help pls ..........!!!!!!!!!!!!!!

We need to find \(L{f(t)} for f(t)=2cos(9t). L(f(t))= s/(s^2 + 81)\) Using the Laplace transform to solve the given initial-value problem.

Given, y′−y=2cos(9t), y(0)=0, and f(t) = 2cos(9t) ,

Here, we need to find the Laplace transform of y′−y=2cos(9t).

Applying Laplace transform to both sides of the equation, we get:

L{y′−y}= L{2cos(9t)}L{y′}= sL{y} − y(0)L{y′}= sL{y} − 0L{y′}= sL{y}L{y′−y}= L{y′} − L{y}= sL{y} − y(0) − L{y}= sL{y} − 0 − L{y}= sL{y} − L{y}

Therefore,

sL{y} − L{y}= s/(s² + 81) (Using L{f(t)} = s/(s² + 81) )L{y}(s) (s - 1) = s/(s² + 81)L{y}(s) = s/(s² + 81) (s - 1)L{y}(s) = s / [(s² + 81) (s - 1)]

Applying partial fractions to the above equation, we get

L{y}(s) = 1/(10 (s - 1)) - 9s/[(s² + 81) (s - 1)]

Therefore, \(y(t) = L^{-1} {L{y}(s)}= L^{-1} [1/(10 (s - 1)) - 9s/[(s^2 + 81) (s - 1)]]\)

Taking inverse Laplace of the above equation, we get:

\(y(t) = (1/10) e^{t} - (9/20) sin(9t)\)

Therefore, the required solution is:

\(y(t) = (1/10) e^{t} - (9/20) sin(9t)\)

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Answer:

the function R is always 2 above on the y axis to the function G

Step-by-step explanation:

adding 2 to x makes the function go up on the y axis

The total distance traveled by the particle over the time interval [1, 5] is 12 units.

To find the total distance traveled, we need to consider both the magnitude and direction of the velocity function. Since the velocity function given is in meters per second (m/sec), the total distance traveled will be measured in meters.

To calculate the total distance, we need to consider the intervals where the velocity function changes its sign. In this case, the velocity function is linear and increasing, starting at t = 1 with a velocity of 3 m/sec. From t = 1 to t = 3, the particle moves in the positive direction, covering a distance of (3t - 9) × (t - 1) = 12 units. From t = 3 to t = 5, the particle moves in the negative direction with the same magnitude, covering a distance of (-1) × (3t - 9) × (t - 3) = 12 unit

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Answer:

15

Step-by-step explanation:

\(using \: pythagoras \: theorem \\ let \: the \: unknown \: side = x \\ 25 {}^{2} = x {}^{2} + 20 {}^{2} \\ 625 = x {}^{2} + 400 \\ x {}^{2} = 625 - 400 \\ x {}^{2} { = 225} \\ x = \sqrt{225} \\ x = 15 \\ lenght \: of \: the \: third \: side = 15\)

Answer: 2/25 *25

Step-by-step explanation:

Answer:

Third step

Step-by-step explanation:

To find the average amount it fell every hour, you need to divide -13 1/5 by 4 2/5. Since you can't do it with a mixed number, you need to make it an improper fraction by multiplying the denominator by the number and adding the numerator.

Now you divide the new numbers. However, in the problem, it is multiplying, so that is what's wrong.

Therefore the third step is wrong.

Hope I helped!!!

Answer:

Parallel lines have to have the same slope, and the only one that has a slope of 1/4 is y = 1/4x - 1/2

Answer:

sadly, 5$.

Step-by-step explanation:

4 people, and 35$ per person. You spend 140 total on tickets alone. +15 for parking adds up to 155. Subtract all of that from 200, and you have 5 bucks left to spend.

Answer:

y=1

Step-by-step explanation:

you add how many you went to one side

Answer:

4 boys

Step-by-step explanation:

\(\frac{1}{3} :\frac{y}{12}\)

3 × y = 1 × 12

3y = 12

3y ÷ 3 = 12 ÷ 3

y = 4

Answer:

220 mph ; 230 mph

Step-by-step explanation:

Given that :

Speed of First boat = x

Speed of Second boat = y

y = (10 + x) mph

Distance apart after 3 hours = 150 miles

Speed of the boats :

Speed / time = distance

First boat distance = x / 3

Second boat distance = (10+x) /3

x/3 + (10+x)/3 = 150

x + 10 + x = 150 * 3

2x + 10 = 450

2x = 450 - 10

2x = 440

x = 220 mph

Speed of second boat = 220 + 10 = 230 mph

Answer:

24.99

Step-by-step explanation:

25.9-6.91=24.99

Answer:

It is important so that people don't get hurt by the natural disasters.

Step-by-step explanation:

I just used common sense..

