Use separation of variables to solve the differential equation with initial condition y(1)=-2
Answers
Answer: A
Step-by-step explanation:
[tex]\frac{dy}{dx}=\frac{1+x}{xy} \\ \\ y \text{ } dy=\frac{1+x}{x} \text{ } dx \\ \\ y \text{ } dy= \left(\frac{1}{x}+1 \right) \text{ } dx \\ \\ \int y \text{ } dy=\int \left(\frac{1}{x}+1 \right) \text{ } dx \\ \\ \frac{y^{2}}{2}=\ln \left| x \right|+x+C[/tex]
Substituting in the initial condition,
[tex]\frac{(-2)^{2}}{2}=\ln \left|1 \right|+1+C\\\\2=1+C\\\\C=1[/tex]
So,
[tex]\boxed{\frac{1}{2}y^{2}=\ln \left|x \right|+x+1}[/tex]
Answer:
[tex]\textsf{A.} \quad \dfrac{1}{2}y^2=\ln|x|+x+1[/tex]
Step-by-step explanation:
To solve the differential equation:
Rearrange the given equation to get all the terms containing y on the left side, and all the terms containing x on the right side:
[tex]\dfrac{dy}{dx}=\dfrac{1+x}{xy}[/tex]
[tex]\implies y\dfrac{dy}{dx}=\dfrac{1+x}{x}[/tex]
[tex]\implies y\:dy=\dfrac{1+x}{x}\:dx[/tex]
[tex]\implies y\:dy=\dfrac{1}{x}+\dfrac{x}{x}\:dx[/tex]
[tex]\implies y\:dy=\left(\dfrac{1}{x}+1\right)\:dx[/tex]
Integrate both sides:
[tex]\displaystyle \implies \int y\:dy=\int \left(\dfrac{1}{x}+1\right)\:dx[/tex]
[tex]\implies \dfrac{1}{2}y^2=\ln|x|+x+C[/tex]
Find the value of C using the given values of x and y:
when x = 1, y = -2
[tex]\implies \dfrac{1}{2}(-2)^2=\ln|1|+1+C[/tex]
[tex]\implies 2=0+1+C[/tex]
[tex]\implies C=1[/tex]
Substitute the found value of C:
[tex]\implies \dfrac{1}{2}y^2=\ln|x|+x+1[/tex]
Related Questions
the radis of the cylinder is (2/7) units and height of the cylinder is (8/11 units find the volume of the cylinder use =22/7
Answers
The volume of the cylinder is 64/3773 cubic units
Volume of a cylinderThe formula for calculating the volume of a cylinder is expressed as:
V = πr²h
where
r is the radius
h is the height
Given the following parameters
r = 2/7units
h =8/11 units
Substitute
V = 22/7 * 2/7 * 2/7* 8/11
V = (2/7)³ * 8/11
V = 8/343 * 8/11
V = 64/3773 cubic units
Hence the volume of the cylinder is 4/3773 cubic units
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y>-3x +3
y≥ 2x-2
O (1,0)
O (-1,1)
O(2,2)
(0,3)
Answers
Answer:
(1,0)
Step-by-step explanation:
y>-3x +3
y≥ 2x-2
If we plot these two inequalities, we can see where the lines intersect, See attached graph.
They intersect at (1,0)
We can also do this mathematically:
y>-3x +3
- (y≥ 2x-2)
0 [tex]\geq[/tex] -5x + 5
5x [tex]\geq[/tex] 5
x [tex]\geq[/tex] 1
If x = 1:
y≥ 2x-2
y≥ 2(1)-2
y≥ 0
(x,y) = (1,0)
The graph of a line goes up and to the right when:
Answers
When the coefficient of x is positive, the graph of a line rises and moves to the right. Option C is correct.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
The complete question is
"The graph of a line goes up and to the right when:
a) the coefficient of x is 0
b) the coefficient of x is negative
c) the coefficient of x is positive
d) there is no coefficient of x"
When the coefficient of x is positive, we know that the graph of a line will move upward and to the right.
Since we are aware that a line's upward and rightward movement indicates that the line is advancing, we will obtain a positive slope for the line, and we are also aware that the slope-intercept of a line is provided as:
y= mx+c
If m is a positive number, then positive is the coefficient of x.
The graph of a line goes up and to the right when the coefficient of x is positive.
Hence option C is correct.
