Under what conditions for the constants a, b, k, and l is (ax by) dx (kx ly) dy = 0 exact? solve the exact ode.
Answers
∫dF=F(x,y)=12ax2+bxy+12ℓy2+c=0 is the exact ode.
What is the exact equation?Specifically, an exact equation is a differential equation that can be solved instantly without the aid of any specialized methods. If the result of a straightforward differentiation, a first-order differential equation (of one variable) is referred to as an exact differential or exact differential. The equation
P(x, y)dy/dx + Q(x, y) = 0,
or in the equivalent alternate notation
P(x, y)dy + Q(x, y)dx = 0,
is exact if
∂P(x, y)/∂x = ∂Q(x, y)/∂y
In this instance, a function R(x, y) will exist whose partial x-derivative is Q and partial y-derivative is P, and whose equation R(x, y) = c (where c is constant) will implicitly establish a function y that will satisfy the initial differential equation.
An exact ODE is one where the equation can be written as dF=0 for some F(x,y). Expanding using chain rule, this means an equation of the form
∂1Fdx+∂2Fdy=0
Now if the second partials of F exist and are continuous, they must be equal due to Clairaut. So, given an equation
Mdx+Ndy=0
if we have
∂2M=∂1N
then there is an F such that
M=∂1F, N=∂2F
and hence that equation is exact, and the solution is simply
∫dF=0
We have
M=ax+by⇒∂2M=b
N=kx+ℓy⇒∂1N=k
so to be exact, we must have that b=k .
Then, integrating M and N , we have
F(x,y)=∫Mdx=12ax2+bxy+g(y)
F(x,y)=∫Ndy=bxy+12ℓy2+h(x)
and comparing these two, we can see that
∫dF=F(x,y)=12ax2+bxy+12ℓy2+c=0
is a solution to the equation for any a,b,c,ℓ . You can solve for y by quadratic methods.
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Related Questions
y=2x+3 y=4x+7 solve by elimination
Answers
Answer:
\(\displaystyle [-2, -1]\)
Step-by-step explanation:
To use the Elimination method, you must get rid of one pair of variables, so that one side is set to zero. So, in this case, we must get rid of \(\displaystyle x,\)therefore we will split the second equation in negative half :
\(\displaystyle \left \{ {{y = 2x + 3} \atop {-\frac{1}{2}[y = 4x + 7]}} \right. \\ \\ \\ \left \{ {{y = 2x + 3} \atop {-\frac{1}{2}y = -2x - 3\frac{1}{2}}} \right. \\ \\ \frac{1}{2}y = -\frac{1}{2}; -1 = y, -2 = x \\ \\ \\ \boxed{[-2, -1]}\)
I am joyous to assist you at any time.
Please help me with edge question .
Answers
\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)
If you used 0.5 ml of sample and 2.5 ml of diluent what is your dilution ratio?
Answers
Answer:
1/6
Step-by-step explanation:
I think it is:
0.5/(0.5+2.5) = 0.5/3 = 1/6
Periodiste Kuta Software Infinite Algebra 2 Solving Multi-Step Equations Solve each equation. Name Sorrentoa Ceballos Date 3/112021 1) 4n - 2n = 4 an=4 2) 2 +50 + 2v 3) 3 = x + 3 - 5x 3-3 = -612 burro xeo 4) x + 3 3= -6Question 9
Answers
Simplify the equation for x.
\(\begin{gathered} 24=6(-x-3) \\ -x-3=\frac{24}{6} \\ -x=4+3 \\ -x=7 \\ -x\cdot(-1)=7\cdot(-1) \\ x=-7 \end{gathered}\)Answer is -7.
Suppose an investment account is opened with an initial deposit of $11,000
earning 6.2% interest compounded monthly.
a) How much will the account be worth after 20 years?
b) How much more would the account be worth if compounded continuously?
