HW4: Problem 8 (1 point) Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: = g" + 1g = sin(Tt)0
Answers
To solve the given initial value problem using the Laplace transform, take the transform of the equation, rearrange for G(s), find the inverse Laplace transform of G(s)/s, and solve for y(t) using partial fraction decomposition and known transforms.
To solve the given initial value problem using the Laplace transform, we will follow these steps:
Step 1: Take the Laplace transform of the differential equation:
Applying the Laplace transform to the equation g'' + g = sin(Tt), we get:
s^2G(s) - sg(0) - g'(0) + G(s) = sin(Ts) / (s^2 + 1).
Step 2: Rearrange the equation to solve for G(s):
Combining like terms, we have:
G(s) = [sin(Ts) - s + (s^2 + 1)(g(0) + s)] / (s^2 + 1)^2.
Step 3: Take the inverse Laplace transform to find the solution y(t):
To find y(t), we need to compute the inverse Laplace transform of G(s) / s. This can be done by using partial fraction decomposition and looking up the inverse Laplace transform in a table or using known transforms.
Step 4: Solve for y(t):
Performing partial fraction decomposition on G(s) / s, we can write it as:
G(s) / s = A / s + B / (s^2 + 1) + C / (s^2 + 1)^2.
Now we need to find the values of A, B, and C by equating the numerators:
[sin(Ts) - s + (s^2 + 1)(g(0) + s)] = A(s^2 + 1)^2 + Bs(s^2 + 1) + C(s).
Expanding the right side and comparing coefficients, we can determine the values of A, B, and C.
Once we have A, B, and C, we can compute the inverse Laplace transform of G(s) / s using the known transforms from the Laplace transform table.
Finally, the solution y(t) will be the inverse Laplace transform of G(s) / s.
Note: The exact form of the solution y(t) will depend on the values of A, B, and C, which are determined by the initial conditions g(0) and g'(0).
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Related Questions
hii I just wasn't sure about how to answer this so could someone help?
There are 2 bran, 3 blueberry and 4 corn muffins in a bag. If Wesley randomly selects two muffins, what is the probability that he selects a corn muffin, eats it, and then selects a bran muffin?
Answers
Answer:
1/2
Step-by-step explanation:
Answer:
1/9
Step-by-step explanation:
BRAINLIEST FOR FIRST CORRECT ANSWER
Answers
Answer:
-1.8
Step-by-step explanation:
The function changes from increasing to decreasing (which is when there is a local maximum) at around where x = -1.8.
Utility from Oranges and Star Fruit. Oranges cost $2 per pound and star fruit costs $5 per pound. Calvin has $26 to spend. If Calvin buys 4 pounds of star fruit and 3 pounds of oranges, how much is his total utility
Answers
The expenditure on oranges is 3 pounds × $2 per pound = $6. Hence, the total utility from star fruit and oranges combined can be determined by summing up the individual utilities.
In total, Calvin's utility from purchasing 4 pounds of star fruit and 3 pounds of oranges can be calculated. To do so, we need to consider the utility derived from each pound of fruit and then sum up the individual utilities. Oranges cost $2 per pound, while star fruit costs $5 per pound. Given that Calvin buys 4 pounds of star fruit and 3 pounds of oranges, his total expenditure would be $26. Now, let's calculate the utility.
For star fruit, the cost is $5 per pound, and Calvin buys 4 pounds. Therefore, the expenditure on star fruit is 4 pounds × $5 per pound = $20. For oranges, the cost is $2 per pound, and Calvin buys 3 pounds. Thus, the expenditure on oranges is 3 pounds × $2 per pound = $6. Hence, the total utility from star fruit and oranges combined can be determined by summing up the individual utilities.
To calculate the utility, we need to consider the subjective satisfaction or enjoyment that Calvin receives from consuming each pound of fruit. However, the problem does not provide any specific information about the utility derived from oranges or star fruit. Therefore, without additional information about the specific utility values associated with consuming these fruits, it is not possible to determine the exact total utility.
