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:
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Answer: c
Step-by-step explanation:
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What is the distance between the points (5,7) and (3, 4) on the coordinate
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D. 8.54 units
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Answer:
C) 3.61 units
Step-by-step explanation:
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distance = √13 = 3.61
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B. $104.95
Step-by-step explanation:
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Answer:
it is likely because the majority of the outcomes are in your favor
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A
Step-by-step explanation:
Impossible, did it on usatestprep
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Answer:
0.0625
Step-by-step explanation:
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Answer:
1/16
Step-by-step explanation:
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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:
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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
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Answer:
-4
Step-by-step explanation:
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B) A herd of lions whose numbers triple every decade.
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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.
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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:
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°
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Answer:
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Step-by-step explanation:
The x-values would all become negative.
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Answer:
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Answer:
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Median x˜ 6
Mode 7
Range 3
Minimum 4
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hope i helped:) can u plz mark me brainlest
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the mean is 5.88888888889
Step-by-step explanation:
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have a good day
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
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hours ( NO LINKS , LINK WILL GET YOU BANNED )
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Answer:
10 hours (I am not positive)
Step-by-step explanation:
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Step-by-step explanation:
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Answer:
Step-by-step explanation:
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78.5 mm² or answer D.Step-by-step explanation:
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A = π*5²
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5² = 25
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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?
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Answer:
7 and 3/5
Step-by-step explanation:
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Answer:
I would say A
Step-by-step explanation:
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A survey of 71 families showed that:
40 have a son(s)
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Answer:
108
Step-by-step explanation:
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Answer:
x=16, y=-4
Step-by-step explanation:
-1(x-y=12)
x+7y=-20
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x+7y=-20
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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)
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Substitute y = -4 in the first equation:
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Answer:
1 cubic inch
Step-by-step explanation:
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Answer: The volume is 1 cubic inch.
Step-by-step explanation:
Volume of 1 cube
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Answer:
I think it is 2 one
Step-by-step explanation:
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Answer:
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Answer:
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Step-by-step explanation: