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Determine the inverse Laplace transforms of: (b) 1 3s²+5s+1

Hence, the required equation is `(24) Xlt)=12 Fo/m Sin (wo-w)t sin (wotw)t 7 Wo² - w² 2 2`.

Given damped forced oscillation equation is,`m d²x/dt² + c dx/dt + kx = Fo sin(wt)`Using trigonometric identities, we can write solution for the given damped forced oscillation equation as,X(t) = Acos(wt + Φ) + Xpwhere Xp = (Fo/k) sin(wt - δ)Let's substitute X(t) in the given equation to get the required equation.```
X(t) = Acos(wt + Φ) + Xp
=> dX(t)/dt = -Awsin(wt + Φ) + (Fo/k)wcos(wt - δ)
=> d²X(t)/dt² = -Aw²cos(wt + Φ) - (Fo/k)w²sin(wt - δ)

```Now, substitute these values in the given damped forced oscillation equation.`md²X(t)/dt² + cdX(t)/dt + kX(t) = Fo sin(wt)`⇒ `m(-Aw²cos(wt + Φ) - (Fo/k)w²sin(wt - δ)) + c(-Awsin(wt + Φ) + (Fo/k)wcos(wt - δ)) + k(Acos(wt + Φ) + (Fo/k)sin(wt - δ)) = Fo sin(wt)`Grouping the terms of sines and cosines, we get⇒ `{-Aw²mcos(wt + Φ) + Awcsin(wt + Φ) + (Fo/k)w²sin(δ) + kAcos(wt + Φ) + (Fo/k)wcos(δ)} = Fo sin(wt) - c(Fo/k)wcos(wt - δ)`Let's solve these equations for `δ` and `A`.```
-Aw²mcos(wt + Φ) + Awcsin(wt + Φ) + kAcos(wt + Φ) = 0      .....................(1)
(Fo/k)w²sin(δ) + (Fo/k)wcos(δ) = Fo sin(wt) - c(Fo/k)wcos(wt - δ)  .....(2)
```Squaring and adding both equations, we get,`(Aw)²m + kA² = (Fo/k)²`or `A = Fo/(k² - mω²)^(1/2)`From equation (1), we have,`(Aw)²m + kA² = 0`or `δ = tan⁻¹(Aw/k)`Substitute values of A and δ in equation (2), we get,`Xp = (Fo/k) sin(wt - δ) = Fo/(k² - mω²)^(1/2) sin(wt - tan⁻¹(Aw/k))`Therefore, solution for the given damped forced oscillation equation is,`X(t) = Acos(wt + Φ) + Xp`= `12 Fo/m Sin (wo-w)t sin (wotw)t / (wo² - w²)²`

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Answer:

y=x+15

Step-by-step explanation:

Answer:

1,176 square centimeters

Step-by-step explanation:

The computation of the area of the mosaic is  shown below:

As we know that

The Area of the triangle is

= 1 ÷ 2 × base × height

= 1 ÷ 2 × 7 × 4

= 14

Now 1 tile would be 14 square centimeters

And, there are 84 tiles in the mosaic

So, the total area is

= 84 × 14

= 1,176 square centimeters

Answer:

63°

Step-by-step explanation:

1) Examing that right triangle, we can find the value of the angle x starting by using a trig ratio and then its reciprocal. Like this:

sin( x ) = 81/91

x = arcsin (81/91)

x = 62.88 = 63

Notice we have the opposite leg and the hypotenuse, so we started with the sine. And to find the value of the angle the arcsin.

2) So, that angle x is 63° (rounding off to the nearest degree)

Answer:

$15

Step-by-step explanation:

107% is the price of $16.05

so, 107% = $16.05

Divide both sides by 107:

1% = $0.15

Multiply both sides by 100:

100% = $15.00

Answer:

500! Just multiply 5 x 1 then add the remaining 2 zeros :)

Step-by-step explanation:

Thank you!

Answer:

[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]

[tex]5 \times 100 \\ = 500[/tex]

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Total votes were casted in election are 4716

Given: The ratio of votes in favor to votes against in an election is 5 to 4. 2,620 votes are in favor.

To find: The total number of votes cast.

Let the number of votes against is 4x.

Given the ratio of votes in favor to votes against is 5 : 4

Then, the number of votes in favor is 5x.

According to the question, 2,620 votes are in favor.

So, 5x = 2,620x = 2,620/5x = 524

The number of votes against = 4x = 4 × 524 = 2096

The total number of votes cast = votes in favor + votes against= 2620 + 2096= 4716

Therefore, there were 4716 votes cast in the

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Answer:

62

Step-by-step explanation:

find the area of each side

(3 * 5) + (2 * 3) + (2 * 5) + (2 * 5) + (2 * 3) + (3 * 5)

add them all

15 + 6 + 10 + 10 + 6 + 15 = 62

Answer:

The number of sliders is 2 and the number of hot dogs is 8.

