] for function \(y=4x^{2}\) is 24.
To find the average rate, follow these steps:
The formula for the average rate of change is expressed as rate= (f (b) - f (a)) / (b - a), where the letters a and b represent two points on the interval that is being analyzed and f (a) and f (b) are the function values of those points. The interval [1, 5] is being considered here so the value of a =1 and value of b=5.So, the average rate of change of y with respect to x is given by;(f(b)−f(a))/(b−a) = [f(5)−f(1)]/(5−1). By substituting x = 5 into the function equation, we get f(5) = \(4(5)^2\) = 100. By substituting x = 1 into the function equation, we get f(1) = \(4(1)^2\) = 4. Substituting these values into the average rate of change formula;[f(5)−f(1)]/(5−1) = (100 - 4) / 4 = 96/4 = 24.Therefore, the average rate of change of y with respect to x over the interval [1, 5] for the function \(y=4x^{2}\) is 24.
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There is 1/3 of a pie shared equally between 5 children. How much of the pie does each child receive?
1/9 pie
1/15 pie
1/18 pie
1/20 pie
Answers
Answer:
1/15 pie
Step-by-step explanation:
An easy way to do this is instead of dividing, multiply the denominator by 5. You get 15. You can say Im just making a coincidence, but try it yourself!
(1/3)/5 is basically multiplication. You may have heard the saying, "division with fractions is multiplication". Thats true. Turn 5 into 5/1 and multiply. 5/1x1/3.
you get 1/15. Hope it helps
Also you have to flip 5/1 to 1/5 and then multiply hehe. thats how you get 1/15
Answer:
Its B, 1/15 hope this helps
Step-by-step explanation:
Please show work and help me understand this multi-step equation.
Answers
Answer:
The correct answer is a = 17/9.
Step-by-step explanation:
To begin this problem, we should use the distributive property on the left side of the equation to get rid of the parentheses. This means that we can multiply each term inside the parentheses by the coefficient outside the parentheses. This is modeled below:
3a - 2 = 3/4a + 2 1/4
Next, we should change the mixed number into an improper fraction so that it is easier to work with.
3a - 2 = 3/4a + 9/4
Now, we can multiply both sides of the equation by 4. This is not a required step, but it will get rid of the fractions on the right side of the equation, so we only have to work in full numbers.
12a - 8 = 3a + 9
The next step is to subtract 3a from both sides and add 8 to both sides to separate the variable and constant terms.
12a - 3a - 8 + 8 = 3a - 3a + 9 + 8
9a = 17
Next, we can divide both sides by 9 to get our variable a alone on the left side of the equation.
a = 17/9
Therefore, the correct answer is a = 17/9.
in the given figure decide when line 1 and line 2 are parrelel or not
Answers
Answer:
they are not parrelel
Step-by-step explanation:
if L1 was straight instead of tilted towards L2, it would be parrelel, but its not.
What is the percent of increase from 40 to 48
Answers
8/40 × 100 = 20% (increase)
Where: 40 is the old value and 48 is the new value. In this case we have a positive change (increase) of 20 percent because the new value is greater than the old value.
Answer: 20%
2.2. South African friends of the Netherlands couple departed from Pretoria at 04h30am to spend the holiday with them. Their journey is described as follows: On their way from Polokwane they took the turn-off to the R521 route. Rest for 45 minutes at Dendron and took 15 minutes to do someshopping and till up the car's fuel tank at All days. 2.2.1. If the scale of the map is given as 1: 3 000 000 and the distance measured on the map between Beitbridge and Musina is 1,3 cm. calculate (in km) the actual distance between Beitbridge and Musina. ● (3)
Answers
The actual distance between Beitbridge and Musina is 3,900,000 kilometers.
To calculate the actual distance between Beitbridge and Musina, given the scale of the map and the measured distance on the map, we can use the concept of scale.
The scale of the map is given as 1:3,000,000, which means that 1 cm on the map represents 3,000,000 cm in real life.
The measured distance on the map between Beitbridge and Musina is 1.3 cm.
To find the actual distance, we can set up a proportion using the scale:
1 cm on the map / 3,000,000 cm in real life = 1.3 cm on the map / x km in real life.
Simplifying the proportion, we have:
1 / 3,000,000 = 1.3 / x.
Cross-multiplying, we get:
x = (1.3 * 3,000,000) / 1.
x = 3,900,000 / 1.
x = 3,900,000 km.
The actual distance between Beitbridge and Musina is 3,900,000 kilometers.
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HELP ASAP!! WILL MARK BRAINLIEST !!!
Write an equation for the area A of the figure. Then determine the maximum possible area of the figure.
Area: A=
Maximum area: ___ square units
Answers
Answer:
Step-by-step explanation:
The maximum area of the figure is 4.5 square units.
Given,
Write an equation for area A of the figure.
Then determine the maximum possible area of the figure.
What is the area of a right-angled triangle?It is given by:
Area = 1/2 x base x height
When we maximize an area we must differentiate the area.
If A is the area.
A' = 0
We have,
From the figure:
Base = 6 - b
Height = b
Now,
Area = 1/2 x base x height
Area = 1/2 x ( 6 - b ) x b
A = (6b - b²) / 2
A = 3b - b²/2
When we maximize an area we must differentiate the area and thus,
A' = 0
So,
A' = 3 - 2b/2
0 = 3 - b
b = 3
Now,
A = 3b - b²/2
A = 3 x 3 - 3²/2
A = 9 - 9/2
A = (18 - 9) / 2
A = 9/2
A = 4.5 square units.
Thus the maximum area of the figure is 4.5 square units.
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Bryce grows a sunflower that contains 1,354 sunflower seeds. Six people share the harvested seeds. If they share the seeds equally, how many seeds will be left over?
Answers
Answer: 4 seeds will left over.
Step-by-step explanation:
Total sunflower seeds = 1354
Number of people shared sunflower seeds equally = 6
By division operation,
Number of seeds each people will get = (Total sunflower seeds) ÷ (Number of people shared seeds equally)
\(= (1354) \div (6)\)
\(=225\dfrac{4}{6}\)
Hence, each people will get 256 sunflower seeds and 4 seeds will left.