(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
The product of two whole numbers is 588 and their sum is 49. What are the two numbers?
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]
Michaela has h hair ties. Michaela's sister has triple the number of hair ties that
Michaela has. Choose the expression that shows how many hair bows
Michaela's sister has.
A. h^3
B.3/h
C. 3h
D. H/3
9514 1404 393
Answer:
C. 3h
Step-by-step explanation:
In algebra, multiplication by a number is indicated by placing the number next to the variable, with or without a multiplication symbol.
3×h = 3·h = 3h
In plain text, the asterisk (*) is sometimes used as a multiplication symbol. Some folks will use a period (decimal point) as a multiplication symbol, but that tends to be confusing.
"Triple" means "three times", so the number of hair ties Michaela's sister has is ...
3 times h = 3h
_____
Additional comment
The caret (^), as in h^3, is used to signify repeated multiplication. The term h^3 means h×h×h. This is not the same as h+h+h = 3h.
The slash is used to signify division.
3/h means 3÷h.
h/3 means h÷3.
If Michaela's sister had h/3 hair ties, she would have one-third the number Michaela has. That is not the same as 3 times the number Michaela has.
Why is cube root of 9 equal to 9 to the one third power question mark (1 point)
9 to the one third power all cubed equals 9 to the one third times 3 power equals 9 to the first power equals 9
9 to the one third power all cubed equals 9 to the one third plus 3 power equals 9 to the first power equals 9
9 to the one third power all cubed equals 9 to the one third divided by 3 power equals 9 to the first power equals 9
9 to the one third power all cubed equals 9 to the one third minus 3 power equals 9 to the first power equals 9
Answer:
3
Step-by-step explanation:
because 3*3ʕっ•ᴥ•ʔっ(づ｡◕‿‿◕｡)づ(づ｡◕‿‿◕｡)づ
is Arithmetic a proper measure of central tendency of data?
Answer:
The arithmetic mean is the most common measure of central tendency.
Step-by-step explanation:
PLS HELP MEE , WILL MARKTHE BRAINLIEST PLS
Step-by-step explanation:
hopefully it is visible and makes sense
:)
Answer:
x=67 degrees
y=63 degrees (vertically opposite angles)
z=32 degrees
Step-by-step explanation:
x=130-63(sum of 2 interior angles of a triangle is equal to the opposite exterior angle)
x=67 degrees
y=63 degrees (vertically opposite angles)
z+y+85=180
z+63+85=180
z+ 148 =180
z =32 degrees
what times we subtract the number 80 by 8
Answer:
Question unclear
Step-by-step explanation:Your probally asking what times 8 gives us 80. If you are than 10!
Explain why each non-zero integer has two square roots but only one cube root.
Refer to the figure to answer the question.
Name the line of intersection of planes GABH and FEHG
HG
GA
FE
FD
Answer:
It's HG
Step-by-step explanation:
The line of intersection is where they cross, and this line is the line HG
Simplify 24 ÷ (3 + 2 square)
Answer:
3.42
Step-by-step explanation:
24/7=3.42
what is 13 x 12 feet converted is how many inches?
To make a cake, one pound of dry cake mix is needed. However, when pouring cake mix into the mixing bowl, 10% spills onto the floor and is unusable. What is the standard amount of cake mix necessary to make a cake
Answer:
it will be ten left
Step-by-step explanation:
the cake max is 20
Answer: 1.10 pounds
Step-by-step explanation:
20. In the above figure, ZAOB = 80°. What does ZACB equal?
A. 10°
B. 160°
C. 80°
O
D. 40°
Answer:
D. 40
Step-by-step explanation:
A central angle is equal to the measure of its corresponding arc.
angle AOB is a central angle and it's corresponding arc is arc AB
this means that arc AB = measure of angle AOB
If angle AOB = 80 degrees then arc AB equals 80 degrees too.
An inscribed angle is equal to half the measure of its intercepted arc.
Angle ACB is an inscribed angle and the arc it intercepts is arc AB
This means that angle ACB = 1/2 of arc AB
We have found that the measure of arc AB is 80 degrees.
This means that angle ACB = 1/2 of 80 which is 40
This year Amanda watched 80 movies. She thought that 56 of them were very good. Of the movies she watched, what percentage did she rate as very good?
a meayerologist at television station reported that a town received 0.90 inches of rain. Which fraction is equivalent to this amount of rain in inches?
Answer:
9/10
Step-by-step explanation:
0.90 = 0.9 = 90/100 = 9/10
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
How do you divide 250÷100
Answer:
250 ÷ 100 (so we'd reciprocate the right side and also change the sign to multiplication one) =250/1 x 1/100 (now we will cut 250 and 100 as much as they can be cut or reduced) =5/1 x 1/2 (now as they can no more be reduced we directly multiply them) =5/2 (now we will divide them both to get our anwer)
Step-by-step explanation:
if you served me crown please
Answer:
By using the GCF/HCF method 5/2 is the simplified fraction for 250/100.
Step-by-step explanation:
The step by step calculation of how to simplify the fraction 250/100 to its lowest term or simplest form. One of two methods used to convert the fraction to its lowest terms is the GCF or HCF method
Given Fraction: 250/100
Find GCF (Greatest Common Factor) for both numerator and denominator.The GCF for 250 and 100 is 50
Divide the numerator and denominator by GCF 50 and rewrite the fraction= (250/50) / (100/50)
= 5/2
Alicia is writing the program for a video game. For one part of the game she uses the rule ( x,y) -> ( x - 3, y + 4) to move points on the screen. A) What output does the rule give when the input is ( -6, 0)? Show your work. B) What output does the rule give when the input is ( 3, -4)? Show your work. C) Is the rule a function? Explain why it is or why it is not. ( Show all work and you'll recieve Brainliest).
