Exercise5 : Find the general solution of the ODE 4y'' – 20y' + 25y = (1 + x + x2) cos (3x). Exercise6 : Find the general solution of the ODE d²y + 49 y = 2x² sin (7x). dr2

Answer:

This is a function, there is no x value that will lead you to getting more than one different y values.

Step-by-step explanation:

If you put these points on a graph and did the vertical line test you wouldn't  have two of the same x values that could cause the line to hit the same points on the graph.

someone else answered this question https://brainly.com/question/14666784

Answer:

Yes, it is a function because none of the x values are repeated.

Step-by-step explanation:

A function is when there is only 1 x value to every y value.

In this relation there is a different set of x values to every y value.

Answer:

(1,5)

(-1,3)

Step-by-step explanation:

The solution is in the image

The zero vector, also known as the additive identity, is a special vector in a vector space. In the vector space M4,2, which consists of 4x2 matrices, the zero vector is a 4x2 matrix with all its elements being zero.

t is called the additive identity because when you add it to any other vector in the vector space, the result is the same vector. In other words, for any vector V in M4,2, V + 0 = V, where 0 is the zero vector.

The zero vector for M4,2 looks like this:

0 = [ [0, 0],
       [0, 0],
       [0, 0],
       [0, 0] ]

So, the zero vector in the vector space M4,2 is a 4x2 matrix with all elements being zero, and it maintains the property that when added to any vector in the space, the result remains unchanged.

To learn more about zero vector: https://brainly.com/question/2094736

#SPJ11

It will take Jill and John \($\frac{6}{5}$\) hours or 1 hour and 12 minutes.

To solve the problem, we can use the formula:

\($ \frac{1}{x} = \frac{1}{a} + \frac{1}{b}$\)

where x is the time it takes for Jill and John to complete the job working together, and a and b are the times it takes for Jill and John to complete the job individually, respectively.

Substituting the given values, we get:

\($ \frac{1}{x} = \frac{1}{2} + \frac{1}{3}$\)

Simplifying this expression, we get:

\($ \frac{1}{x} = \frac{5}{6}$\)

Multiplying both sides by 6x, we get:

\($6 = 5x$\)

Dividing both sides by 5, we get:

\($x = \frac{6}{5} hours$\)

Therefore, it will take Jill and John \($\frac{6}{5}$\) hours or 1 hour and 12 minutes (rounded to the nearest minute) working together to complete the job.

Learn more about time in a collaborative setting

brainly.com/question/27497127

#SPJ11

Answer:

154m , 160m

Step-by-step explanation:

Let width of the rectangle = w

Length = w + 6

Perimeter of rectangle = 628 m

2( length + width ) = 628

2( w + 6 + w) = 628        {Combine like terms}

2*( 2w +6 ) = 628            {Distributive property}

2*2w + 2*6 = 628

4w + 12 = 628         {subtract 12 from both sides}

        4w = 628 - 12

        4w = 616       {Divide both sides by 4}

        w = 616/4

       w = 154 m

Length = w + 6 = 154 + 6 = 160 m

We have shown that for any given ε > 0, we can choose δ = 1/(-B) such that for all x satisfying 0 < |x - 2| < δ, it follows tha\(t |(x - 2)/(x^2 - 2x)| < ε.\)

What is Epsilon-delta?

Epsilon-delta is a concept used in calculus and mathematical analysis to define limits and continuity rigorously. It provides a precise way of expressing the idea of a function approaching a particular value as the input approaches a given point.

To prove the limit statement using formal definitions, we want to show that for any given ε > 0, there exists a δ > 0 such that for all x satisfying 0 < |x - 2| < δ, it follows that \(|(x - 2)/(x^2 - 2x)| < ε.\)

Given -B < 0, we need to find δ > 0 such that for all x, if 0 < |x - 2| < δ, then \(|(x - 2)/(x^2 - 2x)| < -B.\)

Let's begin the proof:

Proof:

Given ε > 0, we need to find δ > 0 such that for all x, if 0 < |x - 2| < δ, then \(|(x - 2)/(x^2 - 2x)| < ε.\)

We can start by manipulating the expression \(|(x - 2)/(x^2 - 2x)|\)to simplify it further:

\(|(x - 2)/(x^2 - 2x)| = |(x - 2)/x(x - 2)|\)

Now, notice that we can cancel out the (x - 2) term from the numerator and denominator since x ≠ 2 (otherwise the denominator would be zero).

