5- By using Laplace transform and Laplace transform solve y" +9y = cos 2t, y) = 1 & y = -1 1-y(t) = (cos 3t + 4sin 3t + 4 cos 3t) 2-y(t) = (cos 2t + 4sin 3t + 4 cos 3t) Option 1 Option 2 3-y(t) =(cos
Answers
The correct option is (1-y(t)) = (cos 3t + 4 sin 3t + 4 cos 3t) 2-y(t)
= (cos 2t + 4 sin 3t + 4 cos 3t) 3-y(t)
= (cos 3t + 4 sin 3t + 4 cos 3t) - 0.2 sin 2t.
Given the differential equation:y" + 9y = cos 2t And the initial conditions:y(0) = 1,
y'(0) = -1
Laplace transform of the given differential equation is:L{y" + 9y} = L{cos 2t} => s² Y(s) - s y(0) - y'(0) + 9 Y(s)
= s / (s² + 4)
Solving this equation for Y(s) gives:
Y(s) = [s cos(2t) + (s+9) sin(2t)] / [(s² + 4) (s² + 9)]
Taking the inverse Laplace transform, we get:y(t) = L⁻¹ [Y(s)]
=> y(t) = (1/10) e^(-3t) [cos(3t) + 4 sin(3t) + 4 cos(3t)] - (1/5) sin(2t)
Therefore, the correct option is (1-y(t))
= (cos 3t + 4 sin 3t + 4 cos 3t) 2-y(t)
= (cos 2t + 4 sin 3t + 4 cos 3t) 3-y(t)
= (cos 3t + 4 sin 3t + 4 cos 3t) - 0.2 sin 2t.
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Related Questions
is someone willing to help me with my math homework? i really don’t understand :/
Answers
Lillian makes 480 sandwiches 25% of them are tuna sandwiches 45% of them are ham sandwiches and the rest are egg sandwiches how many egg sandwiches does Lillian make?
Answers
Answer:
144 egg sandwiches
Step-by-step explanation:
\(25\% + 45\% = 70\%\), and \(100\% - 70\% = 30\%.\) Thus, \(30\%\) of the \(480\) sandwiches are egg sandwiches. Since "of" means multiply, we have \(30\% \cdot 480.\) We know \(30\% = \frac{30}{100} = \frac{3}{10},\) so we can rewrite it as \(\frac{3}{10} \cdot 480.\) We cancel \(480\) with \(10\) which is \(480 \div 10 = 48.\) We multiply \(48\) by the numerator, \(3,\) to get \(48 \cdot 3 = 144.\) Thus, Lillian makes \(\boxed{144 \text{ egg sandwiches.}}\)
Find the values of the six trigonometric functions for the angle in standard position determined by each point.
(-8,-15)
Answers
These are the values of the six trigonometric functions for the angle in standard position determined by the point (-8, -15).
To find the values of the six trigonometric functions for the angle in standard position determined by the point (-8, -15), we can use the coordinates to determine the values.
First, we need to find the hypotenuse of the right triangle formed by the point (-8, -15) and the x-axis. Using the Pythagorean theorem, we get √((-8)^2 + (-15)^2) = √(64 + 225) = √289 = 17.
Next, we can determine the values of the trigonometric functions:
1. Sine (sin): -15/17
2. Cosine (cos): -8/17
3. Tangent (tan): -15/-8 = 15/8
4. Cosecant (csc): 17/-15 = -17/15
5. Secant (sec): 17/-8 = -17/8
6. Cotangent (cot): -8/15
These are the values of the six trigonometric functions for the angle in standard position determined by the point (-8, -15).
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These are the values of the six trigonometric functions for the angle in standard position determined by the point (-8, -15).
To find the values of the six trigonometric functions for the angle in standard position determined by the point (-8, -15), we can use the coordinates to determine the values.
First, we need to find the hypotenuse of the right triangle formed by the point (-8, -15) and the x-axis. Using the Pythagorean theorem, we get √((-8)² + (-15)²) = √(64 + 225) = √289 = 17.
