find the general solution to the differential equation.9d2ydx2 42dydx 49y = 0

Answers

Answer 1

The general solution for the given differential equation is:
y(x) = c1 *\(e^{(-7/3 * x)}\) + c2 * x * \(e^{(-7/3 * x)}\)

To find the general solution to the given differential equation, 9(d²/dx²) + 42(dy/dx) + 49y = 0, first note that this is a second-order linear homogeneous differential equation with constant coefficients. The general solution can be expressed as where c1 and c2 are arbitrary constants, and r1 and r2 are the roots of the characteristic equation.

The characteristic equation for this differential equation is given by:

9r² + 42r + 49 = 0

This quadratic equation can be factored as:

(3r + 7)(3r + 7) = 0

As the quadratic has a double root, r = -7/3.

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Related Questions

What does 0 12 mean regarding the solution to the system?

Answers

If the solution to a system of equations is 0 = -12 when using the linear combination method, it means that there are no solutions to the system.

If the solution to a system of equations is 0 = -12 when using the linear combination method, it means that there are no solutions to the system. This can occur if the equations represent parallel lines, which do not intersect at any point. When the equations represent parallel lines, the solution to the system is considered to be "inconsistent" because there is no set of values for the variables that will make both equations true at the same time.

Alternatively, if the equations represent the same line, then there will be infinitely many solutions to the system. In this case, any set of values for the variables that make one equation true will also make the other equation true. The solution to the system is considered to be "dependent" because the equations are not independent of each other.

Therefore, in the case of 0 = -12, the solution to the system is "inconsistent" because the equations represent parallel lines. There are no solutions to the system because the lines do not intersect at any point.

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During her presentation to a prospective customer, Lea informed the prospect about the superiority of the new wallboard she was selling. She also brought along a sample so that the building contractor could see and feel the superiority of the product. Lea used a __________ to improve the buyer's understanding of her product.

Answers

Lea used a tangible demonstration to ameliorate the buyer's understanding of her product.

By bringing along a sample of the new wallboard for the structure contractor to see and feel, Lea handed a palpable representation of the product's features and quality. This hands-on approach allows the prospective client to witness the superiority of the wallboard firsthand, which can enhance their understanding and perception of the product.

Palpable demonstrations are effective in showcasing the physical attributes, continuity, texture, or any other palpable aspects of a product that can not be completely conveyed through verbal descriptions alone. This approach can help make trust, credibility, and confidence in the product, making it more compelling and memorable for the buyer.

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A cake recipe uses 48 ounces of flour. How many pints of flour are needed to make the cake? (32 ounces = 2 pints)

Answers

To determine the number of pints of flour needed to make the cake, we divide the given amount of flour in ounces by the conversion factor that relates ounces to pints. In this case, since 32 ounces equal 2 pints, we can divide the given amount of flour by 32 to find the equivalent number of pints. we would need 1.5 pints of flour.

To convert 48 ounces of flour to pints, we use the conversion factor 32 ounces = 2 pints. We divide the given amount of flour, 48 ounces, by the conversion factor to find the equivalent number of pints.

48 ounces / 32 ounces = 1.5 pints.

Therefore, 48 ounces of flour is equal to 1.5 pints. This means that to make the cake, we would need 1.5 pints of flour.

It's important to note that when converting between different units of measurement, it is necessary to use the appropriate conversion factors to ensure accurate results. In this case, knowing the conversion factor of 32 ounces to 2 pints allows us to calculate the amount of flour needed in pints.

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"what value of x makes 5x+10=5(11-2x)

"what value of x makes 5x+10=5(11-2x)

Answers

Answer:

5x + 10 = 5(11 - 2x)

5x + 10 = 55 - 10x

5x + 10x = 55 - 10

15x = 45

15x ÷ 15 = 45 ÷ 15

x = 3

so the answer is 3

After eight games the team has won two games lost five and tied one if there season is 24 games how many games will they win at this rate

Answers

120 games in total for the games played

Answer:

Since the games in total add up to 8, we see that 8 is a factor of 24. It goes in 3 times. Therefore, we have to multiply everything by 3 to get the answer out of 24. There will be 6 wins, 15 losses and 3 tie. That adds up to 24.

True or false: the height is always twice the length of the base edge for any triangular pyramid

Answers

Answer:

FALSE

Step-by-step explanation:

The length of the base edge of a triangular pyramid may vary.

The height is not always twice the length of the base edge for any triangular pyramid, the dimensions are not fixed for any shape and can vary from one design to another.

more so, i may require a particular size or dimension of triangular based pyramid for my application that may not suit your application.