\(|(x - 2)/(x^2 - 2x)| = 1/|x|\)

Now, we want to find δ > 0 such that for all x, if 0 < |x - 2| < δ, then 1/|x| < ε.

Since we are given -B < 0, we can choose δ = 1/(-B).

Now, let's consider any x such that 0 < |x - 2| < δ.

From the choice of δ, we have 0 < |x - 2| < 1/(-B), which implies |x| > 1/δ = -B.

Since |x| > -B, we have 1/|x| < 1/(-B) = δ.

Therefore, we have shown that for any given ε > 0, we can choose δ = 1/(-B) such that for all x satisfying 0 < |x - 2| < δ, it follows that \(|(x - 2)/(x^2 - 2x)| < ε.\)

Hence, the limit statement holds, and we have proven it using formal definitions.

To know more about Epsilon-delta visit:

https://brainly.com/question/29994855

#SPJ4

Answer:

f(0)=g(0)

Step-by-step explanation:

The problem is asking for where the output (y value) of one function, f(x), matches the output of another function, g(x), otherwise called an intersection. You can see that the two lines intersect at 0 on the x axis in the graph, therefore f(0)=g(0) meaning the outputs of f(x) are the same as g(x) at x value 0.

Answer:

4 i think i did this yesterday

Step-by-step explanation:

Answer:

$240

Step-by-step explanation:

30 (the weeks in 7 months) times 8 (his weekly savings) = 240

(11) The measure of angle IGJ is  46⁰.

(12) The measure of arc JH is determined as 138⁰.

The measure of the arc or central angle indicated is calculated as follows;

(11) The measure of angle IGJ is calculated as follows;

m∠LGK =  arc angle LK (interior angle of intersecting secants)

m∠LGK = 48⁰

m∠HGI = m∠LGK = 48⁰ (vertical opposite angles are equal)

m∠IGJ + m∠HGI + m∠JGK = 180⁰  (sum of angles in a straight line)

m∠IGJ + 48⁰ + 86⁰ = 180

m∠IGJ = 180 - 134

m∠IGJ = 46⁰

(12) The measure of arc JH is calculated as follows;

arc JH = arc JI + arc IH

arc JI = arc FG

arc FG = 180 - 137⁰ (sum of angle in a straight line)

arc FG = 43⁰

arc FG = arc JI (vertical opposite angles are equal)

arc JH = arc JI + arc IH

arc JH = 43⁰ + 95⁰

arc JH = 138⁰

Learn more about arc angles here: https://brainly.com/question/30543683

#SPJ1

On the last option, since you can substitute y=3x+1 into the other equations to solve for x.

Complete question is;

Ilona is at a friends home that is several miles from her home. She starts walking at a constant rate in a straight line toward her home.

The expression -2t + 10 gives the distance, in miles, that Ilona is from her home after t hours. Select True or False for each of the following.

1. The friends home is 10 miles from Ilonas home

2. The distance Ilona has walked away from her friends home after t hours is given by the absolute value of -2t

3.The negative sign in the term indicates that Ilona is walking toward her home

4. Ilona is walking at a rate of 10 miles per hour

Answer:

Statements 1 & 2 are correct.

Step-by-step explanation:

We are told that the expression -2t + 10 gives the distance, in miles, that Ilona is from her home after t hours.

Now, we know that distance = speed x time

Now, from the expression -2t + 10

It's clear that 2t is a distance value.

This means that the speed used in going home is 2 miles/hr

This means that at t hours, she has walked 2t miles from her friends home.

Thus, statement 2 is true because an absolute value of -2t will be 2t.