Step-by-step explanation:

Since at a particular restaurant, each mini hotdog has 100 calories and each slider has 200 calories, and a combination meal with mini hotdogs and sliders is shown to have 1200 total calories and 4 times as many mini hotdogs as there are sliders, in order to determine the number of mini hotdogs in the combination meal, X, and the number of sliders in the combination meal, Y, the following calculation must be performed:

2X + Y = 1200

800 + 400 = 1200

800/100 = 8

400/200 = 2

Thus, the number of sliders is 2 and the number of hot dogs is 8.

Answer:

No solution

Step-by-step explanation:

The easiest approach here is to divide the second equation by 2:  x + 2y = -4.

Comparing the first equation with this result, we see that the the two lines never intersect, and thus that there is no solution.

Answer:

52 pounds

Step-by-step explanation:

52 pounds

Answer:

It is A

Step-by-step explanation:

If the y2 get subtracted by the 8 then itll be 8

The final temperature of the cylinder is -148.68 °C .

To find the final temperature

Let the final temperature be T₂.

Let the final volume be V₂.

The mass of water inside the cylinder at initial conditions, m₁ = ρV₁

On opening the valve, the water enters the cylinder until the mass doubles. So the mass of water inside the cylinder after the valve is opened, m₂ = 2ρV₁

The pressure and mass are related by the equation, PV = mRT

On simplifying the equation we get,

P = (m/ρ) * RTSo Pρ = mRT ………… (1)

From equation (1),

P₁ρ₁ = m₁R T₁

Substituting the values in equation (1) for final conditions,

P₂ρ = m₂R T₂

We need to find T₂

So, T₂ = (P₂ρ/m₂) * R = (300000 N/m² * 1000 kg/m³)/[2 * 1000 kg] * 8.314 J/(mol K)

= 124.47 K or -148.68 °C

So, -148.68 °C is the final temperature approximately.

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Answer:

20, 18, 14, and 24 are all not perfect squares

Step-by-step explanation:

Answer:

k = 192

Step-by-step explanation:

Given that,

y varies inversely with x. It can be written as :

[tex]y=\dfrac{k}{x}[/tex]

Where

k is the constant of variation

Put x = 16 and y = 12 in the above formula.

[tex]k=yx\\\\k=16\times 12\\\\k=192[/tex]

So, the value of the constant of variation is equal to 192.

Answer:

The distance from Disney to the Golden Gate Bridge is 2,162.56 miles

The distance from Mall of America to The Golden Gate Bridge  is 1,320 miles

The interior angle at The Golden Gate Bridge is 35°

The interior angle at Mall of America is 110°

The interior angle at Disney is 35°

The direction from Mall of America to Disney is South 30° East

Step-by-step explanation:

The bearing from Disney to the Golden Gate Bridge = North 65° West

The bearing from the Golden Gate Bridge to the Mall of America = North 80° East

The bearing from Disney to the Mall of America = North 30° West

The distance from Disney to the Mall of America = 1,320 miles

Let 'A', 'B', and 'C' represent the interior angles at Disney, The Golden Gate bridge and Mall of America respectively

From the drawing of the triangular trip, we find that the interior angle at C = The sum angles complementary to the bearings at B and at C

Therefore, the interior angle at C = (90° - 65°) + (90° - 80°) = 35°

The interior angle at B = The bearing of C from B - The bearing of A from B

∴ The interior angle at B = 65° - 30° = 35°

B = 35°

∠C = 35° and ∠B = 35°, therefore, the triangle is an isosceles triangle

The interior angle at A = 180° - (∠B + ∠A) = 180° - (35° + 35°) =110°

CA = AB = 1.320

By sine rule, a = sin(110) × 1320/sin(35) ≈ 2,162.56  miles

a = CB = 2,162.56 miles

Therefore, we have;

The distance from Disney to the Golden Gate Bridge = 2,162.56 miles

The distance from Mall of America to The Golden Gate Bridge  = 1,320 miles

The interior angle at The Golden Gate Bridge = 35°

The interior angle at Mall of America = 110°

The interior angle at Disney = 35°

The magnitude of the bearing of Mall of America to Disney = The magnitude of the alternate angle to the bearing of Disney to Mall of America = 30°

∴ The direction from Mall of America to Disney = South 30° East

The given system of differential equations is:

dx/dt = 2x + 3y

dy/dt = -x - 2y + 4

To solve this system, we can use various methods such as substitution, elimination, or matrix methods. Let's use the matrix method.