Next, we can determine the values of the trigonometric functions:
1. Sine (sin): -15/17
2. Cosine (cos): -8/17
3. Tangent (tan): -15/-8 = 15/8
4. Cosecant (csc): 17/-15 = -17/15
5. Secant (sec): 17/-8 = -17/8
6. Cotangent (cot): -8/15
These are the values of the six trigonometric functions for the angle in standard position determined by the point (-8, -15).
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Given the system of equations below. Use the Inverse of the matrix method to solve. x+2y+3z=11
2x+4y+5z=21
3x+5y+6z=27
Answers
The solution of the given system of equations is x = -4, y = 5 and z = 2 is the answer.
The system of equations given below:x + 2y + 3z = 11;2x + 4y + 5z = 21;3x + 5y + 6z = 27.
Here, we will solve this system of equations using inverse of the matrix method as follows:
We can write the given system of equations in matrix form as AX = B where, A = [1 2 3; 2 4 5; 3 5 6], X = [x; y; z] and B = [11; 21; 27].
The inverse of matrix A is given by the formula: A-1 = (1/ det(A)) [d11 d12 d13; d21 d22 d23; d31 d32 d33] where,
d11 = A22A33 – A23A32 = (4 × 6) – (5 × 5) = -1,
d12 = -(A21A33 – A23A31) = -[ (2 × 6) – (5 × 3)] = 3,
d13 = A21A32 – A22A31 = (2 × 5) – (4 × 3) = -2,
d21 = -(A12A33 – A13A32) = -[(2 × 6) – (5 × 3)] = 3,
d22 = A11A33 – A13A31 = (1 × 6) – (3 × 3) = 0,
d23 = -(A11A32 – A12A31) = -[(1 × 5) – (2 × 3)] = 1,
d31 = A12A23 – A13A22 = (2 × 5) – (3 × 4) = -2,
d32 = -(A11A23 – A13A21) = -[(1 × 5) – (3 × 3)] = 4,
d33 = A11A22 – A12A21 = (1 × 4) – (2 × 2) = 0.
We have A-1 = (-1/1) [0 3 -2; 3 0 1; -2 1 0] = [0 -3 2; -3 0 -1; 2 -1 0]
Now, X = A-1 B = [0 -3 2; -3 0 -1; 2 -1 0] [11; 21; 27] = [-4; 5; 2]
Therefore, the solution of the given system of equations is x = -4, y = 5 and z = 2.
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-3(4x + 3) + 4(6x + 1) = x +43 - 13x
Answers
Answer:
Hope it helps you☺️☺️
Step-by-step explanation:
-3(4x+3)+4(6x+1)=x+43-13x
or,-12x-9+24x+4=-12x+43
or,12x-5=-12x+43
or,12x+12x=43+5
or,x=48/24
so,x=4
Lol, No one will answer if I don't give this many points! Question: ((x-3)^2) * ((x+3)^2)
Answers
Answer:
x^4-18x^2+81
Step-by-step explanation:
Answer:
x 2 − 6 x + 9
Step-by-step explanation:
the number 2 is a exponent
Is the trapezoidal rule an overestimate or underestimate?
Answers
The trapezoidal rule is a numerical integration method that frequently overestimates the real value of a function's definite integral.
What is trapezoidal rule?The trapezoidal rule is a strategy for approximating the definite integral in calculus. The trapezoidal rule works by computing the area of the region under the graph of the function f(x) that is approximated as a trapezoid. The trapezoidal rule is commonly used to calculate the area under curves. This is achievable if the overall area is divided into smaller trapezoids rather than rectangles. The Trapezoidal Rule integration determines the area by approximating the area under a function's graph as a trapezoid. The midway rule uses rectangular areas to approximate the definite integral, whereas the trapezoidal rule uses trapezoidal approximations to approximate the definite integral. Simpson's approach works by first approximating the original function with piecewise quadratic functions.