Since 2t is subtracted from 10 in the expression and 2t is the distance she has walked from her friends house at Time, t. It means that 10 miles is the distance from her friends house to her house.

Thus, statement 1 is also true

Answer:

Step-by-step explanation:

Solve systems of equations by graphing

A system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

Hope it helps

The final value of x when (x = 1 ; x<10; x ),in this case will be 9.

This is because the initial value of x is set to 1, and the condition for the loop is that x must be less than 10.

Therefore, the loop will continue to execute as long as x is less than 10, and will stop when x is equal to 10. However, since the final value of x is not included in the loop, the final value of x will be one less than the stopping value, or 9.

Steps include:-
1. Set the initial value of x to 1: x = 1
2. Check if x is less than 10: x<10
3. If x is less than 10, execute the loop and increase the value of x by 1: x++
4. Repeat steps 2 and 3 until x is no longer less than 10
5. The final value of x will be one less than the stopping value, or 9.

know more about initial value here

https://brainly.com/question/8223651#

#SPJ11

Answer:

Function rule is option c.

Answer:

(4,-36)

Step-by-step explanation:

Since the roots of the equation are -2 and 10, you can set up the quadratic like this:

\(y=(x+2)(x-10)\)

Expanded:

\(y=x^2-8x-20\)

To find the x-coordinate of the vertex, use: \(x_{vertex}=\frac{-b}{2a}\)

\(x_{vertex}=\frac{-(-8)}{2(1)}=\frac{8}{2}=4\)

Plug in 4 to either quadratic equation to get the y value:

\((4+2)(4-10)=(6)(-6)=-36\)

Thus the vertex is (4,-36)

If I helped, a brainliest would be greatly appreciated!

The first equation has vertical asymptotes at x = -1 and x = -3, while the second equation has a horizontal asymptote at y = 1.

The rational function y = (2x-1)/(x+1)(x+3) has vertical asymptotes at x = -1 and x = -3, and no horizontal asymptotes.

The rational function y = x^3/(x²+4x+5) has no vertical asymptotes, a horizontal asymptote at y = 1, and no slant asymptotes.

To find the asymptotes of a rational function, we look for values of x that make the denominator equal to zero. In the first equation, the denominator (x+1)(x+3) becomes zero when x = -1 and x = -3, so these are the vertical asymptotes.

Horizontal asymptotes are determined by the behavior of the function as x approaches positive or negative infinity. For the first equation, there is no horizontal asymptote because the degree of the numerator is greater than the degree of the denominator.

In the second equation, the degree of the numerator and denominator is the same (both are 3), so we divide the leading coefficients (1/1) to find the horizontal asymptote, which is y = 1.

There are no slant asymptotes for either equation because the degree of the numerator is not greater than the degree of the denominator by 1.

To learn more about function click here

brainly.com/question/30721594

#SPJ11

The ranking of resistors would be, R1 < R3 < R2

The larger the time constant T = RC,  the more time it takes for the capacitor to discharge.

So the more the resistance the more time it takes for the capacitor to discharge.

In the figure, the one with R2 will take the longest time for Vc to be zero. Then R3 will take less time than R2 and R1 will take smallest time to discharge. So R2 is largest followed by R3 and R1 is smalllest.

So the ranking would be, R1 < R3 < R2

To learn more about resistors, refer to

https://brainly.com/question/14883923

#SPJ4

Answer: 127

Step-by-step explanation:

The volume of the cube as a polynomial is 8x³ + 12x² + 6x + 1.

The volume of a cube is expressed as;

V = a³

Where a is the side of the cube.

Given that;

Plug the given value into the above equation and simplify.

V = a³

V = ( 2x + 1 )³

Expand using FOIL method

V = ( 2x + 1 )( 2x + 1 )( 2x + 1 )

V = ( 2x( 2x + 1 ) + 1( 2x + 1 ) )( 2x + 1 )

V = (4x² + 4x + 1 )( 2x + 1 )

V = 2x(4x² + 4x + 1 ) + 1(4x² + 4x + 1 )

V = 8x³ + 8x² + 2x + 4x² + 4x + 1

Collect and add like terms

V = 8x³ + 12x² + 2x + 4x + 1

V = 8x³ + 12x² + 6x + 1

Therefore, the volume is 8x³ + 12x² + 6x + 1.