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A tank contains 350 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Find the number
Answers
The number A(t) of grams of salt in the tank at time is: \(200 - 180e^{-1/40t}\)
How to determine the number of grams of saltTo determine the number of grams of salt in the tank at time t, we would apply the equation of state to have:
dA/dt = R(in) - R(out)
For R(out), we would have:
R(in) = 5g/min
R (out) = A/40 g/min
We would substitute these in the equation and apply a differential limit where A = 20 and t = 0
So,
20 = 200 + C
c = -180
Thus, the equation that expresses the rate = \(200 - 180e ^{-1/40t}\)
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Complete Question:
1. A tank contains 200 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.
A(t) = ____ g
What’s 5 more than twice a number
Answers
Answer:
33 is the correct answer
Answer:
2x+5
Step-by-step explanation:
if the number is x
∴ 5 more than twice a number is
ll ll
V V
+5 *2
So, 2*x+5
What is the best description of thermal energy?(1 point) Responses Thermal energy is the kinetic energy contained in an object or substance due to the movement of its atoms and/or molecules. Thermal energy is the kinetic energy contained in an object or substance due to the movement of its atoms and/or molecules. Thermal energy is a measure of an object or substance’s heat. Thermal energy is a measure of an object or substance’s heat. Thermal energy is kinetic energy. Thermal energy is kinetic energy. Thermal energy is the energy stored in an object’s chemical bonds. Thermal energy is the energy stored in an object’s chemical bonds.
Answers
Answer:
A. Thermal energy is the kinetic energy contained in an object or substance due to the movement of its atoms and/or molecules.
Explanation:
Just took the Quick Check :)
The best description of thermal energy is that it is the kinetic energy contained in an object or substance due to the movement of its atoms and/or molecules.
What is thermal energy?Thermal energy is the kinetic energy contained in an object or substance due to the movement of its atoms and/or molecules.
It is a type of internal energy, which is the energy possessed by a system due to the movement and interactions of its constituent particles.
We have,
Thermal energy is a measure of an object or substance’s heat:
While thermal energy and heat are related, they are not exactly the same thing.
Heat is the transfer of thermal energy between objects or substances due to a temperature difference.
Thermal energy, on the other hand, is the energy contained in an object or substance due to the movement of its particles.
Thermal energy is kinetic energy:
While thermal energy is related to kinetic energy, they are not exactly the same thing.
Kinetic energy is the energy of motion, while thermal energy specifically refers to the kinetic energy of an object's particles.
Thermal energy is the energy stored in an object’s chemical bonds:
While chemical bonds do store energy, this is not the best description of thermal energy.
Thermal energy specifically refers to the energy stored in the movement of an object's particles.
Therefore,
The best description of thermal energy is that it is the kinetic energy contained in an object or substance due to the movement of its atoms and/or molecules.
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Please help me with this Math question its the last one i need please
Answers
Answer:
7 dollars
Step-by-step explanation:
To solve, use this equation:
34.20 - (16 x 1.70) = x
First do 16 x 1.70
This equals 27.2
34.20 - 27.2 = x
Now subtract
34.20 - 27.20 = $7
The student card $7
What is an example of slope-intercept form?.
Answers
Answer:
y = 3x + 1
Step-by-step explanation:
The equation for slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.
Jessica and her best friend found some money under the couch. they split the money evenly, each getting $16.32. how much money did they find?
Answers
Based on the fact that Jessica and her best friend split the money and were able to get $16.32, the total amount that they found was $32.64
How much did Jessica and her friend find?The fact that they split the money evenly means that they split it in half which each person getting the same amount.
This means that the total amount they found was twice the amount that Jessica and her best friend got.
The total amount found is therefore:
= Jessica's share + Best friend's share
= 16.32 + 16.32
= $32.64
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Miko bought a apples and b bananas. Each apple was $2 and each banana was $3. How much money did Miko spent? Write your answer in algebra expression in terms of a and b
Answers
Answer:
3b and 2a
equation - y = 3b + 2a
Step-by-step explanation:
It's 3 dollars for a banana so it'd be 3b and it's 2 for an apple so it's 2a.
I hope this helps!
Answer:
He spent 2a+3b
for
a is apples quantity
b is bananas quantity
Que numero es mayor que -5/4
Answers
Answer:
4 is greater than -5
Step-by-step explanation:
positive are greater than negative
A competency test has scores with a mean of 82 and a standard deviation of 2. A histogram of the data shows that the distribution is normal. Between what two values do about 99.7% of the values lie? SHOW YOUR WORK
(statistics)
Answers
Using the Empirical Rule, it is found that 99.7% of the values lie between 76 and 88.
