Shown above is a slope field for the differential equation dydx=y2(4−y2). If y = g(x) is the solution to the differential equation with the initial condition g(−2)=−1, then, limx→∞g(x) is
Answers
The value limx→∞g(x) is zero option (c) is correct.
What is a differential equation?The differential equation involves the function and its derivative to represent a relationship between the functions and their derivative. In simple words, the differential equation is the mathematical relation that consists of one or more functions with its derivative.
We have a differential equation:
[tex]\rm \frac{dy}{dx} =y^2(4-y^2)[/tex]
[tex]\rm\frac{dy}{y^2(4-y^2)} = dx[/tex] (rearranging the equation to solve)
[tex]\int \rm\frac{dy}{y^2(4-y^2)} = \int dx[/tex]
[tex]\rm \frac{ln(|y+2|)}{16} -\frac{1}{4y} -\frac{ln(|y-2|)}{16} = x+c[/tex] (after integrating both sides)
For the given initial condition g(-2) = -1
When x = -2, y = -1
[tex]\rm \frac{ln(|-1+2|)}{16} -\frac{1}{4(-1)} -\frac{ln(|-1-2|)}{16} = -2+c[/tex]
[tex]\rm \frac{1}{4} -\frac{ln(|-3|)}{16}+2 = c[/tex]
The value of c = 2.18
The equation we get:
[tex]\rm \frac{ln(|y+2|)}{16} -\frac{1}{4y} -\frac{ln(|y-2|)}{16} = x+2.18[/tex]
As we can see the value of g(-2) is negative and from the graph of the above equation it goes to infinity and it touches the x-axis at the infinity.
The value [tex]\displaystyle \lim_{x \to \infty}g(x)[/tex] when x reaches infinity the value of function g(x) becomes zero. ie.
[tex]\displaystyle \lim_{x \to \infty}g(x) =0[/tex]
Thus, the value [tex]\displaystyle \lim_{x \to \infty}g(x)[/tex] is zero option (c) is correct.
Learn more about the differential equation here:
https://brainly.com/question/14620493
Related Questions
Please help........................
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Answer:
I think it is 2 one
Step-by-step explanation:
A swimming pool is to be drained. The pool is shaped like a rectangular prism with length 30 ft, width 18 ft, and depth 4 ft. Suppose water is pumped out of the
pool at a rate of 216 ft per hour. If the pool starts completely full, how many hours does it take to empty the pool?
hours ( NO LINKS , LINK WILL GET YOU BANNED )
Answers
Answer:
10 hours (I am not positive)
Step-by-step explanation:
We first want to find the volume of pool which is 30 x 18 x 4 = 2160.
Then you are going to divide by 216 to find how many hours it takes to drain the whole pool. (I'm not that big of an expert)
What is the missing side?
Answers
Answer:
x=5
Step-by-step explanation:
Area of triangle=1/2 * b * h
In this case b=10, h=x, and A=25
By substituting values in we can say:
[tex]A=\frac{1}{2} * b *h\\25=\frac{1}{2} * 10 * x\\25=5x\\x=5[/tex]
Write the equation in standard form. Y=x+1
Answers
what is 1/2 x 1/2 x 1/2 x 1/2
Answers
Answer:
0.0625
Step-by-step explanation:
Hope this helps :)
Have a nice day <3
Answer:
1/16
Step-by-step explanation:
Just multiply all numerators and all denominators: 1x1x1x1/2x2x2x2. That gives you your total of 1/16.
answer choices
A Function 1
B Function 2
C The Functions have the same Y-intercept
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Answer:
I would say A
Step-by-step explanation:
Have a great day hope this helped!
What is the measure of the missing angle
Answers
Answer:
c. 42°
Step-by-step explanation:
two interior angles= one exterior angle
let x be the other interior angle
90° + x=132°
x=132-90
x=42°
Alex was making pumpkin soup that called for 3 and 4/5 cups of pumpkin. If Alex makes 2 batches of soup how many cups of pumpkin will he need?
Answers
Answer:
7 and 3/5
Step-by-step explanation:
3 and 4/5 times 2 is 7 and 3/5
3.Construct a line perpendicular to the line given through the point P at the right
Answers
Answer:
Step-by-step explanation:
Find the mean of the data set. 5, 4, 5, 7, 7, 7, 5, 7, 6
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Answer:
Mean x¯¯¯ 5.8888888888889
Median x˜ 6
Mode 7
Range 3
Minimum 4
Maximum 7
Count n 9
Sum 53
Quartiles Quartiles:
Q1 --> 5
Q2 --> 6
Q3 --> 7
Interquartile
Range IQR 2
hope i helped:) can u plz mark me brainlest
Answer:
the mean is 5.88888888889
Step-by-step explanation:
to find the mean, add all the data results together and divide by how many results you have.
for example: 5+4+5+7+7+7+5+7+6= 53
53 divided by 9= 5.88888888889
have a good day
Solve the system of equations x - y = 12 and x + 7y = -20 by combining the
equations.
Answers
Answer:
x=16, y=-4
Step-by-step explanation:
-1(x-y=12)
x+7y=-20
-x+y=-12
x+7y=-20
8y=-32
y=-4
x-4=12
x=16
Answer:
x= 8, y= -4
Step-by-step explanation:
You can subtract one equation by another to eliminate x
(x-y)-(x+7y)=12-(-20)
-8y = 32
y= -4
Substitute y = -4 in the first equation:
x-(-4) = 12
x =8
A survey of 71 families showed that:
40 have a son(s)
45 have a daughter(s)
18 had neither a son nor a daughter.
How many families had ONLY son(s)?