Learn more about polynomials here: https://brainly.com/question/20121808

#SPJ1

Answer:

40

Step-by-step explanation:

All you have to do is subtract the biggest number from the smallest in order to get your answer.

45 - 5 = 40. Hence, the answer is 40

Hope this helps! :)

The number of students in the class should be considered as the 40.

= Largest commute time - smallest commute time

= 45 - 5

= 40

Here we basically deduct the  smallest commute time from the largest commute time so that the no of student in the class should come.

Learn more about class here:  https://brainly.com/question/17217914

There are a total of 6 possible combinations of two different types of desserts that Seth can put on plates. They are:
1. Cookies and brownies
2. Cookies and fudge
3. Cookies and cupcakes
4. Brownies and fudge
5. Brownies and cupcakes
6. Fudge and cupcakes

Using the formula for combinations, C(n, k) = n! / (k!(n-k)!), where n is the total number of items (4 desserts) and k is the number of items to choose (2 desserts):

C(4, 2) = 4! / (2!(4-2)!) = 4! / (2!2!) = (4 × 3 × 2 × 1) / ((2 × 1)(2 × 1)) = 6

So, there are 6 possible combinations for two different dessert plates. Here's the list of each combination:

1. Cookies and Brownies
2. Cookies and Fudge
3. Cookies and Cupcakes
4. Brownies and Fudge
5. Brownies and Cupcakes
6. Fudge and Cupcakes

To learn more about combinations click here : brainly.com/question/29594894

#SPJ11

Answer:

m = 17

Step-by-step explanation:

\(4(m - 13) - 8 = 8 \\ 4(m - 13) = 8 + 8 \\ 4(m - 13) = 16 \\ (m - 13) = \frac{16}{4} \\ m - 13 = 4 \\ m = 4 + 13 \\ \huge \red { \boxed{m = 17}}\)

Answer:

Let's start by assigning variables to their present ages. Let R be Rojina's current age and let S be Sujina's current age.From the given statement, we can write an equation:R - x = 2(S - x)where x is the number of years ago when Rojina was as old as Sujina is now.Simplifying the equation, we get:R - 2S = -xNow, we can write a second equation using the fact that the sum of their present ages is 35:R + S = 35We have two equations and two variables, so we can solve for R and S.First, we can rearrange the second equation to get:R = 35 - SSubstituting this into the first equation, we get:35 - S - 2S = -xSimplifying, we get:3S = x - 35We don't know the value of x, but we do know that Rojina's age minus twice Sujina's age equals x. This means that x must be a multiple of 3, since the difference between two multiples of 3 is also a multiple of 3.Let's try some values of x to see if they work:If x = 3, then 3S = -32, which is not possible since S cannot be negative.If x = 6, then 3S = -29, which is also not possible.If x = 9, then 3S = -26, which is still not possible.If x = 12, then 3S = -23, which is not possible.If x = 15, then 3S = -20, which is also not possible.If x = 18, then 3S = -17, which is still not possible.If x = 21, then 3S = -14, which is not possible.If x = 24, then 3S = -11, which is not possible.If x = 27, then 3S = -8, which is not possible.If x = 30, then 3S = -5, which is not possible.If x = 33, then 3S = -2, which is not possible.If x = 36, then 3S = 1, which means S = 1/3. This is also not possible since S must be a whole number.Since none of these values of x work, there must be a mistake in the problem statement. It's possible that Rojina misspoke or there was a miscommunication. Without more information, we cannot find their current ages.

Answer:

Option (3)

Step-by-step explanation:

By the theorem, angle between two tangents intersecting each other outside the circle is half of the difference between intercepted arcs.

From the figure attached,

Two tangents CD and DE are intersecting each other at point D outside the circle A.