What is the Empirical Rule?
It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, we have that:
The mean is of 82.The standard deviation is of 2.99.7% of the values lie within 3 standard deviations of the mean, hence between:
\(82 - 3(2) = 76\)
\(82 + 3(2) = 88\)
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9x/4y=1 and y= 18, what is the value of x
Answers
Answer:
x = 8
Step-by-step explanation:
\(\frac{9x}{4y}=1\)
\(\frac{9x}{4*18} =1\)
9x = 72
x = 8
Help! Will mark brainiest sorry its pretty blurry
Answers
Answer:
As temp. increases, sales increse
Step-by-step explanation:
a- b for
for a= (-7) and b = 30
Answers
Answer:
-37
Step-by-step explanation:
-7-30
=-37
You are adding the negatives therefore, you will get a larger number of negatives.
you would have to plug the numbers given.
“A” would now be (-7) “B” would now be (30) = (-7)-30 = -37
reason it equals a negative is because a positive & a negative = a negative
Cos theta = x/rTan theta = y/xWhat is the angle of view of a sniper who is on top of a building that is 20 meters high and has a slope of 20 meters?
Answers
Now we can use the formula for cos (theta) to find the angle of view:
cos(theta) = adjacent/hypotenuse = 20/28.28
theta = cos^-1(20/28.28) = 45 degrees
So the angle of view of the sniper is 45 degrees.
To find the angle of view for the sniper on top of a building, we can use the trigonometric functions you provided. In this case, we know the height of the building (20 meters) and the horizontal distance (also 20 meters).
Let's denote the height as 'y' and the horizontal distance as 'x'. Given the information, y = 20 meters and x = 20 meters.
We can use the tangent function (tan theta) to find the angle:
Tan theta = y/x
Tan theta = 20/20 = 1
Now, we need to find the angle (theta) by taking the inverse tangent (arctan) of the result:
theta = arctan(1)
Using a calculator or conversion table, we find that:
cos(theta) = adjacent/hypotenuse = 20/28.28
theta = cos^-1(20/28.28) = 45 degrees
theta ≈ 45°
So, the angle of view for the sniper on top of the 20-meter high building with a 20-meter slope is approximately 45 degrees.
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Determine the initial and final values of the signals for each of the following Laplace transforms: (a) X
1
(s)=
s(s+1)(s+2)
6e
−3s
(b) X
2
( s)=
2 s
3
+10 s+10
s
2
+5 s+6
7. Consider an LTI system with unit-impulse response h(t)=t
2
e
−2t
sin(3t)u(t) Find the Laplace transform of the output of this system if the input signal is x(t)=∫
0
t
e
−at
′
dt
′
Answers
(a) The Initial value of X1(s): 0 Final value of X1(s): 0 and (b) Initial value of X2(s): Infinity , Final value of X2(s): 0
(a) To find the initial and final values of X1(s), we can use the final value theorem and the initial value theorem.
Initial value: The initial value of X1(s) is given by lim(s->∞) sX1(s). To find this, we can first factorize X1(s) as follows:
X1(s) = (s(s+1)(s+2))/6 * 6e^(-3s)
Taking the limit as s approaches infinity, we have:
lim(s->∞) sX1(s) = lim(s->∞) (s(s+1)(s+2))/6 * 6e^(-3s)
= lim(s->∞) (s² + 3s + 2) * e^(-3s)
= (0 + 0 + 2) * e^(-3 * ∞)
= 2 * 0
= 0
Therefore, the initial value of X1(s) is 0.
Final value: The final value of X1(s) is given by lim(s->0) sX1(s). Again, we can factorize X1(s) as follows:
X1(s) = (s(s+1)(s+2))/6 * 6e^(-3s)
Taking the limit as s approaches 0, we have:
lim(s->0) sX1(s) = lim(s->0) (s(s+1)(s+2))/6 * 6e^(-3s)
= lim(s->0) s³+ 3s² + 2s * e^(-3s)
= 0 + 0 + 0 * e⁰
= 0
Therefore, the final value of X1(s) is 0.
(b) To find the initial and final values of X2(s), we can again use the final value theorem and the initial value theorem.
