(x^2-y^2)dx+2xydy=0
so this is a problem of a differential equation I've been trying so hard to match with the given answer but failed every time I tried. So, is there anyone who can really can help me out to catch the mistakes that I'm making?
* The last line of my workout is just a dump guess.
The pictures are my workouts also the answer to this question is attached. Please read my solutions by this order : pic-1, pic-3 & pic-2, if necessary.
Answers
[tex](x^2 - y^2) \, dx + 2xy \, dy = 0[/tex]
Multiply both sides by [tex]\frac1{x^2}[/tex].
[tex]\left(1 - \dfrac{y^2}{x^2}\right) \, dx + \dfrac{2y}x \, dy = 0[/tex]
Substitute [tex]y=vx[/tex], so [tex]v=\frac yx[/tex] and [tex]dy=x\,dv+v\,dx[/tex].
[tex](1-v^2) \, dx + 2v (x\,dv + v\,dx) = 0[/tex]
[tex](1 + v^2) \, dx + 2xv \, dv = 0[/tex]
Separate the variables.
[tex]2xv\,dv = -(1 + v^2) \, dx[/tex]
[tex]\dfrac{v}{1+v^2}\,dv = -\dfrac{dx}{2x}[/tex]
Integrate both sides
[tex]\displaystyle \int \frac{v}{1+v^2}\,dv = -\frac12 \int \frac{dx}x[/tex]
On the left side, substitute [tex]w=1+v^2[/tex] and [tex]dw=2v\,dv[/tex].
[tex]\displaystyle \frac12 \int \frac{dw}w = -\frac12 \int\frac{dx}x[/tex]
[tex]\displaystyle \ln|w| = -\ln|x| + C[/tex]
Solve for [tex]w[/tex], then [tex]v[/tex], then [tex]y[/tex].
[tex]e^{\ln|w|} = e^{-\ln|x| + C}[/tex]
[tex]w = e^C e^{\ln|x^{-1}|}[/tex]
[tex]w = Cx^{-1}[/tex]
[tex]1 + v^2 = Cx^{-1}[/tex]
[tex]1 + \dfrac{y^2}{x^2} = Cx^{-1}[/tex]
[tex]\implies \boxed{x^2 + y^2 = Cx}[/tex]
Your mistake is in the first image, between third and second lines from the bottom. (It may not be the only one, it's the first one that matters.)
You incorrectly combine the fractions on the left side.
[tex]\dfrac1{-2v} -\dfrac v{-2} = \dfrac1{-2v} - \dfrac{v^2}{-2v} = \dfrac{1-v^2}{-2v} = \dfrac{v^2-1}{2v}[/tex]
Related Questions
is it possible to see the answer without paying?
Answers
Answer:
yes dear u need not to pay before viewing answer
You should at least answer 1 question to view the answers.
Solve the following equation for W.
P=2L+2W
Answers
**Disclaimer** Hi there! I assumed the question is to represent W in terms of all other variables (P, L). The following answer corresponds to this understanding. If it is incorrect, please let me know and I will modify my answer.
Answer: W = (P/2) - L
Step-by-step explanation:
Given equation
P = 2L + 2W
Factorize 2 out
P = 2 (L + W)
Divide 2 on both sides
P / 2 = 2 (L + W) / 2
P / 2 = L + W
Subtract L on both sides
(P / 2) - L = L + W - L
[tex]\Large\boxed{W=\frac{P}{2} -L}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
[tex]\displaystyle{W = \dfrac{P}{2} - L}[/tex]
Step-by-step explanation:
To solve for W, we have to isolate the W-variable. First, we can factor the expression 2L + 2W to 2(L+W):
[tex]\displaystyle{P = 2(L+W)}[/tex]
Next, we'll be dividing both sides by 2:
[tex]\displaystyle{\dfrac{P}{2} = \dfrac{2(L+W)}{2}}\\\\\displaystyle{\dfrac{P}{2} = L+W}[/tex]
Then subtract both sides by L:
[tex]\displaystyle{\dfrac{P}{2} - L= L+W-L}\\\\\displaystyle{\dfrac{P}{2} - L= W}[/tex]
Therefore, we'll obtain W = P/2 - L.
Note that the given formula is perimeter formula of a rectangle where Perimeter = 2 * Length + 2 * Width.