Answer:
See below.
Step-by-step explanation:
The rule moves points 3 units to the left and 4 units up.
(-6, 0) moves to (-6 - 3, 0 + 4) = (-9, 4)
(3, -4) moves to (3 - 3, -4 + 4) = (0, 0)
The rule is a function because each point is moved to exactly one new location. There is no case in which two different points are moved to the same location.
Tính đạo hàm cấp n của hàm số f(x) = 3x − 1
4x + 3
Answer:
so fx 3x-1 '4x+3
Step-by-step explanation:
please mark me brainliest answer
7 thousands 8hundredsx10
Answer:
78,000
Step-by-step explanation:
Jalessa earned a score of 160 on a recent 50 question spelling contest. The scoring for the contest was +4 for each correct answer, -1 for each incorect answer, and 0 for each unanswered question. If she answered every question, what is the maximum number of questions that Jaleesa could have answered correctly?
Answer:
42 correct answersStep-by-step explanation:
Set a system of equations.
c- correct, i- incorrect.
c + i = 504c - i = 160Add the equations together:
5c = 210c = 42Then find the value of i:
i = 50 - 42i = 8solve for t..................................
Answer:
-4.375
.......................
does the table represent a function
Answer:
Yes, the table represents a function.
Step-by-step explanation:
A function doesn't have multiple x values (inputs).
If the table were to have more than one 5 (or more than one 4 etc.) in the input column then it would not be a function.
Write and solve an equation to find the numben.
The sum of twice a number and 13 is 75
Equation = 75
The number isn=
Answer:
32
Step-by-step explanation:
let number=b
twice a number=2b
Condition:
2b+13=75
2b=75-13
2b=62
b=62/2
b=31
Note:if you need to ask any question please let me know.
What is the answer for this question
Step-by-step explanation:
n/6=3/8
then we will cross
8n=6×3
8n=18
8n/8=18/8
n=2.25
if it is not correct sorry
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Answer:
7.4641
Step-by-step explanation:
Where would radicals come in the order of operations? Explain why.
Answer:
exponents, multiplication division addition and subtraction and radicals. They're gonna come right here with exponents on.
Step-by-step explanation:
The reason for this is because radicals, for example, X to the power or this very day vaccine is the same as X to the power of one. The humor to perhaps is the same as actually the power of 1/3. So really any radical can be expressed is an exploded as well. So this is why radicals are grouped with exponents right here. So after Grant sees in priority, but before multiplication and division
Radicals are expressions with roots (e.g. square roots, cube roots, etc.)
Radicals should be evaluated after all grouping symbols, but before any other arithmetic operators.
The grouping symbols are: brackets and parentheses
The other arithmetic operators are: addition, subtraction, division and multiplication.
Take for instance:
[tex]\mathbf{2\sqrt{4} + (5 \times 3) - 2}[/tex]
First, we evaluate the expressions in brackets
[tex]\mathbf{2\sqrt{4} + (5 \times 3) - 2 = 2\sqrt{4} + 15 - 2}[/tex]
Next, we evaluate the radical
[tex]\mathbf{2\sqrt{4} + (5 \times 3) - 2 = 2 \times 2 + 15 - 2}[/tex]
Then, we solve the remaining expressions.
Read more about radicals at:
https://brainly.com/question/1369233
What is the volume of the pryinid in the diagram
Answer:
25 cm3
Step-by-step explanation:
Step 1: Determine the base area and the height of the pyramid. Step 2: Find the volume using the general formula, V = (1/3) Base Area × Height, or V = a3/6√2 cubic units when the edge length 'a' of the triangular face is known. Step 3: Represent the final answer with cubic units.
Evaluate the expression for the given values of the variables. x2 + 4(x − y) ÷ z2, for x = 8, y = 5, and z = 2
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 8
Blue 8
Green 3
Yellow 7
Purple 16
Based on these results, express the probability that the next spin will land on red or green or purple as a decimal to the nearest hundredth.
Step-by-step explanation:
The probability is the number of desired observations (red, green, blue) divided by total number of observed outcomes.
Select the best answer for the question.
9. The sum of 1/6, 2/3, and 1/4 is
O A. 2/72, or 1/36
O B. 11/12
O C. 13/12, or 1"/12.
O D. 4/12, or 1/3
Mark for review (Will be highlighted on the rev
Answer:
That would be, C
Step-by-step explanation:
1/6 + 2/3= 5/6
5/6 + 1/4= 13/12 or 1"/12
5x+8=3(x+2) anyone know the answer?
Step-by-step explanation
work out the question in bracket first then separate numericals and variables to make it easier.
Answer:
distribute
5 + 8 = 3 ( + 2 )
expand to
5 + 8 = 3 + 6
subtract 8 from both sides
5 + 8 = 3 + 6
5 + 8 − 8 = 3 + 6 − 8
simplify
5 = 3 − 2
subtract 3 from both sides
5 − 3 = 3 − 2 − 3
simplify
2 = − 2
then divide both sides by 2
2 / 2 = − 2/ 2
= − 2/ 2
answer is
= −1
Step-by-step explanation:
Hope that helps>3