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Are the equations -11(x-2)=8 and x-2=8+11 equivalent?
Answers
No, the equations -11(x - 2) = 8 and x - 2 = 8 + 11 are not equivalent.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
Then the equation is given below.
-11(x - 2) = 8
By simplifying, we have
x - 2 = - 8 / 11
No, the equations -11(x - 2) = 8 and x - 2 = 8 + 11 are not equivalent.
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One of the legs of a right triangle measures 13 cm and its hypotenuse measures 17 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Help me please!!!
Answers
Answer: 10.9544511501
Step-by-step explanation:
√ 17 pwr2 - 13pwr2 = 10.9544511501
b=√c2−a2.
evaluate each expression for the value given.r + 2.4; r=16.8
Answers
Given the expression:
\(r+2.4\)if r = 16.8, then we have the following:
\(\begin{gathered} r=16.8 \\ \Rightarrow r+2.4=16.8+2.4=19.2 \end{gathered}\)thus, the simplified expression is 19.2
compute the lower riemann sum for the given function ()=2 over the interval ∈[−1,1] with respect to the partition =[−1,−14,14,34,1].
Answers
The function is f(x)=2 over the interval [−1,1]. Compute the lower Riemann sum with respect to the partition P=[−1,−14,14,34,1].
The formula for calculating the lower Riemann sum is given by:L(f,P)=∑i=1n−1miΔxiWhere mi is the infimum of f on [xi,xi+1], and Δxi is the length of the subinterval [xi,xi+1].To compute the lower Riemann sum with respect to the partition P=[−1,−14,14,34,1], we have to calculate the infimum of the function over each subinterval, and multiply it by the length of the subinterval.Subinterval [-1, -1/4]The infimum of f(x)=2 on [-1, -1/4] is f(-1) = 2.
Therefore, m1 = 2.The length of the subinterval [-1, -1/4] is Δx1 = (-1/4) - (-1) = 1/4.Subinterval [-1/4, 1/4]The infimum of f(x)=2 on [-1/4, 1/4] is f(-1/4) = 2. Therefore, m2 = 2.The length of the subinterval [-1/4, 1/4] is Δx2 = 1/2.Subinterval [1/4, 3/4]The infimum of f(x)=2 on [1/4, 3/4] is f(1/4) = 2. Therefore, m3 = 2.The length of the subinterval [1/4, 3/4] is Δx3 = 1/2.Subinterval [3/4, 1]The infimum of f(x)=2 on [3/4, 1] is f(3/4) = 2. Therefore, m4 = 2.The length of the subinterval [3/4, 1] is Δx4 = 1/4.Therefore, the lower Riemann sum is:L(f,P) = m1Δx1 + m2Δx2 + m3Δx3 + m4Δx4= 2(1/4) + 2(1/2) + 2(1/2) + 2(1/4)= 1/2 + 1 + 1 + 1/2= 3.
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he chart shows specific heat data for four substances.a chart with 2 columns and 5 rows. the first column is labeled substance with entries w, x, y, z. the second column is labeled specific heat with entries 2.542, .900, 3.209, 1.657.which conclusion is best supported by the data?
Answers
The specific heat shows that Substance Y has more atoms per gram than substance W.
Specific heat:
Specific heat is a property of a substance that describes how much heat energy is required to raise the temperature of a certain amount of that substance by one degree. It is typically measured in units of joules per gram per degree Celsius (J/g°C).
Different substances have different specific heats. For example, water has a relatively high specific heat of 4.18 J/g°C, which means that it takes a lot of heat energy to raise the temperature of water by one degree. This is why water is often used as a coolant or in air conditioning systems, as it can absorb a large amount of heat energy without experiencing a significant temperature change.
Therefore, the specific heat shows that Substance Y has more atoms per gram than substance W.
