solve the differential equation.2xy 8x (x2 − 9)dydx = 0

Answers

Answer 1

Therefore, the solution to the differential equation is:

y = (2/9) ln|x-3| - (2/9) ln|x+3| + C'C'.

We are given the differential equation:

2xy - 8x(x^2 - 9) dy/dx = 0

We can simplify this equation by dividing both sides by 2x(x^2 - 9):

dy/dx = 4/(x(x^2 - 9))

Now we need to separate the variables by multiplying both sides by dx and dividing both sides by 4:

(1/4) dy = dx/(x(x^2 - 9))

We can integrate both sides:

∫(1/4) dy = ∫dx/(x(x^2 - 9))

(1/4) y = (1/18) ln|x-3| - (1/18) ln|x+3| + C

where C is the constant of integration.

Multiplying both sides by 4, we get:

y = (2/9) ln|x-3| - (2/9) ln|x+3| + C'

where C' = 4C.

Therefore, the solution to the differential equation is:

y = (2/9) ln|x-3| - (2/9) ln|x+3| + C'C'

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Related Questions

Please help i am confused

Please help i am confused

Answers

Answer:

18 +2

Step-by-step explanation:

it's like 3x you just add each side 3 then you will get the answer. and the (+2) stays the same.

If a negative relation exists between two variables, then low scores on one variable will be associated with _____ scores on the other variable.

Answers

If a negative relation exists between two variables, low scores on one variable will be associated with high scores on the other variable.

In a negative relationship between two variables, a decrease in one variable is accompanied by an increase in the other variable. This means that as scores on one variable decrease (i.e., low scores), the scores on the other variable tend to increase (i.e., high scores). The negative relationship implies an inverse pattern where the variables move in opposite directions.

The exact nature and strength of the negative relationship can vary, but the general trend is that low scores on one variable correspond to high scores on the other variable. This negative association provides insights into the behavior and interactions between the variables being examined.

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The lengths of the bases of a trapezoid are 5 feet and 8 feet. The trapezoid has an area of 104 square feet.
What is the height, h, of the trapezoid?
h = 13 ft
h = 16 ft
h = 20.8 ft
h = 21.4 ft

The lengths of the bases of a trapezoid are 5 feet and 8 feet. The trapezoid has an area of 104 square

Answers

Answer:

B the height is 16 ft

Step-by-step explanation:

Answer:16

Step-by-step explanation: k12

If 1 gallon of orange juice cost 6.25. How much does it cost for 128 ounces of oj?

Answers

Answer:

$6.25

step-by-step explanation:

a gallon of oj coat 6.25

there are 128 ounces in a gallon

so 6.25 for 128 ounces is just a gallon

so 128=1 gallon. so its just $6.25

you and your friend toss a coin continuously, if the sequence hh appears first you win, if th appears first your friend wins, who is more likely to win?

Answers

Both has the equal chances of winning first as the probability is same.

We are given that:

There are two coins that are tossed simultaneously.

Sample space is:
S = { HH, HT, TH , TT}

Now, the probability of appearing HH on the coins is:

P = 1 / 4 = 0.25

The probability of appearing TH on the coins is:

P = 1 / 4 = 0.25

So, the probability of anyone winning is the same.

Both has the equal chances of winning.

Therefore, both has the equal chances of winning first as the probability is same.

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If point Q is between endpoints P and R on a segment, PQ = 4x - 12, QR = 2x + 7, and PR = 31, then find the value of x.

Answers

Answer:

x = 6

Step-by-step explanation:

Here it's sayin that Q is a point in between the end-points P & R. If we join P & R , it forms a line segment & Q is in the line segment PR. Hence PQ & QR are also line segments which combine to form line segment PR. So ,

PR = PQ + QR

Putting the given values of PQ ,QR & PR

=> 4x - 12 + 2x + 7 = 31

=> 6x - 5 = 31

=> 6x = 31 + 5

         = 36

=> x = 36/6 = 6

The points (1,5), (5,10), (7,8), and (8,1) are on the graph of the function p. Which expression belo gives the average rate of change of the function p on 5 less than or equal x less than or equal 8

Answers

Answer:

Step-by-step explanation:

Since it is x that is bound by 5≤x≤8, you should use the points (5,10) and (8,1), since a coordinate is written as (x,y).

Then, use the formula for slope, as the average rate of change means find the slope, \(\frac{y2-y1}{x2-x1}\)

thus, plug in

\(\frac{1-10}{8-5}\), and you get -9/3, or -3. :)

Is (5, 2) a solution to the equation y = 8x?

Answers

Hey there! I'm happy to help!

To satisfy this equation, the y value has to be 8 times the x.

