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
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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:
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anyone want to help me?
no but seriously I need to finish this right now
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3.Construct a line perpendicular to the line given through the point P at the right
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Answer:
Step-by-step explanation:
Write the equation in standard form. Y=x+1
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Find the length of side x in simplest radical form with a rational denominator.
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This is a 30-60-90 right triangle.
In this special triangle, opposite 60 degrees = sqrt{3}. Thus, x = sqrt{3}.
Can someone please help me I will mark u brilliant
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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
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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
Plz guys help me please
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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)
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
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
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Answer:
C,D,E
Step-by-step explanation:
I believe this is the correct answer
What is the measure of the missing angle
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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°
what is 1/2 x 1/2 x 1/2 x 1/2
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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.
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
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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........................
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Answer:
I think it is 2 one
Step-by-step explanation:
What is happening at A?
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Answer:
the last one
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 )
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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)
please help i don't get this
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Answer:
-4
Step-by-step explanation:
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)?
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Answer:
108
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
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°
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!
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
find area and perimeter. plz help very important
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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.
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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 distance between the points (5,7) and (3, 4) on the coordinate
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A. 12.04 units
B. 7.28 units
C. 3.61 units
D. 8.54 units
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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
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Answer:
B. $104.95
Step-by-step explanation:
$160.45-$55.50=$104.95
arrange the following whole numbers in increasing and decreasing order
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Answer:
Increasing Order:
34, 71, 269, 976, 16759, 49753, 796542
Decreasing Order:
796542, 49753, 16759, 976, 269, 71, 34
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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:
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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?
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Answer:
7 and 3/5
Step-by-step explanation:
3 and 4/5 times 2 is 7 and 3/5
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Answer: c
Step-by-step explanation:
A music store conducted a survey. It showed that the number of CDs purchased by a shopper decreases with the
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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?