First, we can rewrite the system in matrix form:

d/dt [x y] = [2 3] [x] + [1]

[-1 -2] [y] + [4]

Next, we define A as the coefficient matrix [2 3; -1 -2], X as the column matrix [x; y], and B as the column matrix [1; 4]. The system can now be written as:

dX/dt = AX + B

To find the solution, we can calculate the eigenvalues and eigenvectors of matrix A. From the eigenvalues, we determine the corresponding eigenvectors and use them to construct the general solution. However, without the specific values of matrix A, it is not possible to provide the exact solution.

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Answer:

4x + 12x = 320

16x = 320

x = 20

Step-by-step explanation:

This is because the diagram shows 4x + 12x and the total being, 320.

4x + 12x = 16x

and 320/16 = 20

so x = 20

hope this helped :)

Answer:

334 - 112 + 100 - 98

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

got it right on edg

Pictures listed in order... from A-C

Answer:

Identify the output values. If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.

Step-by-step explanation:

9514 1404 393

Answer:

  8

Step-by-step explanation:

The Pythagorean theorem tells you of the relation ...

  x² + 6² = 10² . . . . . . . . . squares of sides total to the square of hypotenuse

  x² = 100 -36 = 64 . . . . . subtract 6²

  x = √64 = 8 . . . . . . . . . . square root

The length of side x is 8 units.

A. To save for her payout annuity with an ordinary annuity set up thirty years before her retirement, Holly Krech must make a monthly payment of $175.97.

B. If she sets up the ordinary annuity twenty years before her retirement, Holly Krech must make a monthly payment of $432.00.

To calculate the monthly payment for an ordinary annuity set up thirty years before retirement, we can use the formula for the present value of an ordinary annuity. Given the deposit amount of $218,437.048 and the total amount received from the annuity of $432,000, and solving for the monthly payment, we find that Holly must make a monthly payment of $175.97.

For an ordinary annuity set up twenty years before retirement, we use the same formula for present value. With the deposit amount and total amount received unchanged, we solve for the monthly payment, which comes out to be $432.00.

It's important to note that the monthly payment increases when the annuity is set up closer to the retirement date. This is due to the shorter time period available for saving, resulting in a higher required contribution to reach the desired payout amount.

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Answer:

Around 24.5 minutes

Step-by-step explanation:

Answer:

Estimate of the dividend: -0.37

Estimate of the divisor: -0.02

Estimate of the quotient: 18.5

Step-by-step explanation:

I did the test and it was right and I dubble checked it to

Absolute maximum of f (x, y) = 19 and Absolute minimum of f (x, y) = −3.

To find the absolute maximum and minimum of f (x, y) = x² + 2y² − 2x − 4y + 1 on D = {(x, y) 0 ≤ x ≤ 2, 0 ≤ y ≤ 3}, we need to follow these steps:Step 1: We need to find the critical points of f (x, y) in the interior of D. Step 2: We then need to evaluate f (x, y) at the critical points. Step 3: We need to find the maximum and minimum of f (x, y) on the boundary of D. Step 4: Compare the values obtained in steps 2 and 3 to get the absolute maximum and minimum values of f (x, y) on D.1. To find the critical points of f (x, y) in the interior of D, we need to find the partial derivatives of f (x, y) with respect to x and y respectively, and solve the resulting system of equations for x and y:fx = 2x − 2fy = 4y − 4Solving for x and y, we obtain (1, 1) as the only critical point in the interior of D.2. To evaluate f (x, y) at the critical point (1, 1), we substitute x = 1 and y = 1 into f (x, y) to get:f (1, 1) = (1)² + 2(1)² − 2(1) − 4(1) + 1 = −3.3. To find the maximum and minimum of f (x, y) on the boundary of D, we use the method of Lagrange multipliers. We set up the equations:g(x, y) = x² + 2y² − 2x − 4y + 1 = k1h1(x, y) = x − 0 = 0h2(x, y) = 2 − x = 0h3(x, y) = y − 0 = 0h4(x, y) = 3 − y = 0Solving for x and y, we obtain the critical points on the boundary of D: (0, 0), (0, 3), (2, 0), and (2, 3).4. Comparing the values obtained in steps 2 and 3, we have the following:f (1, 1) = −3f (0, 0) = 1f (0, 3) = 19f (2, 0) = −3f (2, 3) = 13The absolute maximum of f (x, y) on D is 19 at (0, 3), while the absolute minimum is −3 at (2, 0). Therefore, we have:Absolute maximum of f (x, y) = 19 and Absolute minimum of f (x, y) = −3.