Please answer I need it asap you don’t have to show your work !!!

Please answer I need it asap you dont have to show your work !!!

Answers

Answer:

looks like its a 53 dont count on my answer

Step-by-step explanation:

what is the parallel slope of y=7​

Answers

Answer: y = 7 is a horizontal line that has a slope of 0

Step-by-step explanation:

Let x and y be real numbers such that x < 2y. Prove that if
7xy ⤠3x2 + 2y2, then 3x ⤠y.

Answers

To prove that 3x ≤ y, assume the opposite, that is, 3x > y, rearrange the inequality substitute x < 2y and simplify, contradict the given condition that x < 2y, therefore, concluding that 3x ≤ y.

Start by assuming the opposite, that is, 3x > y.

From the given inequality,\(7xy \leq 3x^2 + 2y^2,\), we can rearrange to get:
\(7xy - 3x^2 \leq 2y^2\)

We can substitute \(x < 2y\) into this inequality:
\(7(2y)x - 3(2y)^2 \leq 2y^2\)

Simplifying, we get:
\(y(14x - 12y) \leq 0\)

Since y is a real number, this means that either y ≤ 0 or 14x - 12y ≤ 0.

If y ≤ 0, then 3x ≤ y is trivially true.

If 14x - 12y ≤ 0, then we can rearrange to get:
3x ≤ (12/14)y
3x ≤ (6/7)y
3x < y (since we assumed 3x > y)

But this contradicts the given condition that x < 2y, so our assumption that 3x > y must be false.

Therefore, we can conclude that 3x ≤ y.

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given 2x - 9y - 12 = 0, express 5x - 4y + 7 = 0 in terms of x only

Answers

Answer:

\(4 \frac{1}{9}x\) + \(12\frac{1}{3}\) = 0

Step-by-step explanation:

Based on 2x - 9y - 12 = 0

-9y = 12 - 2x

9y = -12 + 2x

y = \(-1\frac{1}{3} + \frac{2}{9} x\)

Therefore...

5x - 4y + 7 = 0

5x - 4(\(-1\frac{1}{3} + \frac{2}{9} x\)) + 7 = 0

5x + \(5\frac{1}{3}\)  - \(\frac{8}{9} x\) + 7 = 0

\(4 \frac{1}{9}x\) + \(12\frac{1}{3}\) = 0

What is the minimum value of c = 7x 8y, given the constraints on x and y listed below?

Answers

The minimum value of c = 7x + 8y is 42. The minimum value is obtained at point (6, 0).

How to calculate the minimum value?

To calculate the minimum value of the given equation w.r.t the given constraints(inequalities), the steps are:

Step 1: Identify the system of inequalities in the given constraints

Step 2: Graph those inequalities

Step 3: Identify the maximum and minimum values of x and y that satisfy the given inequalities

Step 4: Then, with the obtained coordinates solve the given equation to get the minimum value.

Calculation:

The given equation is C = 7x + 8y, and the constraints list is

2x + y ≥ 0

x + y ≥ 6

x ≥ 0

y ≥ 0

Graphing these inequalities and shading the region that satisfies the given inequalities.

So, from the graph,

the x-values that satisfy all the given inequalities are [6, ∞]

the y-values that satisfy all the given inequalities are [0, ∞]

So, the required coordinate is (6, 0). By this, we can calculate the minimum value of the given equation C = 7x + 8y

Then,

C = 7(6) + 8(0) = 42 + 0 = 42

Thus, the minimum value of the given equation is 42.

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Disclaimer: The given question is incomplete. Here is the complete question.

Question: What is the minimum value of c = 7x 8y, given the constraints on x and y listed below?

2x + y ≥ 0

x + y ≥ 6

x ≥ 0

y ≥ 0

What is the minimum value of c = 7x 8y, given the constraints on x and y listed below?

PLZZZZZZZZZ HELP!!!!!!!!!!
How many angle measurements do you need to figure out the measurements of all the labeled angles in the figure below?


A

1


B

2


C

3


D

4

PLZZZZZZZZZ HELP!!!!!!!!!! How many angle measurements do you need to figure out the measurements of

Answers

Answer:

it’s A

Step-by-step explanation:

i took it on flocabulary

Answer:

lolzz i just got that question. it's A

Step-by-step explanation:

hope ya have a good day

nominal decisions can be broken into which two distinct categories?

Answers

Answer:

Nominal decisions can be broken into two distinct categories: dichotomous decisions and polychotomous decisions.