Hope this helps! :)

The given mass matrix is 2x2 with values m[1 0], and the stiffness matrix is also 2x2 with values k[3 -2; -2 2]. Additionally, the normal modes X are provided as a 2x2 matrix with values [1 -0.366; -0.366 1.366]. The task is to decouple the equations of motion and find the solution in the original coordinates.

To decouple the equations of motion, we start by transforming the system into modal coordinates using the normal modes. The modal coordinates are obtained by multiplying the inverse of the normal modes matrix with the original coordinates. Let's denote the modal coordinates as q and the original coordinates as x. Thus, q = X^(-1) * x.

Next, we substitute q into the equations of motion, which are given by m * x'' + k * x = 0, to obtain the equations of motion in modal coordinates. This results in m * X^(-1) * q'' + k * X^(-1) * q = 0. Since X is orthogonal, X^(-1) is simply the transpose of X, denoted as X^T.

Decoupling the equations of motion involves diagonalizing the coefficient matrices. We multiply the equation by X^T from the left to obtain X^T * m * X^(-1) * q'' + X^T * k * X^(-1) * q = 0. Since X^T * X^(-1) gives the identity matrix, the equations simplify to M * q'' + K * q = 0, where M and K are diagonal matrices representing the diagonalized mass and stiffness matrices, respectively.

Finally, we solve the decoupled equations of motion M * q'' + K * q = 0, where q'' represents the second derivative of q with respect to time. The solution in the original coordinates x can be obtained by multiplying the modal coordinates q with the normal modes X, i.e., x = X * q.

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The expression 8x+2 factored using the GCF is 2(4x + 1)

Equations are expressions separated by an equal sign

Given the expression 8x + 2

First we need to find the factors of each terms

8x = 2 * 4 * x

2 = 2 * 1

From bot factors, we can see that 2 is common. Factoring out 2 from the expression will give;

8x + 2 = 2(4x + 1)

Hence the expression 8x+2 factored using the GCF is 2(4x + 1)

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To determine the values of a(t) using quadratic splines, we will construct quadratic polynomials for each interval between data points and evaluate them at the given values of t.

1. Determine a(2.3) and a(1.6):

For the given data:

t: 0   1.2   2   2.6   3.2

a(t): 3   4.2   5   6.3   7.2

To find a(2.3), we consider the interval between t = 2 and t = 2.6. We construct a quadratic polynomial that passes through the points (2, 5) and (2.6, 6.3). Let's denote this polynomial as P1(t).

Similarly, to find a(1.6), we consider the interval between t = 1.2 and t = 2. We construct a quadratic polynomial that passes through the points (1.2, 4.2) and (2, 5). Let's denote this polynomial as P2(t).

By evaluating P1(2.3) and P2(1.6), we can find the values of a(2.3) and a(1.6), respectively.

2. Determine a(1.7) and a(2.7):

For the given data:

t: 1   1.4   2.2   3.1   3.7

a(t): 2.1   2.7   3.5   4.3   5.2

To find a(1.7), we consider the interval between t = 1.4 and t = 2.2. We construct a quadratic polynomial that passes through the points (1.4, 2.7) and (2.2, 3.5). Let's denote this polynomial as P3(t).

Similarly, to find a(2.7), we consider the interval between t = 2.2 and t = 3.1. We construct a quadratic polynomial that passes through the points (2.2, 3.5) and (3.1, 4.3). Let's denote this polynomial as P4(t).

By evaluating P3(1.7) and P4(2.7), we can find the values of a(1.7) and a(2.7), respectively.

3. Determine a(1.9) and a(2.7):

For the given data:

t: 1.3   1.8   2.3   3   3.8

a(t): 1.1   2.5   3.1   4.2   5.1

To find a(1.9), we consider the interval between t = 1.8 and t = 2.3. We construct a quadratic polynomial that passes through the points (1.8, 2.5) and (2.3, 3.1). Let's denote this polynomial as P5(t).

Similarly, to find a(2.7), we consider the interval between t = 2.3 and t = 3.8. We construct a quadratic polynomial that passes through the points (2.3, 3.1) and (3.8, 5.1). Let's denote this polynomial as P6(t).

By evaluating P5(1.9) and P6(2.7), we can find the values of a(1.9) and a(2.7), respectively.

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Answer:

PAIN

Step-by-step explanation:

Answer:

int option 3

Step-by-step explanation:

Answer:

I think it is option 4

Step-by-step explanation:

could be 3 possiblyu

Answer:

6/12

Step-by-step explanation:

this is because if you do the math it is 6/12

Answer:

Scientific Notation: 3754 × \(10^{-4}\)

Step-by-step explanation:

Have a great summer :)

Answer:

3.754 • 10^-4

Step-by-step explanation:

Put decimal point back until in front of a whole number( not zero ;D). So it would be 3.754 and since it was going left or backwards the exponent would be negative. Therefore, giving our answer!

