take the van der pol equation . (a) set and . convert the above second order differential equation to a two dimensional system of differential equations:
Answers
The van der Pol equation which is a second-order differential equation is given by
d²x/dt² - μ(1 - x²)dx/dt + x = 0
Here we are asked to convert it to a two-dimensional system.
Here we need to set y = dx/dt, where y represents the system's velocity.
Hence we will rewrite it as
d²x/dt² = μ(1 - x²)y + x
Now if we set the derivatives of x and y with respect to time to be equal to different variables we get
dx/dt = y
dy/dt = μ(1 - x²)y + x
Hence we get the above systems of equations as the 2-dimensional representation of the Van der Pol equation where x and y represent the system's position and velocity respectively.
If we set μ = 1 and x = 0, then we get
dx/dt = y
dy/dt = y
Hence we get the system of differential equations representing the behavior of the van der Pol equation with μ = 1 and x = 0 in two dimensions.
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Related Questions
Please any math experts helps thank you
Answers
Answer:
\(\frac{t^2-16}{t^2-8t+16}\)
We can factorise the numerator which the difference of squares formula:
\(x^2-y^2=(x+y)(x-y)\)
---------------------------------
\(\frac{t^2-4^2}{t^2-8t+16} =\frac{(t+4)(t-4)}{t^2-8t+16}\)
Next, factorise the denominator:
\(\frac{t^2-4^2}{t^2-8t+16} =\frac{(t+4)(t-4)}{(t-4)^2}\)
\(\frac{(t+4)(t-4)}{(t-4)(t-4)}\)
Cancel out the common factor of (t-4):
\(\frac{t+4}{t-4}\)
A certain drug is made from only two ingredients: compound A and compound B. There are 7 millimeters of compound A used for every 5 millimeters of compound B. If a chemist wants to make 900 millimeters of the drug, how many millimeters of compound A are needed?
Answers
525 millimeters of compound A are needed.
What is a mixture?
Combining two or more substances and identifying a property of the ingredients or the resulting combination is the focus of mixture problems. For instance, we could need to figure out how much water to add to a saline solution to make it more diluted, or we might need to know how much of an orange juice bottle is concentrated.
Here, we have
Given: A certain drug is made from only two ingredients: compound A and compound B. There are 7 millimeters of compound A used for every 5 millimeters of compound B. If a chemist wants to make 900 millimeters of the drug.
Given the following ratio
A : B = 7 : 5
Mixture = 900 millimeters
To calculate the amount of compound A needed, we make use of the following formula:
A = A/(A+B)×mixture
A = 7/(7+5)×900
A = 525 millimeters.
Hence, 525 millimeters of compound A are needed.
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A loan is being paid off by payments of 1,000, 2,000, ..., 10,000 at the end of years 1, 2, ..., 10.
The effective annual interest rate is 18%.
Determine the amount of interest in the 7th payment.
Answers
Therefore, the interest portion of the seventh payment is:7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7 - 7,000.
We have the following payments and their corresponding times of payment:At the end of year 1: $1,000At the end of year 2: $2,000At the end of year 3: $3,000At the end of year 4: $4,000At the end of year 5: $5,000At the end of year 6: $6,000At the end of year 7: $7,000
At the end of year 8: $8,000At the end of year 9: $9,000At the end of year 10: $10,000The present value of these payments is:PMT x [(1 - (1 + r)-n) / r]where PMT is the payment, r is the interest rate per year, and n is the number of years till payment.