Answers
a) The account will be worth $39,277.54 after 20 years.
b) If compounded continuously $2,434.90 more the account would be worthy.
a) To find the future value of the account after 20 years, we can use the formula:
FV = \(P(1 + r/n)^{(nt)\)
Where FV is the future value, P is the principal (initial deposit), r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the number of years.
Plugging in the given values, we get:
FV = 11,000(1 + 0.062/12)²⁴⁰
FV = $39,277.54
b) If the account is compounded continuously, then we use the formula:
FV = \(Pe^{(rt)\)
Where e is the mathematical constant approximately equal to 2.71828.
Plugging in the given values, we get:
FV = 11,000\(e^{(0.062*20)\)
FV = $41,712.44
Therefore, if the account is compounded continuously, it will be worth $41,712.44 after 20 years. The difference between the two values is $2,434.90, which is the amount the account would earn in interest with continuous compounding over 20 years.
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Hello! please helpp
5x divide 7 = y
turn this into a word problem and solve for x and y.
Answers
Answer:
5x÷7=y
x=7y/5
Step-by-step explanation:
5x÷7=y
5x=7y
x=7y/5
it's about proportion and stuff but I'm confused on this one can someone please explain?
Answers
Answer:
the one clue you have is "30,12" on the left. try to understand how they relate to each other. maybe how many times 12 goes into 30. or maybe how many times it goes into 32 with no decimal so what number do you have to add (sometimes work doesnt mean it like that so that might be wrong). but if you want the answers, they are:
35/5/15/30
14/2/6/12
the way i did it was if it was on the bottom (y) i did 2.5 times the number. if on the top (x) i did the number divided by 2.5. 2.5 was the rate of change (is that the word i think it is but if it isnt just blame me im sorry).
Step-by-step explanation:
a test has a mean of 100 and a standard deviation of 15. a client scores 130 on the test. at what percentile (rounded off) would this client's score place her?
Answers
As per the concept of z - score, the percentile would this client's score is 0.4772
Z - score:
In statistics, z - score is also termed the standard score, is used to determine how much each data point position is away from its mean. Where as in other words, it measures the deviation of x (data point) in terms of the standard deviations. Here the percentage of the population above or below the score can be obtained using z tables.
Given,
A test has a mean of 100 and a standard deviation of 15. a client scores 130 on the test.
Here we need to find at what percentile (rounded off) would this client's score place her.
As per the formula of z score, here we have the values,
mean = 100
standard deviation = 15
Score = 130
Therefore, the z score is calculated as,
=> z score = (130 - 100) / 15
=> z score = 30 / 15
=> z score = 2
According to the z score table the resulting value is 0.4772.
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Which best describes the triangle?
Answers
How to solve absolute value
2|x+9|+3=7
Answers
Answer:
x = -7, -11
Step-by-step explanation:
2|x+9|+3 = 7
subtract 3 from both sides of equation
2|x+9| = 4
divide 2 from both sides of equation
|x+9| = 2
Absolute values:
x+9 = 2 and x+9 = -2
x = -7 and x = -11
Answer these questions about finding the missing
angle measures.
What is the measure of
What is the measure of
What can be concluded about these triangles?
Answer choices/:
what can be concluded?
1.corresponding angles are proportional
2.The triangles are congruent
3.The triangles are similar
Answers
Answer:
Answer number one the
Step-by-step explanation:
the unequal triangles. If measured by angle, they are equivalent.
In the diagram, m angle3=120^ and m angle12=80^. Which angle measures are correct? Check all that apply. m angle1=60^ m angle13=80^ m angle6=80^ m angle5=60^ m angle10=120^ ° m angle 14=100^
Answers
Answer:
There you go, this was actually fun to do!!
Step-by-step explanation:
Answer:
M<1=60
M<13=80
M<5=60
M<14=100
Step-by-step explanation:
Did the assignment
Tom puts 4 fluid ounces of bubble mix into each bowl. How many bowls can he fill with 1 pint of bubble mix?