Initial value: The initial value of X2(s) is given by lim(s->∞) sX2(s). We can express X2(s) as follows:
X2(s) = (2s^3 + 10s² + 10s) / (s² + 5s + 6)
Taking the limit as s approaches infinity, we have:
lim(s->∞) sX2(s) = lim(s->∞) (2s³+ 10s²+ 10s) / (s² + 5s + 6)
= ∞ / ∞ (indeterminate form)
To evaluate this indeterminate form, we can apply L'Hopital's rule by taking the derivative of the numerator and denominator with respect to s:
lim(s->∞) sX2(s) = lim(s->∞) (6s² + 20s + 10) / (2s + 5)
= ∞ / ∞ (still indeterminate form)
Again, we can apply L'Hopital's rule:
lim(s->∞) sX2(s) = lim(s->∞) (12s + 20) / 2
= ∞ / 2
= ∞
Therefore, the initial value of X2(s) is infinity.
Final value: The final value of X2(s) is given by lim(s->0) sX2(s). Using the same expression for X2(s), we have:
lim(s->0) sX2(s) = lim(s->0) (2s³ + 10s² + 10s) / (s² + 5s + 6)
= 0 / 6
= 0
Therefore, the final value of X2(s) is 0.
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If U = 6 feet, V = 8 feet, W = 4 feet, X = 6 feet, Y = 14 feet, and Z = 3 feet, what is the area of the object?
Answers
6983245455445
it's correct
Members of a softball team raised $2089.50 to go to a tournament. They rented a bus for $1087.50 and budgeted $41.75 per player for meals. Write and solve an equation which can be used to determine x, the number of players the team can bring to the tournament.
Answers
The number of players the team can bring to the tournament would be = 24 players
What is softball game?The softball game is the type of game that involves two teams which is made up of 9. - 10 players.
The total amount of money raised by a softball team=
$2089.50
The amount of money spent on rented bus = $1087.50
The amount left after rent deductions= 2,089.50 - 1,087.50 = 1,002
The amount budgeted for meals for each player= $41.75
The number of players that would be brought for tournament= 1,002/41.75
= 24 players.
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1. Ashley invested $210 in a saving account with an 8%
interest rate. How much interest will she earn after 7
years?
What is the interest rate
Answers
Answer:
The intrest rate is 8% and after 7 years she will have made 149.90 in total intrest.
Omar bought a pastry from the bakery near his apartment. The pastry was $2.80, and he paid 5% sales tax. How much did Omar pay in all?
Answers
Answer:2.94
Step-by-step explanation:2.80*1.05=2.94
I HATE MYMATHS HELP ME PLSSSS
Answers
Answer:
801 metres
Step-by-step explanation:
To find the distance we must firstly find the circumference of the wheel;
⇒ \(C = \pi d = \pi (85) = 85\pi cm\)
If the wheel made 300 full revolutions, then we multiply the circumference by 300;
⇒ \(d = 300(85\pi ) = 25500\pi\)
We can now convert this to decimal to give our distance cm. Therefore we must then divide our answer by 100 to get the distance in metres;
⇒ \(d = 25500\pi = 80111cm = 801m\)
Hope this helps! :D
Giving brainlist to who answeres this!
Answers
Answer:
Pretty sure its 20
Step-by-step explanation:
I just did the math
Answer:
5 i think
Step-by-step explanation:
§(*￣▽￣*)§§(*￣▽￣*)§§(*￣▽￣*)§§(*￣▽￣*)§§(*￣▽￣*)§(∪.∪ )...zzz(∪.∪ )...zzz(∪.∪ )...zzz(∪.∪ )...zzz
Is 25% greater than, less
than, or equal to 0.3?
Answers
=========================================================
Explanation:
To convert from a percent to a decimal, move the decimal point over 2 spots to the left
25% = 25.0% converts to 0.25
Think of 0.3 as 0.30
Comparing 0.25 and 0.30, we see that 0.25 is smaller. This is because 25 is smaller than 30.
---------------------
Put another way:
0.3 = 0.30 = 30%
We can see that 25% is smaller than 30%
---------------------
Whichever method you prefer, 25% is smaller than 0.3
Answer:
Less than
Step-by-step explanation:
Converting % to decimal :
Divide % value by 100%Solving :
25%/100%25/1001/40.25Comparing :
Clearly, 0.25 < 0.3Hence, 25% is less than 0.3Carson buys eggs and lemons at the store. he pays a total of $39.62. he pays $6.74 for the eggs. he buys 8 bags of lemons that each cost the same amount.
