(6x-5y+4)dy+(y-2x-1)dx=0​

Answers

Answer 1

(6x - 5y + 4) dy + (y - 2x - 1) dx = 0

(6x - 5y + 4) dy = (2x - y + 1) dx

dy/dx = (2x - y + 1) / (6x - 5y + 4)

Let X = x - a and Y = y - b. We want to find constants a and b such that

dY/dX = (a rational function)

where the numerator and denominator on the right side are free of constant terms. Substituting x and y in the equation, we have

dY/dX = (2 (X + a) - (Y + b) + 1) / (6 (X + a) - 5 (Y + b) + 4)

dY/dX = (2X - Y + 2a - b + 1) / (6X - 5Y + 6a - 5b + 4)

Then we solve for a and b in the system,

2a - b + 1 = 0

6a - 5b + 4 = 0

==>   a = -1/4 and b = 1/2

With these constants, the equation reduces to

dY/dX = (2X - Y) / (6X - 5Y)

Now substitute Y = VX and dY/dX = X dV/dX + V :

X dV/dX + V = (2X - VX) / (6X - 5VX)

The equation becomes separable after some simplification:

X dV/dX + V = (2 - V) / (6 - 5V)

X dV/dX = (2 - V) / (6 - 5V) - V

X dV/dX = (2 - V - (6 - 5V)) / (6 - 5V)

X dV/dX = (4V - 4) / (6 - 5V)

- (5V - 6) / (4V - 4) dV = 1/X dX

Integrate both sides:

-5/4 V + 1/4 ln|4V - 4| = ln|X| + C

Extract a constant from the logarithm on the left:

-5/4 V + 1/4 (ln(4) + ln|V - 1|) = ln|X| + C

-5/4 V + 1/4 ln|V - 1| = ln|X| + C

-5V + ln|V - 1| = 4 ln|X| + C

Get this back in terms of Y :

-5Y/X + ln|Y/X - 1| = 4 ln|X| + C

Now get the solution in terms of y and x :

-5 (y - 1/2)/(x + 1/4) + ln|(y - 1/2)/(x + 1/4) - 1| = 4 ln|x + 1/4| + C

With some manipulation of constants and logarithms, and a bit of algebra, we can rewrite this solution as

-5 (4y - 2)/(4x + 1) + ln|(4y - 4x - 3)/(4x + 1)| = 4 ln|x + 1/4| + 4 ln(4) + C

-5 (4y - 2)/(4x + 1) + ln|(4y - 4x - 3)/(4x + 1)| = 4 ln|4x + 1| + C

-5 (4y - 2)/(4x + 1) + ln|4y - 4x - 3| - ln|4x + 1| = 4 ln|4x + 1| + C

-5 (4y - 2)/(4x + 1) + ln|4y - 4x - 3| = 5 ln|4x + 1| + C


Related Questions

simplify y + 5 - y - 6​

Answers

Answer:

-1

Step-by-step explanation:

Subtract the numbers: y+5-y-6

Combine like terms: y-1-y

= -1

Use the number line to answer the question. Each tick represents 1 unit.



Describe the location of point K.

four more than M
three more than L
seven less than N
two less than J


Please be fast!!

Answers

Answer and Step-by-step explanation:

Essentially, you are describing the position of point K using the location of the other points on the graph.

Let's start listing some descriptions:

K is:

3 more than H

2 more than J

3 less than L

4 less than M

7 less than N

12 less than P

Now look at the answer choices and compare it to what we wrote.

We see that the answer choices A, B, and D are incorrect (based on what we wrote), and that answer choice C is correct.

[C. 7 less than N] is the correct answer.

#teamtrees #PAW (Plant And Water)

I hope this helps!

Answer: LESS THAN FOUR

Step-by-step explanation:

find the defference between 5 2/7 and 2 2/4​

Answers

Answer: 39/14

Step-by-step explanation:

Given

5 2/7 - 2 2/4

Convert mixed fraction to improper fraction

5 2/7 = (5 × 7 + 2) / 7 = (35 + 2) / 7 = 37/7

2 2/4 = (2 × 4 + 2) / 4 = (8 + 2) / 4 = 10 / 4 = 5/2

Find the common denominator for 37/7 and 5/2

First 10 multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

First 5 multiples of 7 = 7, 14, 21, 28, 35

Since 14 is the first common multiple in the lists, 14 would be the common denominator of 37/7 and 5/2

Convert to the common denominator

(37 × 2) / (7 × 2) = 74 / 14

(5 × 7) / (2 × 7) = 35 / 14

Simplify by subtraction of numerator

=74/14 - 35/14

=(74 - 35) / 14

=[tex]\boxed{\frac{39}{14} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Is square root of 11+10 a rational or irrational number

Answers

Answer:

Irrational Number is the answer

Answer:

[tex] \sqrt{11 + 10} = \sqrt{22} = 4.69041576 [/tex]

THIS IS IRRATIONAL

Step-by-step explanation:

The correct answer is irrational and the reason for that is the decimals for sqrt of 22 are non-recurring, are non-terminating and lastly it cannot be expressed in a form of a fraction.