If you multiply 5 by 8, you get 40, not 2, so this is not a solution. The point (5,40) would be.

Have a wonderful day! :D

All we need to do is substitute and check.

5 = x

2 = y

y = 8x

2 = 8(5)

2 does not equal 40

Best of Luck!

The graph represents the piecewise function:

The graph represents the piecewise function:

Answers

Answer:

x if -3is less than x is less than -1

5 is -1 is less than x is less than 1

Step-by-step explanation:

You find the slope of the line for the first piece when the x-values range from -3 to -1.

For the second piece, the line is y=5 because the line is horizontal.

Answer:

x+3; 5

Step-by-step explanation:

The first piece, shows the diagonal part in Quadrant II.

The line segment is colinear with the line y=x+3, because the slope is 1, and the y-intercept is 3. So the piece would be defined as x+3.

The second line segment is the flat one, which has a slope of 0 and its y-intercept is 5. So the piece would be defined as 0x+5 or 5

Graph the linear equation y=2x-1.

Answers

Answer:

https://youtu.be/R0A-fEUWv1Y

Step-by-step explanation: I found this vid just watch this I hope it helps (just copy and paste)

HW 3: Problem 9 Previous Problem List Next (1 point) Suppose that X is normally distributed with mean 110 and standard deviation 21. A. What is the probability that X is greater than 145.28? Probabili

Answers

The probability that X is greater than 145.28 is approximately 0.0465.

Given that X is normally distributed with mean (μ) of 110 and standard deviation (σ) of 21. We are to find the probability that X is greater than 145.28. It can be calculated as follows: We can calculate the Z-score value with the help of the following formula, Z = (X - μ) / σWhere X is the random variable value, μ is the mean, and σ is the standard deviation. Substituting the values in the formula, we get: Z = (145.28 - 110) / 21Z = 1.68476 Using the Z-table, we can find the probability that X is greater than 145.28 as follows: From the Z-table, we get: P(Z > 1.68) = 0.0465

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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a) Calculate the size of angle x in the diagram
below.
b) Work out the bearing of A from B.

a) Calculate the size of angle x in the diagrambelow.b) Work out the bearing of A from B.

Answers

The angle x in the diagram is 98 degrees.

How to find the angles in parallel lines?

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.

Therefore, let's find the angle of x using the angle relationships as follows:

The size of the angle x can be found as follows:

82 + x = 180(same side interior angles)

Same side interior angles are supplementary.

Hence,

82 + x = 180

x = 180 - 82

x = 98 degrees

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ON A TEST PLZ ANSWER This equation represents what type of function?
y=1/2x^3+ 5x
A linear
B quadratic
C exponential
D cubic

Answers

Linear equation is the answer

if costs $2.28 for 12 fluid ounces of dishwashing detergent. what is the cost per fluid ounce?

Answers

5.26. Because you would have to divide 12 by the coast to see the coast for 1 fluid ouce
It is .19 cents per fluid ounce, if you divide $2.28 by 12 there’s your answer.

help PLEASE! WILL GIVE BRAINLYEST IF YOU GET THE CORRECT ANSWER AND IF YOU REMIND ME!​

help PLEASE! WILL GIVE BRAINLYEST IF YOU GET THE CORRECT ANSWER AND IF YOU REMIND ME!

Answers

Answer:

167,225.472ft³

Step-by-step explanation:

1/2 × 8ft × 5ft = 609.6ft² [base area]

609.6ft² × 3ft = 55,741.824ft³ [volume of the bottom half]

(8 × 5 × 3)÷3 = 111,483.648ft³ [volume of pyramid]

111483.648ft³ + 55,741.824ft³ = 167,225.472ft³ [entire volume]

PLEASEEEEEEEEEEEEEEEEE

PLEASEEEEEEEEEEEEEEEEE

Answers

Wait what? X =10 in Roman numbers therefore it’s d

What are the basic rigid motions? *
O Translations, Reflections, and Rotations
O Rise, Run, Slope
O Translations, Dilation, Slope
O Translations, Slope, Rise, Run
A turn is also called?
Rotation
O Reflection
Translation
All the above

Answers

The basic rigid motions are A) Translation, reflections and rotations

In other words, we can shift an object, mirror it over a line, or turn it, to keep the same basic size and shape of the object. The object keeps the same area and perimeter, as well as the angles and sides staying the same as well.

A transformation that isn't a rigid motion would be a dilation. A dilation enlarges or shrinks a figure, so it doesn't keep the same size (though it keeps the same shape to make the before and after figures similar).