Graph square DEFG with vertices

D(4,-2), E(4,2), F(0,2), and G(0,-2)

Find the Perimeter of the shape, answer 16 (I figured it out)

Answers

Answer: 9.01 is the answer

Step-by-step explanation: Because when you add the number in the square you can split the number you add to the nearest sum to the number you get in the outcum.

Please help !!!!
Express your answer as a decimal. *

Please help !!!!Express your answer as a decimal. *

Answers

Answer:

the answer is .08 for your question

two birds are flying in the air. bird A is currently 500 feet in the air and is decending at a constant rate of 75 ceet per minute. bird b who is originally 100 feet in the air begins to increse in altitude at a constant rate of 25 feet per minute. bird a begins to asend in the air at the same time bird b begins to desend in the air


Questions:

What is bird A’s height above the ground?

What is bird B’s height above the ground?

After how many minutes did the two birds reach the same height?

When is bird A above bird B?

When is bird B above bird A?

after 1 minute what is the difference in height between the birds?

Answers

The difference between the two high altitudes is therefore 300 feet.

How to solve

Let 't' denote the time in minutes when both birds are at the same height. If both of these fowls are traveling, one descending and the latter ascending, then we obtain a formulaic value for t using the equations below.

Distance descended by bird A = 75tDistance ascended by bird B = 25tOriginal altitude-distance difference = 500 - 100 = 400 feet

Therefore, if we solve: 75t - 25t = 400, it follows that 50t = 400 and t = 8 minutes.

Given this information, after 8 minutes, the two birds reach the same height.

Consequently, before the 8-minute interval, bird A is situated at a higher level than bird B since the prior's rate of descent is less than the current bird's ascent.

Once they have reached the shared altitude, bird B is above bird A given its continuous upward elevation, contrasting against bird A's descending course.

Their heights after only 1 minute has elapsed; the Height of bird A after 1 minute is calculated to be 425 feet - (500 - 75(1)) and for bird B it is 125 feet - (100 + 25(1)).

The difference between the two high altitudes is therefore 300 feet.

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population variance is a. always known when using probability sampling. b. equivalent to the standard error of the mean. c. a measure of the spread of values from their mean. d. always unknown when using probability sampling. e. an unbiased estimator of sample variance.

Answers

The population variance is a measure of the spread of values from their mean.

We need to define the population variance. The population variance is the variance of the population. Population variance describes how data points are distributed. It is the square of the average distance between each data point in the population and the mean.

In probability theory and statistics, variance is defined as the expectation of a random variable's squared deviation from its population mean or sample mean.

An average is a single number that represents a set of numbers, generally the sum of the numbers divided by the number of numbers in the set.

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prove the following identities.plZzz​

prove the following identities.plZzz

Answers

Answer:

check the file above and got any confusion then comment it .

hope this helped you,

prove the following identities.plZzz

A normal population has a mean of 12.2 and a standard deviation of 2.5.
a. Compute the z value associated with 14.3 (Round your answer to 2 decimal places.)
b. What proportion of the population is between 12.2 and 14.3? (Round your answer to 4 decimal places.)
c. What proportion of the population is less than 10.0? (Round your answer to 4 decimal places.)

Answers

Answer:

Approximately 0.1894 or 18.94% of the population is less than 10.0.

Step-by-step explanation:

On use the z-score formula and the standard normal distribution.

a. To compute the z-value associated with 14.3, we use the formula:z = (x - μ) / σWhere:

x = 14.3 (the value)

μ = 12.2 (mean)

σ = 2.5 (standard deviation)

Substituting the values:

z = (14.3 - 12.2) / 2.5

z = 2.1 / 2.5

z ≈ 0.84

Therefore, the z-value associated with 14.3 is approximately 0.84.

b. To obtain the proportion of the population between 12.2 and 14.3, we need to get the area under the standard normal distribution curve between the corresponding z-scores.

Using a standard normal distribution table or a calculator, we can find the area associated with each z-score.The z-value for 12.2 can be calculated using the same formula as in part a:

z1 = (12.2 - 12.2) / 2.5

z1 = 0 / 2.5

z1 = 0

The z-value for 14.3 is already known from part a: z2 ≈ 0.84.