I hope this makes sense

:)

One week, Rachel earned $250. She spent $120 on food, $30 on miscellaneous items, and saved the rest.

If Rachel makes a pie chart showing how she spends her money, the central angle for the food sector would be __________.


187°


173°


90°


144°

Answers

250 is the total
120 is 48% of 250
A pie chart is a complete circle which is 360 degrees and 48% of 360 is 172.8 round that up to 173 degrees

The answer is 173

can you help me to solve this​

Answers

Answer:

<B = <C(angles in a isoceles traingle)

Answer:

angle B is equal to angle C because it's a isosceles triangle with two equal sides and two equal angles

Okay imma ask a question and The first person to answer and get it correct wins and I will give you a Brillantest


196x84-23+56-109+54x345-56+34x856=

Answers

Answer:

yoooo it equals 1

Step-by-step explanation:

which statement best describes f(x)=-2√x-7+1

Answers

it is under mapping and function

f of x is equal to -2 root x-7 plus one

Need help with solving please

Answers

Answer:

x=8

Step-by-step explanation:

4 ^(1/2x) = 256

Rewriting 256 as a power of 4

4 ^(1/2x) = 4^4

Since the bases are the same, the exponents are the same

1/2x = 4

Multiply each side by 2

1/2x *2 = 4*2

x=8

What is the Answer to 50 + 10 x 0 + 7 + 2

Answers

using pemdas (parentheses, exponent, multiplication, division, addition, and subtraction):

first, we multiply 10 x 0 because m is before a which equals 0.

then, add in the order of the equation, 50 + 0 + 7 + 2 = 59

Arithmetic involves carrying out addition, subtraction, division and multiplication on numbers and expressions. The result of [tex]50 + 10 \times 0 + 7 + 2[/tex] is [tex]59[/tex]

Given that:

[tex]50 + 10 \times 0 + 7 + 2[/tex]

To do this, we apply BODMAS.

First, we evaluate all multiplication operations

[tex]50 + 10 \times 0 + 7 + 2 = 50 + 0 + 7 + 2[/tex]

Then evaluate all addition operations

[tex]50 + 10 \times 0 + 7 + 2 = 59[/tex]

Hence, the result of [tex]50 + 10 \times 0 + 7 + 2[/tex] is [tex]59[/tex]

Read more about arithmetic at:

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The product of two whole numbers is 588 and their sum is 49. What are the two numbers?

Answers

Answer:

Here is your answer. HOPE THIS HELPS YOU! STAY BLESSED.

Answer:

28,21

Step-by-step explanation:

let the numbers be x and y

x+y=49

y=49-x

xy=588

x(49-x)=588

49x-x²=588

x²-49x+588=0

[tex]x=\frac{49 \pm \sqrt{49^2-4*1*588} }{2*1} \\=\frac{49 \pm \sqrt{2401-2352} }{2} \\=\frac{49 \pm\sqrt{49} }{2} \\=\frac{49 \pm 7}{2} \\=\frac{49+7}{2} ,\frac{49-7}{2} \\=28,21[/tex]

A square has a a side lenght of 5 feet what is its area?

Answers

Answer:

25 sq feet

Step-by-step explanation:

Length = 5 feet

Area = (Length)²

        = 5²

        = 25 sq feet

3. Write a word phrase using 10x(14+11)

Answers

Answer:

10 multiplied by the sum of 14 and 11

Step-by-step explanation:

[tex].[/tex]

The university of Michigan football stadium can hold 107,601 people. Michigan states football stadium can hold 75,001 people. 51,000 people can fit in the football stadium at the university of North Carolina and 40,004 people can fit in duke universities stadium which is also in North Carolina. How many more people can fit in the stadiums in Michigan combined than in the stadiums in North Carolina combined

Answers

Answer:

56,601

Step-by-step explanation:

(7 ten thousand 5 hundreds) x 10

Answers

Answer:

The answer is 705,000

Step-by-step explanation:

pls mark brainlest

The value of (7 ten thousand 5 hundreds) x 10 is 705,000.