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W+15x-9y+2z
Terms:
Coefficients:
Answers
In the problem given:
W + 15x - 9y + 2z
The term are single mathematical expressions that separate values.
In the expression, there is a + and -; these concludes 2 terms.
There are 3 coefficients next to each variable.
The coefficients are 15x, -9y, and 2z.
That means there are 3 coefficients.
Cheers
- ROR
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex] \sf{W \rightarrow coefficient = 1} [/tex][tex] \sf{15x \rightarrow coefficient = 15} [/tex][tex] \sf{-9y\rightarrow coefficient = -9} [/tex][tex] \sf{2z\rightarrow coefficient = 2} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Term refers to each variable or constant separated by a mathematical operator.
Coefficient refers to the numberic part of variable or a constant number present in an expression.
[tex]\qquad \tt \rightarrow \: 12a - 10b + 6[/tex]
[tex] \large\textsf{Terms :} [/tex]
[tex] \texttt{W } [/tex][tex] \texttt{coefficient = 1} [/tex]
[tex] \texttt{15x} [/tex][tex] \texttt{coefficient = 15} [/tex]
[tex] \texttt{-9y} [/tex][tex] \texttt{coefficient = -9} [/tex]
[tex] \texttt{ 2z} [/tex][tex] \texttt{coefficient= 2} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Jose bought 750 bags of peanuts for $375.00. He intends to sell each bag for $0.15. More than he paid . How much should he charge?
Answers
The amount of charge for one bag of peanuts will be $0.65.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Jose bought 750 bags of peanuts for $375.00.
He intends to sell each bag for $0.15 more than he paid.
Then the amount of charge for one bag of peanuts will be
⇒ $375 / 750 + $0.15
⇒ $0.5 + $0.15
⇒ $0.65
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Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the best estimate of the speed Morris is traveling?
1 mile = 5,280 feet
45 miles per hour
46 miles per hour
47 miles per hour
48 miles per hour
Answers
Answer:
48 miles per hour I hope I helped you have a nice day
6.
(06.01 LC)
Choose the correct classification of 4x4 − 4x3 + 10x6. (1 point)
4th degree trinomial
12th degree trinomial
3rd degree trinomial
6th degree trinomial
Answers
solve for x -3x > 12
Answers
Answer:
x < -6
Step-by-step explanation:
x -3x > 12
Combine like terms
-2x>12
Divide by -2, remembering to flip the inequality
-2x/-2 < 12/-2
x < -6
Answer:
x < -6
Step-by-step explanation:
Sweet corns purchased for $9 are markup by 10%. When no one bought the sweet corns, they decided to markdown the corn by 10% from the markup price. What is the selling price of the corn?
Answers
For more explanation, please see the attachment
The sides of a square bedroom measure 3.5 yards. if carpet costs $16 per square yard, how much will it cost to cover the floor?if one side of a square notebook measures 20 cm, what is the area of the front cover of the notebook?
Answers
Answer:
£196 and 400cm
Step-by-step explanation:
3.5^2 = 12.25 will give the whole floor
12.25 × 16 = 196
20^2= 400cm is the front cover of the book
y = −x + 4
y = 3x + 3
Answers
x=0.25
I think
what is the answer for this please 23÷23
Answers
Answer:
1
Step-by-step explanation:
Any number divided by itself equals 1. So, 23 divided by 23 is 1.
Solve the 2 problem s hurrryyyy
Answers
Answer:
3. n>or=0
5. n>or=0
Step-by-step explanation:
3. -1<or=2n+4-5
=-1<or=2n-1
=1-1<or=2n
=0<or=2n
=n>or=0.
5. 0<or=2n+3n
=0<or5n
=n>or=0
please help me to find the answer Y=2X 3X+4Y=22 Y=2X 3X+4Y=22
Answers
[tex]\left\{\begin{array}{ccc}y=2x&(1)\\3x+4y=22&(2)\end{array}\right[/tex]
Put (1) to (2):
[tex]3x+4(2x)=22\\3x+8x=22\\11x=22\qquad|\text{divide both sides by 11}\\\boxed{x=2}[/tex]
Substitute the value of x to (1):
[tex]y=2\cdot2\\\boxed{y=4}[/tex]
Solution:
[tex]\huge\boxed{\left\{\begin{array}{ccc}x=2\\y=4\end{array}\right}[/tex]
a 48 gram sample of a substance that’s used for drug research has a k value of 0.1325
Answers
Using an exponential function, it is found that the half-life of the substance is of 5.23 units of time.