Hope this helped, good luck! :)

The polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. -5, -1, 2 is,

⇒ f (x) = x³ + 4x² - 7x - 10

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

For a polynomial,

A leading coefficient = 1,

And, the given zeros = -5, -1, 2

Now, We know that;

The standard polynomial is given by:

⇒ f (x) = a (x - p) (x - q) ...

Where, 'a' is leading coefficient and p, q, .. are zeroes.

Here, A leading coefficient = 1,

And, the given zeros = -5, -1, 2

Hence, The polynomial is,

⇒ f (x) = 1 (x - (-5)) (x - (- 1)) (x - 2)

⇒ f (x) = (x + 5) (x + 1) (x - 2)

⇒ f (x) = (x + 5) (x² - 2x + x - 2)

⇒ f (x) = (x + 5) (x² - x - 2)

⇒ f (x) = x³ - x² - 2x + 5x² - 5x - 10

⇒ f (x) = x³ + 4x² - 7x - 10

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We can say that the value of k will be equal to the y-coordinate of the center of the circle (since k represents the y-coordinate of the center).

To answer this question, we need to use the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

Where h and k represent the coordinates of the center of the circle, and r represents the radius. In this case, we are given that the circle has center (h, k) and radius 10. So we can write:

(x - h)^2 + (y - k)^2 = 10^2

We are asked to find the value of k. To do this, we need to look at the equation of the circle and notice that the y-coordinate is paired with k. This means that we can isolate k by rearranging the equation as follows:

(y - k)^2 = 10^2 - (x - h)^2

y - k = ±√(10^2 - (x - h)^2)

k = y ±√(10^2 - (x - h)^2)

Since we don't have any information about the x-coordinate, we can't solve for a specific value of k. However, we can say that the value of k will be equal to the y-coordinate of the center of the circle (since k represents the y-coordinate of the center). Therefore, the answer is:

k = y

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Answer:

\(7999 \div 4\#\) lies between 163.245 and 199.975

Step-by-step explanation:

Given

2 digit = 4#

Required

The range of \(7999 \div 4\#\)

Let

\(\# = 0\) --- the smallest possible value of #

So:

\(7999 \div 40 = 199.975\)

Let

\(\# = 9\) --- the largest possible value of #

So:

\(7999 \div 49 = 163.245\)

Hence, \(7999 \div 4\#\) lies between 163.245 and 199.975

Answer: C

Step-by-step explanation:

Answer: I think the answer is A.

Step-by-step explanation:

Answer:

7 because length times width = volume

Answer:

\(2.50x\) ,or \( 2.5x \)

Step-by-step explanation:

All of the expressions are right, but I doubt that there's a notebook that costs 25 dollars or 32 dollars.

Answer:

b must be positive

Step-by-step explanation:

if a is less than -1

that means to get smaller numbers

b needs to be positive

so that when a is multiplied by b you would have

numbers that are more negative

Answer:

b > 1

Step-by-step explanation:

Given:

Substituting a = -1 into ab < a

⇒ (-1)b < -1  

⇒ -b < -1

⇒ b > 1

If a < -1 then a is negative.  If ab < a then ab is also negative.  

In order for ab to be negative (when a is negative) b must be positive.

For ab < a then b > 1.

Proof

If b = 0.5 and a = -1.5 then ab = -0.75

As -0.75 > -1.5 then ab > a so this cannot be true.

If b = 1.5 and a = -1.5 then ab = -2.25

As -2.25 < -1.5 then ab < a so this is true.

Therefore b > 1

Answer:

Yes, they have the same answer because because 150/15 = 10 and in the equation 15g = 150, you have to solve it by dividing 150 by 15 which gets 10. Therefor, they are the same.

Step-by-step explanation:

Answer: They have the same solution.

Step-by-step explanation: 15g=150 has an answer of 10 ft. (divide 150 by 15 to get g alone.) 150/15=g has an answer of 10 as well. (Simplify to find g.)

Answer:

No

Step-by-step explanation:

no you do not get the same answer

This is the order in which you should approach problems, doing otherwise may lead to a wrong answer

P - parenthesis -- meaning solve whatever is the the parenthesis

E - exponents -- an example of an exponent is \(2^{3}\) which equals 8

MD - multiplication/division

AS - addition / subtraction

for our particular problem, we have

9 + 2(3)

multiplication trumps addition thus we perform multiplication first

9 + 6 = 15 ---CORRECT

if we were to addition first we would get

9 + 2(3) = 11(3) = 33 This would be WRONG

note: multiplication and division are on the same level

         subtraction and addition are on the same level

if you encounter a problem like 4 ÷ 2 * 3. perform the calculation from left to right thus we would have 4 ÷ 2 = 2 and then 2 * 3 = 6

same applies for addition subtraction