Answers
Answer:
108
Step-by-step explanation:
A music store conducted a survey. It showed that the number of CDs purchased by a shopper decreases with the
number of songs he downloaded. What can we likely say?
Answers
Answer: there is a correlation between a number of songs downloaded. there may or may not be causation. further studies would ave to be done to determine this.
Step-by-step explanation:
Answer:
There is a correlation between number of CDs purchased and number of songs downloaded. There may or may not be causation. Further studies would have to be done to determine this.
Step-by-step explanation:
A music store conducted a survey. It showed that the number of CDs purchased by a shopper decreases with the number of songs she downloaded. What can we likely say?
hellp me for a brainly
Answers
Answer:
25π or 78.5mm²
Step-by-step explanation:
[tex]A=3.14*5^{2} \\ =3.14*25\\ =78.5[/tex]
Answer:
78.5 mm² or answer D.Step-by-step explanation:
The formula for the area of a circle is
A = π*r²
Now we can rewrite with the radius. *Note* I am using 3.14 for pi to make it easier*
A = π*5²
Solve
5² = 25
25 * 3.14 = 78.5
Now since the measurements were done in millimeters, we will add mm to the end.
Also since it is area, we need to add ²
78.5 mm²
Select all the expressions that show a way to decompose 512. A. 3 1/2+2 1/2 B. 3/6+2/6 C. 1 1/2+2 1/2+2 1/2 D. 1 1/2+1 1/2+3 1/2 E.1 1/2+1 1/2+2 1/2+2 1/2
Answers
Answer:
C,D,E
Step-by-step explanation:
I believe this is the correct answer
Plz guys help me please
Answers
Answer:
G(-4,2), H(-3,-4), J(-1,1)
Step-by-step explanation:
The x-values would all become negative.
G(-4,2), H(-3,-4), J(-1,1)
An initial population of 535 quail increases at an annual rate of 25%. Write an exponential function to model the quail population. What will the approximate population be after 5 years?
Answers
Answer: c
Step-by-step explanation:
anyone want to help me?
no but seriously I need to finish this right now
Answers
arrange the following whole numbers in increasing and decreasing order
Answers
Answer:
Increasing Order:
34, 71, 269, 976, 16759, 49753, 796542
Decreasing Order:
796542, 49753, 16759, 976, 269, 71, 34
find area and perimeter. plz help very important
Answers
Answer:
To find the perimeter of a rectangle, add the lengths of the rectangle's four sides. If you have only the width and the height, then you can easily find all four sides (two sides are each equal to the height and the other two sides are equal to the width). Multiply both the height and width by two and add the results.
Step-by-step explanation:
Which of these situations can be modeled by an exponential function?
A) The declining population of a city if 100 people move away every year.
B) A herd of lions whose numbers triple every decade.
C) The amount of money Grant has saved up if he makes $18.50 an hour.
D) Total distance if we drive 75mph for x hours.
Answers
Answer:
B) A herd of lions whose numbers triple every decade.
Step-by-step explanation:
Situations that can be modeled by exponential functions:
A situation can be modeled by exponential functions when the change is a multiplication or a division, not a sum or subtractions.
In this question:
In option A, C and D the measures are a sum or subtractions, as the rate of change is always the same. So it rests option B as the answer, as tripling is multiplying by 3.
What is the value of x?
Answers
Answer:
122
Step-by-step explanation:
122 + 58 = 180
Answer:
x=122°
Step-by-step explanation:
58° and x form a straight angle, which is 180°.
x+58°=180°
x=180°-58°=122°
Find the length of side x in simplest radical form with a rational denominator.
Answers
This is a 30-60-90 right triangle.
In this special triangle, opposite 60 degrees = sqrt{3}. Thus, x = sqrt{3}.
A single 6-sided die is rolled. Which BEST describes the probability of rolling a number 4 or less? 1) A ) impossible B) unlikely likely certains
Answers
Answer:
it is likely because the majority of the outcomes are in your favor
Answer:
A
Step-by-step explanation:
Impossible, did it on usatestprep
please help i don't get this
Answers
Answer:
-4
Step-by-step explanation:
What is the distance between the points (5,7) and (3, 4) on the coordinate
plane?
A. 12.04 units
B. 7.28 units
C. 3.61 units
D. 8.54 units
Answers
Answer:
C) 3.61 units
Step-by-step explanation:
5 - 3 = 2
7 - 4 = 3
distance² = 2² + 3³ = 4 + 9 = 13
distance = √13 = 3.61
Can someone please help me I will mark u brilliant
Answers
Answer:
1 cubic inch
Step-by-step explanation:
For rectangular prism:
[tex]l = 4 \times \frac{1}{2} = 2 \: in \\ \\ w= \frac{1}{2} \: in \\ \\ h = 2 \times \frac{1}{2} = 1 \: in \\ \\ volume \: of \: prism = lbh \\ = 2 \times \frac{1}{2} \times 1 \\ = 1 \: {in}^{3} [/tex]
Answer: The volume is 1 cubic inch.
Step-by-step explanation:
Volume of 1 cube
V= l*w*h
V= 1/2*1/2*1/2
V= 1/8 or 0.125
Volume of Prism
8*1/8= 1
Someone Please help me
Answers
Answer:
B. $104.95
Step-by-step explanation:
$160.45-$55.50=$104.95
Can you guys help me with this, please?
Answers
Answer:
G) y ≥ 1
Step-by-step explanation:
Range is all the y-values seen on the graph.
Since it starts at (0, 1), the lines just keep increasing so:
y ≥ 1
What is happening at A?
Answers
Answer:
the last one