So if we solve for W (Width) then we'll get Width = Perimeter / 2 - Length which can be useful to find width with given perimeter and length.
Identify an acute angle and give its measure.
Answers
Angle HEJ measures 15 degrees.
Jasmine got a new puppy for her birthday. He's full of energy, so she takes him for a walk along a 1.2-mile loop in a nearby park. If they walked a total of 3.6 miles, how many loops did they do?
Answers
Answer: 3 loops
Step-by-step explanation: The loop is 1.2 miles, and the total walk is 3.6 miles. You want to find out how many laps are in the 3.6 miles. This can be found using division. 3.6/1.2= the number of 1.2 mile laps inside the 3.6 mile walk, which is 3 laps. hope this helped!
A rectangle has a width w that is 5units longer than its lenght/. Which equation expresses the rectangle's area, A?
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Area equals Length times Width.
since the width of this equation is 5 units Longer then its Length
W = L + 5
To put this area in a equation we could say
L(L+5)=A
Simplify the equation, L^2 + 5L = A.
Determine which quadrilaterals have the properties given in the table.
kite
square trapezoid rectangle
Opposite sides are congruent.
Diagonals are perpendicular.
Exactly one pair of opposite angles are
congruent.
rhombus
parallelogram
Diagonals are congruent.
Diagonals bisect opposite interior angles.
Consecutive interior angles are
supplementary.
Answers
The two quadrilateral with the listed properties are kite and rhombus respectively.
Properties of a kiteIt has two diagonals intersecting at right anglesA kite is symmetrical about its main diagonalAngles opposite to the main diagonal are equalThe kite can be viewed as a pair of congruent triangles with a common baseIts diagonals are perpendicularProperties of a rhombusAll sides of the rhombus are equalThe opposite sides are parallelOpposite angles are equalDiagonals bisect each other at right anglesDiagonals bisect the anglesThe sum of two adjacent angles is equal to 180 degrees, that is, are supplementaryThus, the two quadrilateral with the listed properties are kite and rhombus respectively.
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Answer:
your welcome
Step-by-step explanation:
just need these 3 please and thanks in advance
Answers
The conclusion that can be made based on the hypothesis is:
1. It's a valid conclusion.
2. It is a valid conclusion.
3. It is a valid conclusion.
How to illustrate the information?According to the law of detachment, when the conditional and the hypothesis are true, the conclusion will be true.
Therefore, if 6x < 42, the value of x will also be less than 6. This is valid.
When an angle is more than 90°, it's an obtuse angle and since A is 103°, it's valid.
Also, the statement about the violin being a string instrument is logically valid.
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Find the measures of angles a and b when 0=44
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⦁ Mr. A likes playing a game and the probability that he wins this game is p. He enters the casino and he promises himself that he plays the game until he wins one time and then he stops. Let X be the number of plays in order to win one time. ⦁ What are the values of X? ⦁ What is the probability that X=n?. Prove that it satisfies the PMF conditions. ⦁ Calculate E(X) ⦁ Calculate V(X) ⦁ Study the memoryless property of X.
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The possible values of X for this game are 0, 1, 2, 3, 4.......n, where n ≥ 1
How to determine the values of X?From the complete question, we understand that Mr. A wants to plays the game until he wins
This means that
He might win at the first game and he might win after n attempts
So, the values of X are
X = 0, 1, 2, 3, 4.......n
Hence, the possible values of X for this game are 0, 1, 2, 3, 4.......n, where n ≥ 1
The probability that X = nThe probability of x is represented as:
P(x) = nCx * p^x * (1 - p)^(n-x)
So, the probability that X = n is:
P(n) = nCn * p^n * (1 - p)^(n - n)
Evaluate the exponent
P(n) = nCn * p^n * 1
Evaluate the combination expression
P(n) = 1 * p^n * 1
This gives
P(n) = p^n
Hence, the probability that X = n is p^n
Prove that it satisfies the PMF conditions.The distribution satisfies PMF conditions because
The sum of the probabilities is 1 No probability is negativeEach probability value is between 0 and 1 (inclusive)Calculate E(X)The expected value E(x) is calculated using
E(x) = n * p
So, we have:
E(x) = np
Hence, the value of E(x) is np
Calculate V(X)The variance V(x) is calculated using
V(x) = √n * p * (1 - p)
So, we have:
V(x) = √np(1 - p)
Hence, the value of V(x) is √np(1 - p)
Study the memoryless property of X.The memoryless property of X is that each probability of X is independent
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Classify the figure. Identify its vertices, edges and bases.