Now, we obtain the proportion by subtracting the area associated with z1 from the area associated with z2:

Proportion = Area(z1 < z < z2)

Using a standard normal distribution table or a calculator, we obtain:

Area(z < 0) ≈ 0.5000 (from the table)

Area(z < 0.84) ≈ 0.7995 (from the table)

Proportion = 0.7995 - 0.5000

Proportion ≈ 0.2995

Therefore, approximately 0.2995 or 29.95% of the population is between 12.2 and 14.3.

c. To obtain the proportion of the population less than 10.0, we need to get the area under the standard normal distribution curve to the left of the corresponding z-score.Using the z-score formula:z = (x - μ) / σ

Where:

x = 10.0 (the value)

μ = 12.2 (mean)

σ = 2.5 (standard deviation)

Substituting the values:

z = (10.0 - 12.2) / 2.5

z = -2.2 / 2.5

z ≈ -0.88

Now, we obtain the proportion by looking up the area associated with z ≈ -0.88 using a standard normal distribution table or a calculator:

Area(z < -0.88) ≈ 0.1894 (from the table)

Therefore, approximately 0.1894 or 18.94% of the population is less than 10.0.

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Anastasia makes a good salary but wants to be sure she has good credit so she can buy a condominium when she has saved
enough money for a down payment on a mortgage. What is the best thing she can do to improve her creditworthiness?
She should take out more debt to improve her credit score.
She should pay down her student loan and credit card debt.
She should apply for more credit cards to improve her credit history.
She should get a second job to make more money.

Answers

Answer:

She should pay down her student loan and credit card debt.

Step-by-step explanation:

Because the others would result in more debt or overwork and she has a good salary already

The best thing Anastasia can do to improve her creditworthiness is to pay down her student loan and credit card debt.

Option B is the correct answer.

We have,

The best thing Anastasia can do to improve her creditworthiness is to pay down her student loan and credit card debt.

This will lower her credit utilization ratio, which is a significant factor in determining her credit score.

Having a high credit utilization ratio can indicate to lenders that she may be at risk of defaulting on her debts, which could make it more difficult for her to obtain a mortgage or other loans in the future.

Paying down her debts can help improve her credit score and make her a more attractive borrower to potential lenders.

Thus,

The best thing Anastasia can do to improve her creditworthiness is to pay down her student loan and credit card debt.

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Fernandez Corporation has a line of credit with Bank of Commerce for P5,000,000 for the 2020. For any amount borrowed, the bank requires the borrower a maintaining balance of 6%. Assuming the company needed P2,000,000 cash on June 30, 2016 and availed of the credit line of 10% Interest payable on December 31, 2021. Assuming further that the company has no existing deposit with the bank, what is the EIR from this transaction? a. 10.60% b. None of the above c. 10.61% d. 10.62%

Answers

the EIR from this transaction is 16.25% (Option B, None of the above).

To find the EIR from the transaction, we need to calculate the effective interest rate (EIR) on the loan. The formula for EIR is:

EIR = [(1 + r/n)ⁿ - 1] x 100

where r is the nominal interest rate, and n is the number of compounding periods per year.

In this case, the nominal interest rate is 10%, and the loan is payable on December 31, 2021, which is 5.5 years from June 30, 2016. Therefore, the number of compounding periods per year is 2 (since interest is payable semi-annually). Substituting these values into the formula, we get:

EIR = [(1 + 0.10/2)₂ - 1] x 100 = 10.25%

However, the bank requires a maintaining balance of 6% for any amount borrowed. Therefore, the effective interest rate is increased by this amount. Adding 6% to the EIR, we get:

EIR = 10.25% + 6% = 16.25%

Therefore, the EIR from this transaction is 16.25% (Option B, None of the above).

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you find a significant correlation between two variables. can you imply that x causes the effect in y? additionally, how do you evaluate the strength of the relationship between the two variables?

Answers

Correlation does not necessarily imply causation. Evaluating the strength of the relationship between two variables requires examining the correlation coefficient, which ranges from -1 to 1.

Correlation is a statistical measure that indicates the degree to which two variables are related. However, it does not necessarily imply causation, as there may be other factors that are responsible for the observed correlation. For example, the correlation between ice cream sales and crime rates does not mean that ice cream causes crime. Instead, both variables may be influenced by a third variable, such as temperature. Therefore, it is important to exercise caution when interpreting correlations.

To evaluate the strength of the relationship between two variables, it is necessary to examine the correlation coefficient. The correlation coefficient is a statistical measure that ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation. A correlation coefficient of 0.8 or higher is generally considered a strong correlation, while a coefficient between 0.5 and 0.8 is considered moderate, and a coefficient below 0.5 is considered weak. However, it is important to note that the strength of the relationship between two variables also depends on the context and the specific research question being investigated.

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NO MAMES WEY QUE TE PASA

Answers

Answer:

No se wey

Step-by-step explanation:

Answer:

yo no se que es esa?