Answers
The algebraic equation is used to determine the costs of each bag of lemons is 8x = $39.62 - $6.74
According to the question,
Cost of 1 bag of lemons = $x
Cost of 8 bags of lemons = 8*x = 8x
Cost of 8 bags of lemons = Total cost - cost of the egg
8x = $39.62 - $6.74
Hence, the algebraic equation is used to determine the costs of each bag of lemons is 8x = $39.62 - $6.74.
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Evaluate the expression for d = 1.
87d − 91 =
Answers
87-91
Therefore 87-91=-4
9th grade maths solution
Answers
The value of y that satisfies the equation is 3.35 or - 5.35.
What is the value of y?The value of y that satisfies the equation is calculated as follows;
The given equation;
√ (y + 3) + √ ( y - 2) = 5
Square both sides of the equations as follows;
[√ (y + 3) + √ ( y - 2) ]² = 5²
y + 3 + 2(y + 3)(y - 2) + y - 2 = 25
2y + 1 + 2(y² + y - 6) = 25
2y + 1 + 2y² + 2y - 12 = 25
Collect similar terms and simplify the equation;
2y² + 4y - 36 = 0
divide through by 2;
y² + 2y - 18 = 0
Solve the quadratic equation using formula method as follows;
a = 1, b = 2, c = -18
y = 3.35 or - 5.35
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HELP PLEASE—lindo pours 5 gallons of water into 3 buckets. He pours the same amount into each bucket. How much water is in each bucket?
Answers
Answer:
5/3 or 1 2/3
Step-by-step explanation:
Simply do 5 / 3 to get your answer. You can either say it is 5/3 or 1 2/3.
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Which Point of Concurrency is NOT always inside a triangle?* A:Centroid
B:Incenter
C:Circumcenter
Answers
explanation; the circumcenter is something that is not always inside of a triangle, unlike the centroid, which is always found. the point of concurrency of the angle bisectors defines the incenter, which leads me to believe that the answer is C.
Circumcenter Point of Concurrency is NOT always inside a triangle. Hence, option (C) is correct.
What are Centroid, Incenter and Circumcenter of triangle?The centroid of a triangle is the location where the triangle's three medians intersect. It can alternatively be described as the location where the three medians come together. A line connecting a side's midpoint and the triangle's opposite vertex is called the median.
The intersection of the three interior angle bisectors of a triangle forms the triangle's incenter. Due to the junction point of the central axis being the center of the inscribed circle of the triangle, this point is equally spaced from each of its sides.
The intersection of all of the triangle's sides' perpendicular bisectors—that is, the lines that are perpendicular to each side's midpoint—indicates the location of the triangle's circumcenter.
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we need to calculate a) mean b) variance c) standard
deviation
(2) clarining cinif requang, For the frequency: table on the left, compete (as the main (8), 4) the variance [5] and w the standard deviation 8]. 2 3 6 9. 7 12 4 Sum=20
Answers
The mean is ≈ 8.793. The variance is approximately 9.641. The standard deviation is approximately 2.964
Given frequency table:
Value: 2 3 6 9 12
Frequency: 3 6 9 7 4
a) Mean:
\(\[\text{{Mean}} = \frac{{\text{{Sum of (Value * Frequency)}}}}{{\text{{Total number of observations}}}}\]\[\text{{Mean}} = \frac{{(2 \times 3) + (3 \times 6) + (6 \times 9) + (9 \times 7) + (12 \times 4)}}{{3 + 6 + 9 + 7 + 4}}\]\[\text{{Mean}} = \frac{{189}}{{29}}\]\)
≈ 8.793
b) Variance:\(\[\text{{Variance}} = \frac{{(3 \times (2 - \text{{Mean}})^2) + (6 \times (3 - \text{{Mean}})^2) + (9 \times (6 - \text{{Mean}})^2) + (7 \times (9 - \text{{Mean}})^2) + (4 \times (12 - \text{{Mean}})^2)}}{{29}}\]\)
≈ 8.793
c) Standard Deviation:
\(\[\text{{Standard Deviation}} = \sqrt{{\text{{Variance}}}}\]\)
Therefore, the standard deviation is approximately \(\sqrt{8.793} \approx 2.964\)
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