Two intercepted arcs are minor arc CE and major arc CBE,

Measure of arc CE = 112°

Therefore, measure of major arc CBE = 360° - 112°

                                                               = 248°

m(∠CDE) = \(\frac{1}{2}(\text{arcCBE}-\text{arcCE})\)

                 = \(\frac{1}{2}(248-112)\)

                 = \(\frac{1}{2}\times 136\)

                 = 68°

Option (3) will be the correct option.

Answer:

C

Step-by-step explanation:

Answer:

-16.22

^THERE IS YOUR ANSWER^

Answer:

-16.22

Step-by-step explanation:  

I am sorry if this is wrong

Answer:

f(x) = x² + 2x + 1

Step-by-step explanation:

you know how to multiply 2 expressions ?

let's say in general we have

(a + b)(c + d)

you take one part of one expression and multiply it with all parts of the other expression, then you take the second part of the first expression and multiply it with all parts of the other expression, then a potential third part, then a fourth part and so on, and you add all these things together (well, depending on the actual signs, of course).

so, we get for this simple generic example

a×c + b×c + a×d + b×d

now we use that understanding for our question here.

(x+1)(x+1) = x×x + 1×x + x×1 + 1×1 = x² + x + x + 1 = x² + 2x + 1

Answer:

The awnser is 2432

Step-by-step explanation:

12x28x22= 2432

Correlation analysis:

a. The variables used in the research study are "age" and "number of times eaten out in an average month." The level of measurement for age is an interval, and the level of measurement for the number of times eaten out is ratio.

b. Pretest Checklist for NormalityAge Histogram Interpretation:

A histogram with a bell curve, skewness equal to 0, and kurtosis equal to 3 indicates normality.

Mean = 45.17, Standard deviation = 14.89, Skewness = -.08, Kurtosis = -0.71.

The histogram for the age of respondents is approximately bell-shaped, indicating normality.

Number of times eaten out Histogram Interpretation:

A histogram with a bell curve, skewness equal to 0, and kurtosis equal to 3 indicates normality.

Mean = 8.38, Standard deviation = 8.77, Skewness = 2.33, Kurtosis = 9.27.

The histogram for the number of times the respondent eats out in an average month is positively skewed and not normally distributed. Therefore, it is not normally distributed.

Linearity:

Age vs. Number of times Eaten Out

Scatterplot Interpretation:

A scatterplot indicates linearity when there is a straight line and all data points are scattered along it. The scatterplot displays that the number of times respondents eat out increases as they get older. The relationship between the variables is linear and positive.

Homoscedasticity:

Age vs. Number of times Eaten OutScatterplot Interpretation: The scatterplot displays no fan-like pattern around the regression line, which indicates that the assumption of homoscedasticity is met.

c. Bivariate Correlation and Descriptive Statistics

Age and the number of times eaten out in an average month have a correlation coefficient of.

150, which is a small positive correlation and statistically insignificant (p = .077). The mean age of the respondents was 45.17 years, with a standard deviation of 14.89. The mean number of times the respondent eats out in an average month was 8.38, with a standard deviation of 8.77.

The scatterplot with regression line shows a positive slope that indicates a small and insignificant correlation between age and the number of times the respondent eats out in an average month.

d. The research study aimed to determine whether there is a correlation between age and the number of meals eaten outside the home. The data were analyzed using a bivariate correlation analysis, scatterplot with regression line, and descriptive statistics. The results indicated a small positive correlation (r = .150), but this correlation was statistically insignificant (p = .077).

The mean age of the respondents was 45.17 years, with a standard deviation of 14.89. The mean number of times the respondent eats out in an average month was 8.38, with a standard deviation of 8.77. The findings showed that there is no correlation between age and the number of times the respondent eats out in an average month.

Therefore, the researcher cannot conclude that age is a significant factor in the number of times a person eats out. The implications of the findings suggest that other factors may influence a person's decision to eat out, such as income, time constraints, and personal preferences. Further research could be done to determine what factors are significant in the decision to eat out.

learn more about Correlation on:

https://brainly.com/question/13879362

#SPJ11