Answers
((((4 bowls))))
Robert can row 24 miles in 3 hrs w/ the Current Against the current, he can row 2 of this distance in 4hrs. Find 3 Roberts Rowing Rate of the current.
Answers
Robert's rowing rate in still water is 8 miles per hour, and the speed of the current is 2 miles per hour.
Let's start by assuming that the rate of the current is c, and Robert's rowing rate in still water is r. As a result, the following equation can be used to determine the rate of travel downstream:24 = (r + c) × 3
This equation can be simplified by dividing both sides by 3 and then subtracting c from both sides, giving:8 - c = r
Then, to figure out Robert's speed upstream, we'll use the following equation:2r - 4c = 24
Multiplying the first equation by 2 and then subtracting it from the second equation yields:
2r - 4c
= 24 - 2r - 2c-4c
= -3r + 12-3r = -4c + 12
Dividing both sides by -3, we obtain
:r = (4c - 12)/3Substituting this into the first equation:
24 = (4c - 12)/3 + cMultiplying both sides by 3 and then simplifying:
72 = 4c - 12 + 3c7c
= 84c = 12Therefore, the rate of the current is 2 miles per hour, and Robert's rowing rate in still water is 8 miles per hour.
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A box of 15 cookies costs $ 9 What is the cost for 1 cookie?
Answers
Answer:
60 cents or $0.60
Step-by-step explanation:
9.00/15 = 0.6
Answer:
$.60
Step-by-step explanation:
This is just 9 divided by 15 which is $.60
Write a function create_folders that takes in a nested 2d list of strings and creates a folder structure based on this. The strings indicate the names of the folders. The list should always contain the name of the folder, followed by a list of its subfolders. You can assume that the list you are given in your function follows this structure. Create your own list of folders and call your function with it to test your code. Here is an example of the list structure, but I'm sure you can come up with funnier examples (not relevant for grading): structure = [f1, [subf11, subf12], f2, [subf21, subf22, subf23], f3] Note: Like f3 in the example, not every folder will have subfolders. Therefore you have to check wether the next entry is a string or a list. Therefore this would also be a valid structure: structure = [f1, f2,[subf21, subf22, subf23]
Answers
Make sure to adjust the folder structure according to your needs when testing the code.
Here is the implementation of the `create_folders` function that takes a nested 2D list of strings representing folder structure and creates the corresponding folder structure:
```python
import os
def create_folders(structure):
for item in structure:
if isinstance(item, str):
# Create the folder
os.makedirs(item, exist_ok=True)
elif isinstance(item, list):
# Recursively create subfolders
folder_name = item[0]
subfolders = item[1:]
os.makedirs(folder_name, exist_ok=True)
os.chdir(folder_name)
create_folders(subfolders)
os.chdir('..')
```
You can test the function by creating your own folder structure and calling the `create_folders` function with it. For example:
```python
structure = ['f1', ['subf11', 'subf12'], 'f2', ['subf21', 'subf22', 'subf23'], 'f3']
create_folders(structure)
```
This will create the following folder structure:
```
- f1
- subf11
- subf12
- f2
- subf21
- subf22
- subf23
- f3
```
Make sure to adjust the folder structure according to your needs when testing the code.
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4cm 2cm 5cm 5cm.......
Answers
Answer:
33 / the second one
Step-by-step explanation:
5 x 5 = 25
4 x 2 = 8
25 + 8 = 33
4 * 2 = 8
5 * 5 = 25
25 + 8 = 33
evaluate the expression 6x + 4 9/10 when x = 2/3.