What is the exponential function for the amount of a substance?The function is given by:
[tex]A(t) = A(0)e^{-kt}[/tex]
In which:
A(0) is the initial value.k is the exponential decay rate.The parameters are given by:
A(0) = 48, k = 0.1325.
Hence the equation is:
[tex]A(t) = 48e^{-0.1325t}[/tex]
The half-life is the amount of time for which A(t) = 0.5A(0) = 24, hence:
[tex]A(t) = 48e^{-0.1325t}[/tex]
[tex]24 = 48e^{-0.1325t}[/tex]
[tex]e^{-0.1325t} = 0.5[/tex]
[tex]\ln{e^{-0.1325t}} = \ln{0.5}[/tex]
[tex]0.1325t = -\ln{0.5}[/tex]
[tex]t = -\frac{\ln{0.5}}{0.1325}[/tex]
t = 5.23.
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If the events have the same theoretical probability of happening, then they are called:-
A- Mutually exclusive events
B- Mutually exhaustive events
C- Equally likely events
D- Impossible events
Answers
C- Equally likely events
Step-by-step explanation:
Equally Likely Events. Equally likely events are events that have the same theoretical probability (or likelihood) of occurring.
(｡♡‿♡｡)
Answer:
Equally Likely Events
Step-by-step explanation:
What is the solution to -2|x − 1| = -4? A. x = 3 B. x = -1 or x = 3 C. x = 1 or x = 3 D. No solutions exist.
Answers
Answer:
B
Step-by-step explanation:
-2|x - 1| = -4
|x - 1| = 2
since we are dealing with a function that brings 2 values to the same result, the reverse function (needed to find the values of x that create the result y) has 2 branches :
(x - 1) = 2
and
(x - 1) = -2
x - 1 = 2
x = 3
x - 1 = -2
x = -1
therefore, B is the right answer.
Two rigid transformations are used to map TriangleJKL to TriangleMNQ. The first is a translation of vertex L to vertex Q. What is the second transformation?
a reflection across the line containing LK
a reflection across the line containing JK
a rotation about point L
a rotation about point K
Answers
Triangle JKL is mapped to Triangle MNQ by two rigid transformations. Vertex L to vertex Q translation is the first. a rotation about point L is the second transformation. Option A is correct.
What is the triangle?A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.
Two rigid transformations are used to map Triangle JKL to Triangle MNQ. The first is a translation of vertex L to vertex Q.
The second transformation is a rotation about point L.
Hence option A is correct.
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Answer: Option 3 or C. a rotation about point L
Step-by-step explanation:
I took the quiz and got 100% correct on Edge 2022. Trust me if you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful. Good luck everyone! :)
2.2.5a (Part 1): For the graph below, what is the x-intercept? *
-4 -2
2
-2
-4
y
2
4
0 points
X
Answers
An x-intercept is the point where the line of a graph passes through the x-axis. Thus, you should look for this point on the given graph.
What is a graph?A graph can be defined as a type of chart that is used for the graphical representation of data on both the horizontal and vertical lines of a Cartesian coordinate i.e x-axis and y-axis.
In Mathematics, x-intercept refers to the point where the line of a graph passes through the x-axis as shown in the image attached below. Since the graph wasn't provided for this question, you should look for the point where the line passes or crosses through the x-axis.
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Which is precisely defined using the undefined terms point and plane?
O circle
O line segment
O perpendicular lines
O ray
Answers
Answer:
Option A: circle
Step-by-step explanation:
A circle is a set of points in a plane that are equidistant from a common center point.
For my math assessment, I need to apply trigonometry in a real life situation and explain about it. I've been thinking of 1. trigonometry applied in cricket 2. music (sound waves)... but still not quite sure how to. If anyone has knowledge on how I could work on these or any other new ideas that would be relevant, PLEASE help me!!! Thank you!! <3
Answers
Answer:
I know you said relevant so i have two answers.
1) (not so relevant).
You could use it to show how NASA and astronomers use it to calculate the distance between planets and connect it to building rockets and all that cool stuff.
2) (relevant).
For the one about music, you could connect it to sound engineers and use sine and cosine graphs to calculate wavelengths
Answer: Answers below.