For the first payment (end of year 1), the present value is:1,000 x [(1 - (1 + r)-1) / r]which equals
1,000 x (1 - 1 / (1 + r)) / r = 1,000 x ((1 + r - 1) / r) = 1,000
For the second payment (end of year 2), the present value is:2,000 x [(1 - (1 + r)-2) / r]which equals 2,000 x (1 - 1 / (1 + r)2) / r = 2,000 x ((1 + r - 1 / (1 + r)2) / r) = 2,000 x (1 + r) / r2
For the seventh payment (end of year 7), the present value is:
7,000 x [(1 - (1 + r)-7) / r]
which equals
7,000 x (1 - 1 / (1 + r)7) / r = 7,000 x ((1 + r - 1 / (1 + r)7) / r) = 7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7
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E and F are mutually exclusive events. P(E)=0.3; P(F) =0.2. Find P(E | F)
Answers
Answer:
0
Step-by-step explanation:
P(E|F) = P(E and F)/P(F) = 0/0.2
Events that are mutually exclusive exclude each other. That means if one
occurs, the other is excluded. That means if one occurs, the other cannot
occur.
So that tells us that the probability of them both happening is impossible,
which mean P(E and F) = 0
In chemistry class, Bob recorded the volume of a liquid as 12.2 mL. The actual volume was 11.8 mL. Use
the formula to find percent error of Bob's measurement to the nearest tenth of a percent.
Percent Error =
Experimental Value - Actual Value]
Actual Value
The percent error of Bob's measurement is
96.
x 100
Answers
Answer:
The percent error to the nearest tenth is:
3.6%
Step-by-step explanation:
In chemistry class, Bob recorded the volume of a liquid as 13.2 mL. The actual volume was 13.7 mL.
HELP!!!!!!!!!!!!!!!!!!
Answers
Answer:
D 0.89275
Step-by-step explanation:
27. Write a linear equation in slope-intercept form. An auto repair shop
charges $ 40 plus $ 20 per hour.
Help plz
Answers
Answer:
Put the 4 at the beggining at line then always at +20 to it
9(40÷5+9)+15-9
I need help solving this problem
Answers
Answer:
The answer to the problem is 159
2) Evaluate each expression if x=3 and y=-1
a) 3y/2 -2x
Answers
Answer:
-15/2, -7 1/2, or -7.5 (All are equivalent)
Step-by-step explanation:
3(-1) / 2 - 2(3) =
-3/2 - 6 =
-15/2, -7 1/2, or -7.5
Find the missing angle.
Answers
Answer:
Your answer is K= 60
I hope it's helps you
Trapezoid pqrs has vertices p(0, 0), q(0, 4), r(6, 4), and s(12, 0). What is the length of the midsegment?.
Answers
The midsegment of the trapezoid PQRS, which has sides P(0, 0), Q(0, 4), R(6, 4), & S(12, 0), is 11.07 units long.
What is the most accurate way to define a trapezoid?A trapezoid or ellipse is an open, flat shape having three full sides and one pair of parallel sides. The equivalent sides of a trapezium are refer to as the bases, and the non-parallel sides have been known as the legs.
Half of the distances of the two adjacent sides, PQ and RS, make the total width of the trapezoid's middle section.
The vertices' points are designated as P(0, 0), Q(0, 4), R(6, 4), or S. (12, 0).
The sides PQ and RS's lengths are indicated as -.
The line segment PQ = √(x2 - x1)² + (y2 - y1)²
PQ = √(0 - 0)² + (4 - 0)²
PQ = √0² + (4)²
PQ = √0 + 16
PQ = √16
PQ = 4 units
The line segment RS = √(x2 - x1)² + (y2 - y1)²
RS = √(12 - 6)² + (0 - 4)²
RS = √(6)² + (-4)²
RS = √36 + 16
RS = √50
RS = 5√2 units
Adding the lengths of PQ & RS will reveal the mid section.
So, the equation will be -
Midsegment = PQ + RS
Midsegment = 4 + 5√2
Midsegment = 11.07 units
Midsegment length is 11.07 units as a result.
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Write the following numbers in words
6 500 000
Answers
Answer:
six million five hundred thousand
A vehicle is running at a constant speed of 60 miles per hour on a highway. When it started, it had 10 gallons of gasoline in its cylinder. The vehicle travels 30 miles on each gallon of gasoline. Ignore the initial acceleration at the start and final deceleration when the vehicle runs out of gasoline and comes to halt. The amount of gasoline in the vehicle can be modeled as a linear function G(t)=10−2t, where t is time, in hours. How much gas is consumed in the first 3 hours?