Step-by-step explanation:

yo hablo un poco español pero no mucho por eso yo no se que "mames wey" significa

Un prisma cuadrangular regular tiene 4 m de arista de la base y 6m de altura Calcula el area y el volumen

Answers

Answer:

El área y volumen del prisma cuadrangular mencionado son respectivamente:

Área = \(16m^{2}\) Volumen = \(96m^{3}\)

Step-by-step explanation:

Para solucionar este ejercicio debes recordar que un prisma cuadrangular tiene como base y como superficie cuadrados, por lo tanto, para calcular el área de dicho cuadrado puedes utilizar la siguiente fórmula:

Área de un cuadrado = \(arista^{2}\)

Ya que el ejercicio nos da el valor de la arista (4 metros), podemos reemplazarla en la ecuación y calcular:

Área de un cuadrado = \((4m)^{2}\)Área de un cuadrado = \(16m^{2}\)

Por último, para calcular el volumen debes multiplicar el área superficial, el área del cuadrado calculado, por la altura del prisma, cuyo valor dentro del enunciado es de 6 metros, de esta forma:

Volumen de un prisma cuadrangular = área superficial * alturaVolumen de un prisma cuadrangular = \(16m^{2}\) * \(6 m\)Volumen de un prisma cuadrangular = \(96m^{3}\)

Como puedes ver tras los cálculos, el área superficial del prisma es de \(16m^{2}\) y su volumen es \(96m^{3}\).

In the coordinate plane, the point A (-2,2) is translated to the point A (2,-3). Under the same translation, the points B (-4,-1) and C (-6,5) are translated to B and C respectively. What are the coordinates of B and C?

Answers

In the coordinate plane, the point A (-2,2) is translated to the point A (2,-3). Under the same translation, the points B (-4,-1) and C (-6,5) are translated to B and C respectively. What are the coordinates of B and C?

Answer: B(0,-6); C(-2,0)

Step-by-step explanation:

A was translated 4 units to the right (x) and 5 units down (y)

Do the same for the other points

B(-4+4, -1-5)                        C(-6+4, 5-5)

B(0, -6)                                C(-2, 0)

help pls....................................

help pls....................................

Answers

Answer:

Answer 1 is 3712000000

answer 2 is 8.624X10^10

answer 3 is 820

answer 4 is 380

answer 9 is 9200

answer 10 is 400

answer 11 is 8832000000

answer 12 is 1.3104X10^10

Can someone plss help me with this question!

QUESTION: Solve and graph for x and y.

Can someone plss help me with this question!QUESTION: Solve and graph for x and y.

Answers

Answer:

\(y = 1-\frac{x}{2}\)

\(y = 1-\frac{x}{2}\)

Step-by-step explanation:

x+2y = 2

2y = 2-x

\(y=\frac{2-x}{2}\)

\(y = 1-\frac{x}{2}\)

2x+4y = 4

4y = 4-2x

\(y=\frac{4-2x}{4} \\y =1-\frac{x}{2}\)

They are the same. When you will graph it they will be on top of another. It will be one single line.

To graph this equation follow the slope-intercept form: y=mx+b

b is y-intercept  and m is slope.

From this equation y-intercept is 1 and slope is -1/2. Y=intercept is the value of y when x is 0. So one point will be (0,1) on the graph.

Slope = rise/run. Rise means going up and down. Run means going left and right. When the number is negative you go down and left. If it's positive you go up and right.

To put the slope go down 1 and right 2 to input another point from the point (0,1). So the new point will be (2,0). Now draw a line between (0,1) and (2,0) and you have your graph.

3 3/4+ (2 1/6 - 1 1/3)

Answers

Answer:

The answer to your question would be 4 7/12

Step-by-step explanation:

I hope this helps and have a wonderful day!

How to convert 115 f to c?

Answers

The required converted value of the temperature Fahrenheit to Celsius for the value 115°F is given by 46.1111°C .  

Fahrenheit and Celsius both are the units used to measure the temperature.

To convert Fahrenheit to Celsius use the following formula we have:

( F − 32 ) × ( 5 / 9 ) = °C

Substitute the 115 Fahrenheit to convert into Celsius we get,

= ( 115°F − 32 ) × ( 5 / 9 )

= ( 83 )  × ( 5 / 9 )

= ( 415 / 9 )°C

= 46.1111 °C

Therefore, the converted unit of Fahrenheit to Celsius using standard relation between the two is equal to 46.1111°C .

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At a football game
number of men : number of women : number of children = 13:5:7
There are 4152 more men then women.
Work out the number of children at the game

Answers

Answer:

Step-by-step explanation:

let the ratio of men women and children be 13x 5x and 7x

now

13x + 5x + 7x = 4152

25x = 4152

x = 4152/25

x = 166.08

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