Here,

The written expression is,

(7 ten thousand 5 hundreds) x 10

We have to find the value of given written expression.

What is Mathematical expression?

Mathematical expression is a finite combination of symbols that is well-formed according to the rules.

Now,

The written expression is,

⇒ (7 ten thousand 5 hundreds) x 10 = 70, 500 x 10 = 705,000

Hence,

The value of (7 ten thousand 5 hundreds) x 10 is 705,000.

Learn more about the Mathematical expression visit:

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Help please! Describe how figure 20 will look like

Answers

9514 1404 393

Answer:

  Each colored block in Figure 20 will be a 20×20 square of smaller squares of the same color. The red-green pattern will be identical.

Step-by-step explanation:

Each colored block in Figure N is an N×N array of small blocks the same color. The pattern of red and green N×N blocks is the same from one figure to the next. We expect Figure 20 to fit this description.

Francisco Typed a 36-word paragraph in minute. What is his typing speed, in
words per minute?

Answers

Answer:36

Step-by-step explanation:

It says he typed 36 words in a paragraph in a minute which means he types 36 per minute

Show Work! There are 380 students, teachers, and chaperones going on school buses for a field trip. Each school bus can hold 68 passengers. Everyone will ride on a school bus. How many school buses does this group need?

Answers

Answer:

6 buses

Step-by-step explanation:

i believe you just have to divide 380/68

then it'll give you 5.5 and then have to round to the nearest integer

eg jammu jdndhdbshsbsbs​

Answers

Answer:

A: [tex]3\frac{1}{3}[/tex]

B: [tex]3\frac{2}{3}[/tex]

I hope this helps!

pls ❤ and mark brainliest pls!

(c) 5 points possible (graded) The problem you encountered in part (b) is called separation . It occurs when the can be perfectly recovered by a linear classifier, i.e., when there is a such that In order to avoid this behavior, one option is to use a prior on . Let us investigate what happens if we assume that is drawn from a distribution, i.e., What is the joint log likelihood of this Bayesian model

Answers

We have that these are the key points given below

The Bayesian Theorem is a theorem that centers or basis its claim on the facts that the probability of an event occurring is based on Prior Knowledge that of situation or Prior factors of the Event.

Likelihood function is a function that take into account all statistical model and determine there best application given the statistical data given.

Bayesian Theorem

The Bayesian Theorem is a theorem that centers or basis its claim on the facts that the probability of an event occurring is based on Prior Knowledge that of situation or Prior factors of the Event

i'll explain further with an example

Given that when two unfair dice are thrown a 100 times the probability of getting the higher figure in the range of 6-8 , Therefore the Bayesian Theorem simply assumes that this range of 6-8 to be the highest for all 100 throws of two dice.

The Bayesian model is given  as

[tex]B=Prior * Likelihood=Posterior * Marginal[/tex]

Bayesian model is a statistical model.

This leads us to the definition of the Likelihood function

Likelihood function is a function that take into account all statistical model and determine there best application given the statistical data given.

For more information on this visit

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A display case of plastic bracelets are marked 13 for $3. If Nate has $60, how many plastic bracelets can Nate get? (assume no other taxes or fees)

Answers

Answer:

$4

Step-by-step explanation:

We can write a ratio to solve

15 stickers       30 stickers

----------------- = -------------

2 dollars           x stickers

Using cross products

15x = 2*30

15x = 60

Divide by 15

15x/15 = 60/15

x = 4

3.0040916 to the nearest hundred thousandth

Answers

Answer:

3.004

Step-by-step explanation:

If you were to round it like this: 3.0041, the thousands place would still be 4, so it would come out to be 3.004. Hope that helps!!

Find the quotient.

154 divided by 14

Answers

Answer:

11

Step-by-step explanation:

[tex]\frac{154}{14} =11\\\\check: 11*14=154[/tex]

154 divided by 14 equals 11.

To find the quotient of 154 divided by 14, we perform long division as follows:

     11

14 | 154

First, we consider how many times 14 can be divided into 15, which is 1. We write the quotient, 1, above the line.

Next, we multiply 14 by 1, which equals 14. We subtract 14 from 15, resulting in 1. We bring down the next digit, which is 4.

We now consider how many times 14 can be divided into 14, which is 1. We write the quotient, 1, next to the 1 above the line.