1, 3 gallons
2, 4 gallons
3, 6 gallons
7, gallons
Answers
The quantity of gas that was consumed in the first 3 hours is; 6 gallons.
What quantity of gas is used in the first 3 hours?As evident in the task content;
Speed refers to the magnitude of the velocity or the rate distance is traversed in a given time.
the speed of the vehicle = 60 miles per hour
the quantity of gasoline = 10 gallons.
Since G (t) = 10 - 2t
When t = 3
G (3) = 10 - 2(3)
G(3) = 4 gallons
Ultimately, the quantity of gas consumed in the first 3 hours is;
10 gallons - 4 gallons
= 6 gallons.
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y = 3x + 4, what is y when x is 1, 2, and 3?
Answers
Answer:
When x is 1, y=7
When x is 2, y=10
When x is 3, y= 13
Step-by-step explanation: Plug in each number for x and solve
Answer:
If x=1, y=7
If x=2, y=10
If x=3, y=13
Step-by-step explanation:
For every equation substitute x in y = 3x + 4, with the value you want.
For example the first one says when x=1, so simply substitute x with 1 in y = 3x + 4.
So it'll look something like this:
y = 3(1) + 4.
Simply solve the equation from there, and you'll get y=7, and we know that x is already equal to 1.
So if x=1, then y=7
Let f(x) = -5x – 1 and g(x)=x2- 3.Find (fog)(1).Then (fog)(1)= (Simplify your answer.)
Answers
Let f(x) = -5x – 1 and g(x)=x2- 3.
Find (fog)(1).
Remember that
(fog)(x)=f(g(x))
so
f(g(x))=-5(x^2-3)-1
(fog)(1).=f(g(1))=-5(1^2-3)-1=-5(-2)-1=9
therefore
f(g(x)
what is one-fifth as a percentage?
Answers
Answer: 20%
Step-by-step explanation:
1=100%
1/5=
100%/5=20%
Answer: 20 percent
Step-by-step explanation: how you college level and not know this one
Which list represents integers ordered from least to greatest?
A 4,-7, -6, 10
B 4, -5, -6, 10
C -7, -6, 4, 10
D-6, 4, 5, 10
OA
B
OC
D
Answers
It’s C
Why:
Because i’m smart duh
Answer:
C,-7,-6,4,10
Step-by-step explanation:
I guessed and that is all I did
y/3 = 5
X - 32 = 74
X + 13 = 65
x/2 = 3
x/4 = 1
3x = 12
Answers
X=104
X=52
X=6
X=4
X=4
If the mean GPA among students is 3.25 with a standard deviation of 0.75, what is the probability that a random sample of 300 students will have a mean GPA greater than 3.30
Answers
Answer:
The value is \(P(X > 3.30) = 0.12405\)
Step-by-step explanation:
From the question we are told that
The mean GPA is \(\mu = 3.25\)
The standard deviation is \(\sigma = 0.75\)
The sample size is n = 300
Generally the standard error of mean is mathematically represented as
\(\sigma_{\= x} = \frac{\sigma }{\sqrt{n} }\)
=> \(\sigma_{\= x} = \frac{0.75}{\sqrt{300} }\)
=> \(\sigma_{\= x} = 0.0433\)
Generally the probability that a random sample of 300 students will have a mean GPA greater than 3.30 is mathematically represented as
\(P(X > 3.30) = P(\frac{X - \mu}{\sigma_{\= x}} > \frac{3.30 -3.25}{ 0.0433} )\)
\(\frac{\= X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ \= X )\)
\(P(X > 3.30) = P(Z> 1.155 )\)
From the z table the probability of (Z > 1.155 ) is
\(P(Z> 1.155 ) = 0.12405\)
\(P(X > 3.30) = 0.12405\)
If the function y=sin(x) is transformed to y = sin(2x), how does the graph change?