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Hello everyone, I was wondering what 50+8x2 is for my project that I am doing. Thanks
Answers
Answer:
66
Step-by-step explanation:
Multiplying 8 by 2 which gives you 16.
Then 16 Add 50 = 66
Check all the options that apply to the number below.
| -21
Rational Number
Whole Number
Irrational Number
Natural Number
Answers
Answer: SHEEEEEEsh
Step-by-step explanation: BC SHEEEESH
College Algebra Applied Problem Four A medical professional is helping an individual balance their diet. The individual has asked for some certain foods to remain in their diet. They will always get 600 calories from carbohydrates. The individual says that they can be flexible about how many calories they consume in fats and proteins. The goal of the diet is to keep the individual at 1,800 calories per day ( 600 of which come from carbohydrates). Part One Write an equation that models the amount of calories from fats " f ' and protein "p" that the individual can consume in order to reach 1,800 calories. Part Two The diet being prescribed to the individual calls for calories from protein to be three times the calories from fat. Write an equation based on this information that relates calories from protein "p" to calories from fat " f ". Part Three Use your equations from parts "b" and "c" to solve this system of equations and determine the amount of calories that the individual should consume from fats and proteins. Part Four If the individual no longer required 600 calories from carbohydrates, and instead said that they would be flexible about how many carbohydrates they would consume, how many variables would there be for this problem on calories?
Answers
The system equation that models the amount of calories from fats (f) and proteins (p) that the individual can consume to reach 1,800 calories is: f + p = 1,200. The equation that relates calories from protein (p) to calories from fat (f) based on the prescribed diet is: p = 3f. Solving the system of equations, we find that the individual should consume 300 calories from fats and 900 calories from proteins.
To find the equation that models the amount of calories from fats and proteins that the individual can consume in order to reach 1,800 calories, we consider that 600 calories will come from carbohydrates. Since the total goal is 1,800 calories, the remaining calories from fats and proteins should add up to 1,800 - 600 = 1,200 calories. Therefore, the equation is f + p = 1,200.
Based on the prescribed diet, the individual is required to consume calories from protein that are three times the calories from fat. This relationship can be expressed as p = 3f, where p represents the calories from protein and f represents the calories from fat.
To solve the system of equations, we substitute the value of p from the second equation into the first equation: f + 3f = 1,200. Combining like terms, we get 4f = 1,200, and dividing both sides by 4 yields f = 300. Substituting this value back into the second equation, we find p = 3(300) = 900.
Therefore, the individual should consume 300 calories from fats and 900 calories from proteins to meet the diet requirements and achieve a total of 1,800 calories.
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(4x2 + 7x - 4) + (x2 – 7x + 14)
What is the answer?
Answers
Answer:
\(5x^2 + 10\)
Step-by-step explanation:
\(4x^2 + x^2 = 5x^2\\7x + (-7x = 0\\-4 + 14 = 10\)
How are the properties of exponents used when dividing a polynomial by a monomial?
Answers
Answer:
a couple different obes
Step-by-step explanation:
there are five
A right triangle has one leg of length y and hypotenuse of length x. What is the length of the other leg of this triangle
a x+y−−−−√
b x2+y2−−−−−−√
c x−y−−−−√
d x2−y2−−−−−−√
Answers
Answer:
Step-by-step explanation:
You have a bucket with 100 gallons of water in it. That bucket is losing water at a rate of 7 gallons per minute. How much water
have you lost after 8 minutes?
How much water is left in the bucket at this time?
Answers
8×7=56
then subtract it from 100-56=44 so you lost 56 gallons in 8 minutes and there is 44 left.