Step-by-step explanation: Suppose you want to find the best angle to kick a soccer ball so that it enters the goal. A triangle can be formed with angle ζ facing the goal. Increasing ζ or decreasing ζ will allow you to see the best angle that is the maximum amount of time that you should wait until scoring the ball.
Sine, Cosine, and Tangent waves are used everyday in phones, tablets, computers, and in quantam and normal technology by imitating and creating waves that can be sent to a destination.
You can use inverse trigonometric functions to find the height of a roof, the height of a tree, the height of a pole, and more.
Light waves are, in reality, sine and cosine waves intertwined together.
You can even use trigonometry every day in work places, such as in software engineering. In fact, calculus 1 and 2, as well as Multivariate Calculus, which heavily and fundamentally uses trigonometry, is used widely across computer science. These help you to get $100,000 jobs.
In the diagram, the measure of angle 6 is 98°.
A transversal intersects 2 lines to form 8 angles. Clockwise from top left, the angles are 1, 2, 3, 4; 5, 6, 7, 8.
What is the measure of angle 7?
Answers
The measure of angle 7 is 82°.
What is transversal line?
A transversal is defined as a line that passes through two lines in the same plane at two distinct points in the geometry
Given:
angle 6= 98°
As, angle 6 and 7 forms a linear pair then
angle 6 + angle 7 = 180
98 + angle 7= 180
angle= 180-98
angle 7 = 82°
Hence, angle 7 is 82°.
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Find the interest rate for a principal of $8635 and charged $33549 in interest for 11 years.
Round your answer to 1 decimal place.
Answers
Answer:
rate = 0.4 %
Step-by-step explanation:
Interest = principal x rate x time
33549 = 8635 x r x 11
33549 = 94985r
r = 33549/94985
r = 0.3532
r = 0.4
rate = 0.4 %
What is the length of side BC of the triangle?
Enter your answer in the box.
Answers
Answer:
28
Step-by-step explanation:
2x + 7 = 4x - 7
14 = 2x
x = 7
BC = 4x = 4(7) = 28
is the ratio 16: 4 equivalent to 12:3
Answers
Yes, because 16 divided by 4 is 4, and 12 divided by 3 is also 4
Pls answer thissssssss
Answers
Answer:
Area of room = 21 * 16
= 336 m²
Area of Carpet = (21 - 1)* (16-1)
= 20*15
= 300
Area of border = Area of room - Area of carpet
= 336 - 300
= 36 m².
can someone help me with this question with details
Answers
Answer:
I think the answer is 5 ( if wrong then do a low rating)
Step-by-step explanation:
The way I found the answer was by using PEDMAS so first I handled [(4 - (-5)) x (-7)] which is the same as 4 + -5 which equals -1 and when multiplied by -7 equals positive 7 because whenever you multiply 2 negatives you get a positive.
Next I solved 6 / (-3) which is -2 since whenever a positive is divided by a negative the quotient is negative. Now the equation is:
-2 + 7 and when solved is -2 + 7 = 5
In the given figure, lines AC and BD intersect each other at point E.
If ∠AEB:∠BEC = 9 : 11, find all the angles.
Answers
The value of the angle AED = 99 degree , Angle BEC is 99 degree , angle DEC = 81 degree , angle AEB is 81 degree
What is angle of a Straight Line ?The straight line has an angle of 180 degree.
The two lines AC and BD intersects such that
∠AEB:∠BEC = 9 : 11
Let angle BEC be x
Then
Angle AEB is 9x/11
and angle AEC + BEC = 180 degree
(9x/11) + x = 180
9x +11x = 11 * 180
20x = 11 * 180
x = 99 degree
Angle BEC is 99 degree
and angle AEB is 81 degree
As Angle AED is vertically opposite to angle BEC
Therefore angle AED = 99 degree
As Angle DEC is vertically opposite to angle AEB
Therefore angle DEC = 81 degree.
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Assembly of a television set in the factory is set to 45 minutes. Some workers take a shorter time (t) at this while some take longer. However, each varies no more than 8 minutes. Which inequality below represents this scenario?
Answers
Answer:
a
Step-by-step explanation:
Is (x + 7) a factor of f(x) = x³ - 3x² + 2x - 8?
Answers
Answer:
x=-7
0=(-7)³-3(-7)²+2(-7)-8
=-343-147-14-8
0≠-512
x+7 isn't a factor