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The simplified expression of integral 3 (x-2 ] 3 +4 dx is (A/3) + 12tanh[tex](sinh^{(-1)}[/tex](3(x-2))) + B

To find the integral ∫3(x-2)³+4 dx using the substitution sinh(y) = 3(x-2), we can start by differentiating both sides of the equation with respect to x to find the differential of y:

d(sinh(y))/dx = d(3(x-2))/dx

cosh(y) * dy/dx = 3

dy/dx = 3/cosh(y)

Now, let's solve for dx in terms of dy:

dx = (cosh(y)/3) dy

Substituting this value of dx in the integral:

∫3(x-2)³+4 dx = ∫(3/cosh(y)) * (3(x-2)³+4) dy

Now, we need to substitute the expression for x in terms of y using the given substitution:

3(x-2) = sinh(y)

x - 2 = sinh(y)/3

x = sinh(y)/3 + 2

Substituting this in the integral:

∫(3/cosh(y)) * (3((sinh(y)/3 + 2) - 2)³+4) dy

Simplifying:

∫(3/cosh(y)) * (sinh(y)³+4) dy

To integrate the expression ∫(3/cosh(y)) * (sinh(y)³+4) dy, we can simplify it first:

∫(3/cosh(y)) * (sinh(y)³+4) dy = 3∫(sinh(y)³/cosh(y)) dy + 12∫(1/cosh(y)) dy

To integrate the first term, we can use the substitution u = cosh(y), which implies du = sinh(y) dy:

3∫(sinh(y)³/cosh(y)) dy = 3∫(u³/u) du = 3∫(u²) du = u³/3 + C

For the second term, we can directly integrate 1/cosh(y) using the identity sech²(y) = 1/cosh²(y):

12∫(1/cosh(y)) dy = 12∫sech²(y) dy = 12tanh(y) + D

Now, substituting back y = [tex]sinh^{(-1)}(3(x-2))[/tex]:

u = cosh(y) = cosh[tex](sinh^{(-1)}(3(x-2))[/tex]) = √(3(x-2)² + 1)

Thus, the integral becomes:

∫(3/cosh(y)) * (sinh(y)³+4) dy = (u³/3 + C) + 12tanh(y) + D

Substituting back u = √(3(x-2)² + 1):

= (√(3(x-2)² + 1)³/3 + C) + 12tanh(y) + D

= (√(3(x-2)² + 1)³ + 3C)/3 + 12tanh(y) + D

= (√(3(x-2)² + 1)³ + 3C)/3 + 12tanh[tex](sinh^{(-1)}(3(x-2)))[/tex] + D

To simplify the expression and combine constants, let's assume (√(3(x-2)² + 1)³ + 3C)/3 = A, and 12D = B.

The simplified expression becomes:

(A/3) + 12tanh[tex](sinh^{(-1)}[/tex](3(x-2))) + B

Since [tex]sinh^{(-1)}(3(x-2))[/tex] is the inverse hyperbolic sine function, we can simplify it using the identity sinh[tex](sinh^{(-1)}(x))[/tex] = x:

(A/3) + 12tanh(3(x-2)) + B

This is the simplified form of the integral ∫(3/cosh(y)) * (sinh(y)³+4) dy after combining constants and simplifying the expression.

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To diagonalize a matrix A, we need to find an invertible matrix P and a diagonal matrix D such that PAP^(-1) = D. Here's how to find the diagonalization of matrix A

1. Find the eigenvalues of A:

  - Calculate the characteristic polynomial by subtracting λI from A, where λ is a scalar variable and I is the identity matrix of the same size as A.

  - Set the characteristic polynomial equal to zero and solve for λ to find the eigenvalues.

2. Find the eigenvectors corresponding to each eigenvalue:

  - For each eigenvalue, substitute it back into the equation (A - λI)x = 0, where x is a vector, and solve for x.

  - Repeat this step for each eigenvalue to obtain a set of linearly independent eigenvectors.

3. Construct the matrix P:

  - Arrange the eigenvectors found in Step 2 as columns to form the matrix P.

4. Construct the diagonal matrix D:

  - Place the eigenvalues obtained in Step 1 on the diagonal of a matrix of the same size as A, with zeros elsewhere.

5. Verify the diagonalization:

  - Calculate PAP^(-1) and check if it equals D. If PAP^(-1) = D, then A is diagonalizable.

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Answer:

The ordered pair is one of the solution to the system of equations. See below.

Step-by-step explanation:

To tell if the ordered pair is the solution to the system of equations or not, we can do by substituting the ordered pair in both equations.

(x, y) = (5,-6)

Substitute x = 5 and y = -6 in both equations.

First Equation

6x+3y=12

6(5)+3(-6)=12

30-18=12

12=12

Second Equation

4x+y=14

4(5)-6=14

20-6=14

14=14

Because both equations have same sides which mean that both equations are true for (5,-6). Therefore (5,-6) is part of the equations.

Answer:

27

Step-by-step explanation:

Length * width * height to find the volume so it is 3*3*3=27