Write the direct variation function given that y varies directly with x, and y = 1.5 when x = 5.
1. x = 0.3y
2. y = 0.3x
3. y = 3x
4. y = 0.25x
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The direct variation function is y = 0.3x
How to determine the direct variation function?The direct variation from y to x is represented as:
y = kx
When y = 1.5 and x = 5, we have
1.5 = 5k
Divide by 5
k = 0.3
Substitute k = 0.3 in y = kx
y = 0.3x
Hence, the direct variation function is y = 0.3x
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The graph of a cosine function has an amplitude of 5, a vertical shift of −1, and a period of 4. These are the only transformations of the parent function.
Use the Sine tool to graph the function.
The first point must be on the midline, and the second point must be a maximum or minimum value on the graph closest to the first point.
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See attachment for the graph of the cosine function f(x) = 5 cos(π/2x) - 1
How to graph the cosine function?From the question, the given parameters are:
Amplitude, A = 5
Vertical shift, D = -1
Period, T = 4
A cosine function is represented as:
f(x) = A cos(B(x + C)) + D
Where
Amplitude = A
Period = T
Horizontal shift = C
Vertical shift = D
Since the horizontal shift is not stated in the question, we can assume that the horizontal shift is 0
i.e. C = 0
So, the equation of the cosine function becomes
f(x) = A cos(Bx) + D
Calculate the value of B using
B = 2π/T
So, we have:
B = 2π/4
Evaluate
B = π/2
So, we have:
f(x) = A cos(π/2x) + D
Substitute the known values of A and D in the above equation
f(x) = 5 cos(π/2x) - 1
Next, we plot the graph of the cosine function on a graphing tool
See attachment for the graph of the cosine function f(x) = 5 cos(π/2x) - 1
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Which value of w makes 14 = 11 + w/8 x 6 a true statemen?
choose 1 answer:
w = 1
w = 4
w = 16
w = 24
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answer
is true statement w= 4
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
Sin A= Answer
Answers
Check the picture below.
Mrs. Smith has a total of 28 kids in her class. There are 5 more boys than there are girls. Write a system of equations to model this.
Answers
Answer:
x+(x+5)=28
Step-by-step explanation:
girls(g)should be equal to x
boys(b) will therefore be x+5
x+(x+5)=28
2. Us i ng the filled table above,
a) calculate just one PED.
b) Is the demand elastic or inelastic?
c) Based on your answer to c) what price change would you recommend to increase TR?
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The price elasticity of demand of the pen will be -0.2.
How to compute the elasticity?The demand and supply schedule will be:
Price Qd. Qs
$10. 250. 100
$20. 200. 90
$30. 180. 80
The price elasticity of demand from $1 to $2 will be:
= Percentage change in quantity demanded/percentage change in price
Percentage change in quantity demanded will be:
= (200 - 250)/250 × 100
= -20%
Percentage change in price will be:
= (20 - 10)/10 × 100
= 100%
Therefore, the elasticity of demand will be:
= -20/100
= - 0.2
The value gotten illustrates an inelastic demand.
In order to increase the total revenue, the price can be reduced as it will lead to more sales.
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Complete question:
Choose any product or service. Create the demand and supply schedule.
Calculate just one PED.
Is the demand elastic or inelastic?
What price change would you recommend to increase TR?
Show Work Please Thank You
Answers
The angles in degrees to radian is as follows:
-54 degrees = -3π / 10 radian
How to convert from degree to radian?The measurement is in degrees. Let's convert it to radian with respect to π.
Therefore,
180 degrees = π radian
-54 degrees = ?
cross multiply
Hence,
angle in radian = -54 × π / 180
angle in radian = - 54π / 180
angle in radian = - 6π / 20
angle in radian = -3π / 10 radian
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the size of the second application is 3.45 MB less than he first application. What is the size of the second application
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The size of the second application given the size of the first application and the expression ( x - 3.45 mb) for the size of the second application is 293.55 MB.