Answers
x=2/3
6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10
Answer:
2x-1=y,2y+3=x
Step-by-step explanation:
no explanation
y=-2x - 7
4y - 3x = 16
Answers
Answer:
x=−4 and y=1
Step-by-step explanation:
Rewrite equations:
y=−2x−7;−3x+4y=16
Step: Solvey=−2x−7for y:
y=−2x−7
Step: Substitute−2x−7foryin−3x+4y=16:
−3x+4y=16
−3x+4(−2x−7)=16
−11x−28=16(Simplify both sides of the equation)
−11x−28+28=16+28(Add 28 to both sides)
−11x=44
-11x/-11=44/-11
x=−4
Step: Substitute−4forxiny=−2x−7:
y=−2x−7
y=(−2)(−4)−7
y=1(Simplify both sides of the equation)
x=−4 and y=1
Answer:
Step-by-step explanation:
find z and x
please help i’ll mark the first one or whoever right brainliest
Answers
I need some help please
Answers
What is the greatest common factor between 18 and 30 and 54
Answers
The greatest common factor (GCF) of 18, 30, and 54 is 6.
The greatest number that divides two or more numbers without leaving a residue is known as the GCF.
The prime factorization approach is the most effective way to resolve this issue.
Using this technique, you will first determine the largest common factor amongst each number's prime factors.
The prime factorization of 18 is 2 x 3 x 3.
The prime factorization of 30 is 2 x 3 x 5. The prime factorization of 54 is 2 x 3 x 3 x 3.
The largest common factor amongst all of them is 6, which is the GCF.
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The radius of the circle is 13cm. what is the circumference of the circle 3.14
Answers
Answer:
Step-by-step explanation:
81.64
right rectangular prism of 0.25 m, 0.36m, and 0.14 m. what is the volume of the prism
Answers
Answer:
1.26 m^3
Step-by-step explanation:
0.25*0.36*0.14=1.26
Simplify: -(-x + 1) -x − 1 x − 1 -x + 1 x + 1
Answers
Answer:
x -1
Step-by-step explanation:
-(-x + 1)
Distribute the minus sign
- 1 * -x + -1 (-x)
x -1
Steps to solve:
-(-x + 1)
~Distribute the negative sign
(- * -x) + (- * 1)
~Simplify
x - 1
Best of Luck!
Can you please help me
Answers
Answer:
Supplementary angle = 98°
Complementary angle = 8°
Step-by-step explanation:
By definition, sum of complementary angles is equal to 90°.
Therefore, complementary angle of 82° = 90° - 82°
= 8°
Similarly, sum of supplementary angles is equal to 180°.
Therefore, supplementary angle of 82° = 180° - 82°
= 98°
The supplementary angle 98°
The complementary angle 8°.
Keelie has a triangular-shaped card. The lengths of its sides are 2.8 cm, 3.5 cm, and 4.2 cm. Is the card a right triangle? (select), the card (select) ▼ a right triangle.
Answers
Answer:
if it says select we cannot give you an answer
Step-by-step explanation:
please help me!!
write the equation of a line that is perpendicular to y=-x-6 and passes through the point (-9,-4)
Answers
Answer:
y = x + 5
Step-by-step explanation:
Solve -8x + 3 + 2x = 5(x - 6) with steps
Answers
Answer:
Step-by-step explanation:
-8x+3+2x=5(x-6)
-6x+3=5x-30
-11x=-33
x=3
What is the largest country in europe by population?.
Answers
The largest country in Europe by population is Russia. With a population of over 144 million people, Russia holds almost twice as many inhabitants as the second-largest country in Europe, Germany.
The reason why Russia has the largest population in Europe is mainly due to its vast geographical area, which includes diverse ethnic groups and natural resources, thus supporting a larger population. Additionally, historical factors such as migration, urbanization, and economic growth have also contributed to Russia's high population numbers.
One of the main reasons for Russia's large population is its size. As the largest country in the world, Russia covers almost 1/8th of the world's landmass, providing ample room for its citizens to reside. Additionally, Russia's population growth has been influenced by various factors throughout history, including immigration, wars, and government policies. Despite declining birth rates in recent years, Russia's population remains the largest in Europe.
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