It is stretched vertically.
It is compressed vertically.
It is stretched horizontally.
It is compressed horizontally..
Answers
Step-by-step explanation:
The transformation y = sin(2x) affects the graph of y = sin(x) by compressing it horizontally.
The function y = sin(2x) has a coefficient of 2 in front of the x variable. This means that for every x value in the original function, the transformed function will have half the x value.
To see the effect of this transformation, let's compare the graphs of y = sin(x) and y = sin(2x) by plotting some points:
For y = sin(x):
x = 0, y = 0
x = π/2, y = 1
x = π, y = 0
x = 3π/2, y = -1
x = 2π, y = 0
For y = sin(2x):
x = 0, y = 0
x = π/2, y = 0
x = π, y = 0
x = 3π/2, y = 0
x = 2π, y = 0
As you can see, the y-values of the transformed function remain the same as the original function at every x-value, while the x-values of the transformed function are compressed by a factor of 2. This means that the graph of y = sin(2x) appears narrower or more "squeezed" horizontally compared to y = sin(x).
Therefore, the correct statement is: It is compressed horizontally.
cuanto es 1 mas 1? dende ecuaciones y detalles es para mi examen virtual please
Answers
Answer:
2
Step-by-step explanation:
1+1=2
valuate −8 + 10 × 4 ÷ (−2). Question 25 options: −4 −28 −3 −20
Answers
Answer: its -28
Step-by-step explanation:
i dont know i used a app
Which three lengths CANNOT be the lengths of the sides of a triangle?
A: 16 m, 5 m, 11 m
B: 23 m, 20 m, 15 m
C: 11 m, 15 m, 11 m
D: 8 m, 7 m, 12 m
Answers
Answer:
I think B and C cannot be lengths of the sides of a triangle
Can someone please help me with 13-16 it’s urgent I’m begging
Answers
Answer:
13.
100(256+347)=?
14.
100(64-36)=?
15.
Distributive and associative
example:
5( 2 + 3 ) + 4 =
16.
B
Step-by-step explanation:
What is the constant rate of change of the
function represented in the table?
Answers
Answer: it is -4 or c
Step-by-step explanation:
у-2=-3 (x+6)
Use the point slope form to identify a point the line passes through and the slope of the line.
Answers
Answer:
point = ( -6, 2)
slope = -3
Step-by-step explanation:
point slope formula;
y - y1 = m ( x - x1) ,
where m= slope , (x1, y1) = the coordinates of a point
y - 2 = -3 ( x + 6)
a point the line passes through = (-6 , 2)
slope of the line = -3
A bag contains nine balls labeled 1 through 9. One ball will be randomly picked. What is the probability of picking a multiple of 3?
Answers
Answer: 3/9 or 1/3
Step-by-step explanation:
3, 6 and 9 are all multiples of 3 equal or below 9.
Find the value of y.
Answers
The value of y is 4√3
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.
Also , the ratio of corresponding sides of similar triangles are equal.
There are two triangles that are similar
Therefore;
y /16 = 4/y
y² = 48
y = √48
y = √16 × √ 3
y = 4√3
Therefore, the value of y is 4√3
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The whole number m is a term in an arithmetic sequence with common difference 2. Show that the sum of the term m and the next two terms is a multiple of 3, no matter what the value of m.
Answers
Answer:
S
ThenSn=n(a1+an)2Sn=n(a1 + an)2 , where nn is the number of terms, a1a1 is the first term and anan is the last term. The sum of the first nn terms of an arithmetic sequence is called an arithmetic series .
Step-by-step explanation:
Solve for x to make A||B
Answers
Answer: x = 50
Step-by-step explanation:
In the given image, the alternate interior angles are equal. Therefore, 80 + x = 180 - 50 (since straight angles measure 180 degrees). Simplifying this equation, we get 130 + x = 180, which gives us x = 50 degrees. Thus, A||B when x = 50 degrees.