What is the volume of the cylinder to the nearest whole number? a) 942 cm3 b) 3,534 cm3 c)471 cm3 d) 9,420 cm3
Answers
Answer:
V = 3534 cm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
the radius is 7.5 and the height is 20
V = pi ( 7.5)^2 * 20
V =1125 pi cm^3
Using the pi button for pi
V =3534.291735 cm^3
Rounding to the nearest whole number
V = 3534 cm^3
Answer:
b)3534 cm^3
Step-by-step explanation:
To find the area of a cylinder, you first have to find the area of the base which is in the shape of a circle. The area of a circle is given by the equation πr^2. In this case r, the radius, is 7.5 cm. So plugging in 7.5 for r you get 7.5^2 × π. Plugging in 3.1415 for π you get ~176.671. Now all you do is multiply this by the height, 20cm, and get the answer of ~3534 cm^3.
what is the probability that a randomly chosen subject comples more than the expected number of puzzles in the five minute
Answers
The probability that a randomly chosen subject comples more than the expected number of puzzles in the five minute is equals to the 0.40. So, option (b) is right one.
We have a Random variables X denotes the number of puzzles complete by random choosen subject. The above table contains probability distribution of random variable X. The expected number of puzzles in the 5-minutes period while listening to smoothing music is calculated by following formula, \(E(x) = \sum x_i p(x_i)\)
= 1(0.2) + 2(0.4) + 3(0.3) + 4(0.1)
= 0.2+ 0.8+ 0.9+ 0.4
= 2.3
Now, the probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music, that is possible value values of X are 1,2,3,4 but for X > 2.3 only 3 and 4. So, P(X>2.3)= P(X=3) + P(X=4)
=0.30+ 0.10=0.40
Hence, required value is 0.40.
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Complete question:
The above table complete the question
what is the probability that a randomly chosen subject comples more than the expected number of puzzles in the five minute period while losing music
a. 0.1
b. 0.4
c. 0.8
d. 1
e. Cannot be determined
addison and kelsey are running on a path modeled by x^2+y^2-10x-18y-378=0, where the distance is in meters. what is the maximum distance between the runners at any given time
Answers
The maximum distance between them is the diameter of the circle, which is of 44 units.
The equation of a circle of center \((x_0, y_0)\) and radius r is given by:
\((x - x_0)^2 + (y - y_0)^2 = r^2\)
The diameter is twice the radius, and is the maximum distance between two points on the same circle.
They are running on a circular path, modeled by:
\(x^2 + y^2 - 10x - 18y = 378\)
Completing the squares, the equation is:
\((x - 5)^2 + (y - 9)^2 = 378 + 5^2 + 9^2\)
\((x - 5)^2 + (y - 9)^2 = 378 + 25 + 81\)
\((x - 5)^2 + (y - 9)^2 = 484\)
Then, the radius is: \(\sqrt{484} = 22\), which means that the maximum distance between the runners at any given time is of 44 units.
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(60 + 10)
130
Solve for a
Answers
Answer:
Step-by-step explanation:
here you go mate'
step 1
(60 + 10)130 equation
step 2
(60 + 10)130 simplify with the brackets
step 3
130(70) multiply the numbers
answer
9100
I need help asap !!!!!!!!!!!
Answers
Explanation: (x,y) first number is where the parabola meets the bold horizontal line your looking at. Don’t get messed up even if the answer is backwards remember that x is always the first number and since your looking for the x intercept the y value is always 0.
Hope this helps you :)
There are 36 coins consist of nickels, dimes, and quarters. There are three fewer quarters than nickels and six more dimes than quarters. How many of each kind of coin is there?
Answers
Answer:
Number of Nickels is 12
Number of Dimes is 9
Number of Quarters is 15
Step-by-step explanation:
Given that there are a total of 36 coins, which consists of nickels, dimes, and quarters.
That is, when we sum the numbers of nickels, dimes, and quarters, we have 36.
Let number of nickels be N
Let number of dimes be D
Let number of quarters be Q
Then
N + D + Q = 36 .................................(1)
- There are three fewer quarters than nickels.
This implies that
N = Q - 3 ..............................................(2)
Or
Q = N + 3 .............................................(3)
- There are six more dimes than quarters.