EquationLet
Size of the first application = xSize of the second application= x - 3.45 mbFor instance,
if the size of the first application is 297 MB
Size of the second application= x - 3.45 mb
= 297 MB - 3.45 MB
= 293.55 MB
Therefore, the size of the second application given the size of the first application and the expression for the size of the second application is 293.55 MB
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PLEASE HELP ME .IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answers
Answer: [tex]\frac{10\pi}{3}[/tex] m
Step-by-step explanation:
[tex](2)(\pi)(4) \left(\frac{150}{360} \right)=\frac{10\pi}{3}[/tex]
Can someone help on this?
Answers
Step-by-step explanation:
this just means that the first function with input value x = 0 is calculated. that result becomes the input value x for the second function. and that result becomes the input value x for the 3rd function. and that result is then our result.
to answer a and b we only need to look at the main operation of each function :
the first one uses only basic multiplication and subtraction.
the second one uses squaring.
the third one is a 1/x operation.
a.
since the final result is a negative number (-31), the second function with the square operation cannot be last.
because a square operation always delivers a positive result.
+a × +a = +a²
-a × -a = +a²
remember, for a square operation we multiply the same number by itself. therefore we cannot mix signs like -a × +a, because then they would not be the same numbers anymore.
b.
since the initial input value is 0, the third function (1/x) cannot be the first, because 1/0 is not defined.
c.
because of the "large" -32 term in the first function I guess that this will be the last one to create such a low negative result of -31.
since 1/x cannot be first, (x - 2)² is then first. that makes 1/x second, and (4x - 32) third, as mentioned.
let's try :
x = 0
(x - 2)² = (0 - 2)² = (-2)² = 4
x = 4
1/x = 1/4
x = 1/4
4x - 32 = 4×1/4 - 32 = 1 - 32 = -31
hurrah ! we are correct !
What is the first step to solve the equation A. Square both sides of the equation. B. Add 5 to both sides of the equation. Square. 5, and -3. C. D. None, because there is no solution. 2x-5--3?
Answers
Hi :)
I'd start by adding 5 to both sides of the equation. That would make the equation easier.
[tex]\boldsymbol{\sqrt{2x}-5=3}}[/tex]
[tex]\boldsymbol{\sqrt{2x}=2}[/tex]
The next step is to get rid of the radical sign.
Which operation will undo the square root? Squaring.
So that's why we square both sides:
[tex]\boldsymbol{2x=4}[/tex]
And Now we just divide both sides by 2
[tex]\boldsymbol{x=2}[/tex]
~[tex]\textit{\textbf{Learn More; Work Harder}}[/tex]~
:)
ball is thrown vertically upward at an initial speed of Its height (in feet) after t seconds is given by h(t)t(16t). After how many seconds does the ball reach its maximum height? Round answer to two decimal places.
Answers
If the height of ball is shown by h(t)=52t-16[tex]t^{2}[/tex] then the ball will reach after 1.625 seconds.
Given that height in t seconds is shown by h(t)=52t-16[tex]t^{2}[/tex].
We are required to find the time after which the ball will attain its maximum height.
The maximum height is the y coordinate of vertex of the parabola. Then we can use the following value of t.
h(t)=52t-16[tex]t^{2}[/tex]
Differentiate with respect to t.
dh/dt=52-32t
Again differentiate with respect to t.
[tex]d^{2}h/dt^{2}[/tex]=-32t
Because tim cannot be negative means the height is maximum.
Put dh/dt=0
52-32t=0
-32t=-52
t=52/32
t=1.625
Hence if the height of ball is shown by h(t)=52t-16[tex]t^{2}[/tex] then the ball will reach after 1.625 seconds.
Question is incomplete as the right and complete equation is
h(t)=52t-16[tex]t^{2}[/tex] .
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Let x, y, z be three natural numbers such that x < y < z. If GCF(x, y, z) = 3, GCF (y, z) = 15, LCM (x, y, z) = 3150, and x is even number greater than 10, then find the values of x, y and z.