Multiplying 14 by 1 gives us 14. Subtracting 14 from 14 gives us 0.

Since there are no more digits to bring down, we can conclude that the quotient is 11.

Therefore, 154 divided by 14 equals 11.

Long division is a method used to find the quotient and remainder when dividing two numbers. It involves dividing, multiplying, subtracting, and bringing down digits until there are no more digits to bring down. In this case, the quotient is 11, indicating that 154 can be divided by 14 precisely 11 times without any remainder.

To learn more about the division;

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Aim: I can solve two-step word problems involving per
1. A supermarket stocks 300kg of potatoes. 25% of the potatoes are
are sold in 1.5kg bags. What mass of potatoes are sold in 1.5kg b

Answers

Answer:

75 kg

Step-by-step explanation:

300*25/100

3*25

75 Kg

Answer:

75kg

Step-by-step explanation:

potatoes are stocked =300kg

25% of potatoes in kg= 25% * 300kg

=75kg

75kg potatoes are sold in 1.5kg bags.

find the derivative of the function y= x^20

Answers

Answer:

Step-by-step explanation:

[tex]\frac{dy}{dx} =20x^{19}[/tex]

evaluate the expression

Answers

Step-by-step explanation:

13

[tex]3 + (20 \div 5) - ( {2}^{2}) [/tex]

[tex]3 + 4 - 4 = 3[/tex]

15

[tex] \frac{10 - {3}^{2} }{20 - (3 \times 4)} [/tex]

[tex] \frac{10 - 9}{20 - 12} [/tex]

[tex] \frac{1}{8} [/tex]

calculate the absolute value
| 4 - 3x | = 5x + 4 ​

Answers

Recall the definition of absolute value:

• |x| = x if x ≥ 0

• |x| = -x if x < 0

So we have 2 cases to consider:

• If 4 - 3x ≥ 0, then |4 - 3x| = 4 - 3x, and we have

4 - 3x = 5x + 4

8x = 0

x = 0

• If 4 - 3x < 0, then |4 - 3x| = -(4 - 3x) = 3x - 4, which gives

3x - 4 = 5x + 4

2x = -8

x = -4

However, keep in mind that |x| is always non-negative. If x = -4, then the right side of the equation becomes

5(-4) + 4 = -20 + 4 = -16 < 0

so the solution in this case is extraneous.

38. Evaluate f (3x +4y)dx + (2x --3y)dy where C, a circle of radius two with center at the origin of the xy
C plane, is traversed in the positive sense.

please i need real time help

Answers

It looks like the integral is

[tex]\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy[/tex]

where C is the circle of radius 2 centered at the origin.

You can compute the line integral directly by parameterizing C. Let x = 2 cos(t ) and y = 2 sin(t ), with 0 ≤ t ≤ 2π. Then

[tex]\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy = \int_0^{2\pi} \left((3x(t)+4y(t))\dfrac{\mathrm dx}{\mathrm dt} + (2x(t)-3y(t))\frac{\mathrm dy}{\mathrm dt}\right)\,\mathrm dt \\\\ = \int_0^{2\pi} \big((6\cos(t)+8\sin(t))(-2\sin(t)) + (4\cos(t)-6\sin(t))(2\cos(t))\big)\,\mathrm dt \\\\ = \int_0^{2\pi} (12\cos^2(t)-12\sin^2(t)-24\cos(t)\sin(t)-4)\,\mathrm dt \\\\ = 4 \int_0^{2\pi} (3\cos(2t)-3\sin(2t)-1)\,\mathrm dt = \boxed{-8\pi}[/tex]

Another way to do this is by applying Green's theorem. The integrand doesn't have any singularities on C nor in the region bounded by C, so

[tex]\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy = \iint_D\frac{\partial(2x-3y)}{\partial x}-\frac{\partial(3x+4y)}{\partial y}\,\mathrm dx\,\mathrm dy = -2\iint_D\mathrm dx\,\mathrm dy[/tex]

where D is the interior of C, i.e. the disk with radius 2 centered at the origin. But this integral is simply -2 times the area of the disk, so we get the same result: [tex]-2\times \pi\times2^2 = -8\pi[/tex].

Graph step by step:
f(x)=-2x+1

Answers

Step-by-step explanation:

Root:(1/2, 0)

Domain: x∈R

Range: y∈R

Vertical intercept: (0, 1)

Does this picture indicate that < JAC =

Answers

Answer:

No

Step-by-step explanation:

<JAC = 93

< DBE = 90

The two angles are not equal

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