This implies that
Q = D + 6 .............................................(4)
Comparing (3) with (4), we see that
N + 3 = D + 6
N - D = 6 - 3
N - D = 3 ................................................(5)
Using (3) in (1)
N + D + (N + 3) = 36
2N + D = 36 - 3
2N + D = 33 ..........................................(6)
Solving (5) and (6) simultaneously
From (5): D = N - 3
From (6): D = 33 - 2N
=> N - 3 = 33 - 2N
N + 2N = 33 + 3
3N = 36
N = 36/3 = 12..........................................(7)
Using (7) in (6)
2(12) + D = 33
24 + D = 33
D = 33 - 24
D = 9 ........................................................(8)
Using (7) and (8) in (1)
12 + 9 + Q = 36
21 + Q = 36
Q = 36 - 21 = 15.......................................(9)
Therefore,
Number of Nickels, N = 12
Number of Dimes, D = 9
Number of Quarters, Q = 15
Ellie wants to work out the height of a building which has a fence all around it
From P she sees that the angle of elevation of the top is 28 degrees
From Q 20m closer the angle of elevation is 40 degrees
Work out the height of the building
Answers
The Height of the Building is 28.87 m .
in the question ,
it is given that
distance between P and Q \(=\) 20 m
From P the angle of elevation is 28°
and from Q the angle of elevation is 40°
From the figure
In triangle BAQ
tan40° = BA/AQ
tan40° = h/x
h = x * tan40°
In triangle BAP
tan28° = BA/AP
tan28° = h/(x+20)
h = (x+20) * tan28°
Equating both the h , we get
x * tan40° = (x+20) * tan28°
x* tan40° = x*tan28° + 20* tan28°
x*(tan40° - tan28°) = 20* tan28°
x*(0.840 - 0.531) = 20*(0.531)
x*(0.309) = 10.62
x = 10.62/0.309
x = 34.368
Substitute h = 34.368 in h = x * tan40°
we get ,
h = (34.368)*(0.840)
h = 28.8699
h = 28.87
Therefore , The Height of the Building is 28.87 m .
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A serving of rice is 5/6 of a cup. How many servings are there in a 4 1/6-cup bag of rice?
Answers
Answer:
5
Step-by-step explanation:
4 1/6 or 25/6 dived by 5/6 = 5
21. Find the distance between the points. Leave your answer
as a simplified square root
(-8,5), (-1.1)?
PLEASE answer as fast as you can. thanks
Answers
Answer:
The answer is
\( \sqrt{65} \: \: \: units\)
Step-by-step explanation:
To find the distance between two points we use the formula
\( \sqrt{ ({x1 - x2})^{2} + ( {y1 - y2})^{2} } \)
where
( x1 , y1) and ( x2 , y2) are the points
From the question the points were
(-8,5), (-1.1)
Substitute the values into the above formula
That's
\( \sqrt{ ({ - 8 + 1})^{2} + ({5 - 1})^{2} } \)
\( \sqrt{ ({ - 7})^{2} + {4}^{2} } \)
\( \sqrt{49 + 16} \)
We have the final answer as
\( \sqrt{65} \: \: units\)
Hope this helps you
11r + s; r=12; s=15
I'm stuck on this qestion please help!!!
Answers
Answer:
147
Step-by-step explanation:
To solve this first plug in the values for their respective variables. This gets you 11*12+15. Then use PEMDAS to solve, remember PEMDAS stands for: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Following PEMDAS, the first step is 11*12,
11*12+15
132+15
Then add,
147
Select the correct answer. what is the completely factored form of this expression? 3x2 − 17x − 28 a. (3x 4)(x 7) b. (3x 4)(x − 7) c. 3x2 − 17x − 28 d. (3x2 4)(x − 7)
Answers
Answer:
A. (3x + 4)(x-7)
Step-by-step explanation:
3x times x = 3x^2
3x times -7 = -21x
4 times x = 4x
4 times -7 = -28
-21x + 4x = -17x
3x^2 - 17x - 28