-------------------------

A turn is also called A) rotation

A rotation needs to have information about what center point you're turning around. Often this is the origin. You'll also need the amount of rotation applied, as well as if you're going counterclockwise or clockwise.




Identify the x- and y-intercepts of the graph. у 361 25 20 15 10 5 X 5 10 x-intercept (x, y) = y-intercept xy) (X, 1) = ( [ Need Help? Read It

Answers

The x-intercept of the graph is at the point (20, 0) and the y-intercept is at the point (0, 25).

To identify the x-intercept of a graph, we look for the point(s) where the graph intersects the x-axis.

At these points, the y-coordinate is always 0.

From the given information, we can see that the x-intercept occurs at x = 20 because at that point, the y-coordinate is 0.

To identify the y-intercept of a graph, we look for the point(s) where the graph intersects the y-axis.

At these points, the x-coordinate is always 0.

From the given information, we can see that the y-intercept occurs at y = 25 because at that point, the x-coordinate is 0.

In this case, the x-intercept is located at the point (20, 0) on the graph, which means when x = 20, the y-coordinate is 0.

This represents the point where the graph intersects the x-axis.

The y-intercept is located at the point (0, 25) on the graph, which means when y = 25, the x-coordinate is 0.

This represents the point where the graph intersects the y-axis.

Therefore, the x-intercept of the graph is at the point (20, 0) and the y-intercept is at the point (0, 25).

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melanie is using the spinner to play a card game. the spinner has six sections of equal size. What is the probability that melanie will have to take cards when she spins the spinner. A.1/6. B.1/4. C. 1/3. D.2/3. E.3/4​

Answers

Answer:

The answer is very clear is 2/3

Step-by-step explanation:

use a model for security purposes a jewelry company prints a hidden watermark on the logo of its official documents. the watermark is a chord located 0.7 cm from the center of a circular ring that has a 2.5 cm radius. to the nearest tenth, what is the length of the chord?

Answers

The length of the chord located 0.7 cm from the centre of a circular ring with a 2.5 cm radius is approximately 3.5 cm.

To calculate the length of the chord, we can use the following formula:

Chord Length = 2 x √(r^2 - d^2)

Where r is the radius of the circular ring and d is the distance between the chord and the centre of the circle.

In this case, r = 2.5 cm and d = 0.7 cm. Plugging these values into the formula, we get:

Chord Length = 2 x √(2.5^2 - 0.7^2) ≈ 3.5 cm (rounded to the nearest tenth)

Therefore, the length of the chord is approximately 3.5 cm. This hidden watermark technique is a simple but effective security measure that can help prevent counterfeiting or tampering with important documents. By incorporating a unique and difficult-to-replicate watermark, the jewellery company can protect its brand identity and ensure the authenticity of its official documents.

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Find the value of f(x)= 3x to the power of 2 - x +23 for x=-4

Answers

Answer:

This is not a real equation

Step-by-step explanation:

You cant do it when there are multiple resudents

Jim had €80 he spent 0.3 of it how much did he spend?

Answers

Answer:

€24

Step-by-step explanation:

If he had €80 and spent 0.3 of it, he spent 30% or 30/100 of it.

€80*\(\frac{30}{100}\) =  €80*\(\frac{3}{10}\) =  €24.

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A craftsman wants to build this fiddle. He needs to know the area of the face of the fiddle. How could he use the measurements shown to find the​ area?

Answers

The Area of Trapezium is 50, 267 mm².

We have,

base 1 = 224 mm

base 2 = 77 mm

Height = 334 mm

Now, Area of Trapezium

= 1/2 (Sum of parallel side) x height

= 1/2 (224 + 77) x 334

= 1/2 x 301 x 334

= 50, 267 mm²

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Simplify: (just give the answer)
6²+4²

Answers

Answer:

10 squared

Step-by-step explanation:

Answer: 52

Step-by-step explanation:

6*6 = 36 4*4 = 16

36+16=52

for what real values of $x$ is $-4

Answers

This is a simple inequality problem involving absolute values.