Answers
Answer:
one of several possible solutions :
18, 75, 105
Step-by-step explanation:
prime factors of 3150 :
3150 ÷ 2 = 1575
1575 ÷ 2 no
1575 ÷ 3 = 525
525 ÷ 3 = 175
175 ÷ 3 no
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 5 no
7 ÷ 7 = 1
3150 = 2¹ × 3² × 5² × 7¹
these are the product of the longest streaks of prime factors in x, y and z.
the GCF(y, z) = 15.
the prime factors of 15 are simply 3¹×5¹.
so, y and z share only the factors 3 and 5.
the GCF(x, y, z) = 3.
since x is an even number, the elimination of 5 in the GCF is not surprising.
let's try the following :
x = 2¹ × 3² = 2×9 = 18
y = 3¹ × 5² = 3×25 = 75
z = 3¹ × 5¹ × 7¹ = 3×5×7 = 105
that uses all the factors of 3150, and their LCM is as the product of the longest streaks of their prime factors is
2¹ × 3² × 5² × 7¹.
fits.
the GCF(75, 105) is the product of the prime factors they have in common : 3¹ × 5¹ = 15.
fits.
the GCF(18, 75, 105) is the product of the prime factors ask 3 numbers have in common, which is only 3¹ = 3.
fits.
18 < 75 < 105
fits.
18 is an even number greater than 10.
fits.
there are more than 1 solutions.
e.g.
z = 2¹ × 3¹ × 5¹ × 7¹ = 210
is also possible.
IF THE PROBABILITY THAT A FOOTBALL TEAM WILL WIN THEIR NEXT GAME IS 80%,
WHAT ARE THE ODDS IN FAVOR OF THEM WINNING?
Answers
The odds in favor of them winning is 20%
How to determine the probability
From the information given, we have that the probability of them winning the next game is 80%
P( winning) = 80% = 0. 8
The odds against them winning is given as;
1 - probability of winning
We have;
= 1 - 0. 8
= 0. 2
The odds in favor of them winning is simply the probability of them losing;
= 0. 2 × 100
= 20%
Thus, the odds in favor of them winning is 20%
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PLEASE HELP ME SOLVE THIS
Answers
This only happens when x is greater than or equal to -1 [-1, infinity) or when x is less than or equal to -1 (-infinity, -1].
Non decreasing means the slope is zero or positive, so it has to be the first option for the domain [-1, infinity]
The inverse of f(x) = (x + 1)^2
y = (x + 1)^2
x = (y + 1)^2
Sq rt x = y + 1
(sq rt x) - 1 = y
f^-1(x) = (sq rt x) - 1
We cannot take the square root of -1, so the domain of the inverse of f is [0, infinity]
For the straight line y =1/2x-4 what are the slope and y intercept
Answers
Answer:
Step-by-step explanation:
slope-- 1/2
y intercept-- -4
If f(x) = 5x, what is ƒ˜¹ (x)?
Answers
[tex]y = 5x \\ switch \: y \: and \: x \\ x = 5y \\ solve \: for \:y \\ y = \frac{x}{5} [/tex]
Alyssa was given a gift card for a coffee shop each morning Alyssa uses the gift card to buy one cup of coffee let a represent the amount of money of money remaining on the card after buying X cups of coffee that the table below has selected values showing the liner relationship between X and a determine the original amount of money on the gift card
Answers
Answer:20.00
Step-by-step explanation: next time include the table but i managed to find it anyway
A closed box with a square base is to have a volume of 16000 cubic centimeters. The material
for the top and bottom of the box costs $3 per square centimeter while the material for the sides
costs $1.50 per square centimeter. Find the dimensions of the box that will minimize the total
cost of materials. What is the minimum total cost?
Answers
The most suitable measurements for a box with a square base are 5cm (width) x 5cm (length) x 640cm (height). This box would be worth $4875
How to calculate the minimum value of the box?To find the minimum value of a box that must have a square base and 16000 cm³, we must try different measurements to find the variable that represents the least value.
In this case, the variable that represents less value is a base of 5cm x 5cm and a height of 640cm. This means that the box would be worth $4875 as shown below.
Base
5cm × 5cm = 25cm²25cm² x 3 = $75Sides
5cm × 640cm = 3200cm²3200cm² × $1.50 = $4800$4,800 + $75 = $4,875Additionally, we can check that the volume of the box is the required 16000cm³, as shown below:
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Find the x-intercept.
x + 3
X-2
y =
([?], [_])
Answers
Answer: 1
Step-by-step explanation: It's subtraction and add ion look at the right side
The question is attached
Answers
Answer:
We call the denominator rational.
Step-by-step explanation:
For example:
[tex]\frac{1}{\sqrt{2}} = \frac{\sqrt2}{\sqrt2 \cdot \sqrt2} = \frac{\sqrt2}{2}[/tex]
It's clear that the denominator is now a rational number, not an irrational one anymore.