The given inequality is: $-4 < |x-3|$.We need to find the range of real values of $x$ that satisfy this inequality.
First, let's consider the case when $x-3$ is positive. In this case, the absolute value of $x-3$ is simply $x-3$. So, we can write the inequality as: $-4 < x-3$
Adding $3$ to both sides, we get: $-1 < x$

This means that all values of $x$ greater than $-1$ satisfy the inequality when $x-3$ is positive.
Now, let's consider the case when $x-3$ is negative. In this case, the absolute value of $x-3$ is $-(x-3)$. So, we can write the inequality as: $-4 < -(x-3)$. Expanding the right-hand side, we get: $-4 < -x + 3$

Subtracting $3$ from both sides, we get: $-7 < -x$. Multiplying both sides by $-1$ (which reverses the inequality), we get: $x < 7$.This means that all values of $x$ less than $7$ satisfy the inequality when $x-3$ is negative. Putting both cases together, we have:$x < 7$ or $x > -1$
This is the final answer. We can express it more concisely as:
$-1 < x < 7$

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What is one way the Federal Reserve can reduce the amount of money available in the economy?
A. Raising the discount rate
B. Selling treasury securities
C. Buying treasury securities
D. Lowering the interest on reserves​

Answers

Answer:

B. Selling treasury securities

Step-by-step explanation:

I'm taking the quiz

The Federal Reserve can reduce the amount of money available in the economy is buying treasury securities.

What is a federal reserve?The Federal Reserve can decrease the money supply by increasing the discount rate. a. Raising the discount rate provides depository institutions a minor incentive to borrow, thereby decreasing their reserves and lending activity. The U.S. government created the Federal Reserve, the nation's central bank, to control the money supply and contain economic calamities.One of the primary objectives of the Federal Reserve exists to function as the lender of last resort, permitting banks to borrow from the central bank when needed.The Fed operates three immediate tools in handling the money supply and observing stable economic growth. The tools exist (1) reserve needs, (2) the discount rate, and (3) open market operations.Each of these controls the money supply in different forms and can be utilized to obtain or develop the economy.The Federal Reserve can decrease the amount of money general in the economy stands buying treasury securities.

Therefore, the correct answer exists as option B. Selling treasury securities.

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Please help Quickly Look At Image.

Please help Quickly Look At Image.

Answers

Answer:

abc- 130

ebd-130

abe-50

Step-by-step explanation:

f the pattern in the table is extended to represent more equivalent ratios for 2:6, which pair of numbers would be in the columns? A multiplication table. In the column labeled 2, the numbers 2, 4, 6, 8, 10, 12, 14, 16, and 18 are highlighted. In the column labeled 6, the numbers 6, 12, 18, 24, 30, 36, 42, 48, and 54 are highlighted. 20 would be in the column for 2, and 60 would be in the column for 6. 20 would be in the column for 6, and 60 would be in the column for 2. 20 would be in the column for 2, and 56 would be in the column for 6. 20 would be in the column for 6, and 56 would be in the column for 2. please hurry im in a rush

Answers

The pair of numbers that would be in the columns, considering the proportional relationship, is given as follows:

20 would be in the column for 2, and 60 would be in the column for 6.

What is a proportional relationship?

A proportional relationship is a special linear function, with intercept having a value of zero, in which the output variable is obtained with the multiplication of the input variable and the constant of proportionality k, as shown as follows:

y = kx

The table is extended to represent more equivalent ratios for 2:6, hence the constant of the relationship is given as follows:

k = 6/2 = 3.

Hence the equation is:

y = 3x.

The values given by each column are given as follows:

Column 2: values of x.Column 6: values of y.

When x = 20, the numeric value of the relationship is of:

y = 3 x 20 = 60.

Hence the first option is correct.

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hi hello! please help me.

hi hello! please help me.

Answers

Answer:

x= -4

Step-by-step explanation:

hope it's helpful to you

Answer:

A) x= -4

Step-by-step explanation:

To solve you must isolate the variable. Do this by using the properties of equality to subtract and divide numbers from both sides of the equation. First, subtract 8x to move all x terms to the right side.

-48=12x

Then, divide both sides by 12

-4=x

give 5 key assumptions in formulating the mathematical
model for evaporator provide total mass balance,

Answers

In the formulation of a mathematical model for an evaporator, the following are five key assumptions:

1. Constant volume and density of the system.

2. Evaporation takes place only from the surface of the liquid.

3. The transfer of heat takes place only through conduction.

4. The heat transfer coefficient does not change with time.

5. The properties of the liquid are constant throughout the system.

Derivation of the total mass balance equation:

The total mass balance equation relates the rate of mass flow of material entering a system to the rate of mass flow leaving the system.

It is given by:

Rate of Mass Flow In - Rate of Mass Flow Out = Rate of Accumulation

Assuming that the evaporator operates under steady-state conditions, the rate of accumulation of mass is zero.

Hence, the mass balance equation reduces to:

Rate of Mass Flow In = Rate of Mass Flow Out

Let's assume that the mass flow rate of the feed stream is represented by m1 and the mass flow rate of the product stream is represented by m₂.

Therefore, the mass balance equation for the evaporator becomes:

m₁ = m₂ + me

Where me is the mass of water that has been evaporated. This equation is useful in determining the amount of water evaporated from the system.

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