Peter is making an "X marks the spot" flag for a treasure hunt. The flag is made of a square white flag with sides of 12 centimeters. He will make the "X" by stretching red ribbon diagonally from corner to corner.

The Inverse Laplace Transform of each of the following:

1. 42/9s-30 is 14/3 * e^(10t/3).

2. 9s-8/s^2+24s is (-1/3) + (10/3) * e^(-24t).

3. 3s-16/s^2-24s-69 is (5/8) * e^(3t) + (19/8) * e^(23t).

To find the inverse Laplace transform of each expression, we'll use partial fraction decomposition and consult a table of Laplace transforms. Here are the solutions for each case:

1. To find the inverse Laplace transform of 42/(9s - 30):

First, let's factor out the denominator: 9s - 30 = 9(s - 10/3).

The inverse Laplace transform of 42/(9s - 30) is then given by:

L^-1 {42/(9s - 30)} = L^-1 {42/[9(s - 10/3)]}

We can use the property that the inverse Laplace transform is linear and the following table entry:

L{1/(s - a)} = e^(at)

Using these, the inverse Laplace transform can be simplified as follows:

L^-1 {42/[9(s - 10/3)]} = 42/9 * L^-1 {1/(s - 10/3)}

                        = 14/3 * L^-1 {1/(s - 10/3)}

                        = 14/3 * e^(10t/3)

Therefore, the inverse Laplace transform of 42/(9s - 30) is (14/3) * e^(10t/3).

2. To find the inverse Laplace transform of (9s - 8)/(s^2 + 24s):

The denominator s^2 + 24s can be factored as s(s + 24).

Now, we need to perform partial fraction decomposition on the expression:

(9s - 8)/(s^2 + 24s) = A/s + B/(s + 24)

To find the values of A and B, we can multiply both sides of the equation by the common denominator (s(s + 24)) and equate the numerators:

9s - 8 = A(s + 24) + B(s)

Expanding and equating coefficients, we get:

9s - 8 = (A + B)s + 24A

Equating coefficients of s:

9 = A + B

Equating constant terms:

-8 = 24A

Solving the above equations, we find A = -1/3 and B = 10/3.

Now, we can express the original expression as:

(9s - 8)/(s^2 + 24s) = (-1/3) * 1/s + (10/3) * 1/(s + 24)

Using the Laplace transform table, the inverse Laplace transform of 1/s is 1, and the inverse Laplace transform of 1/(s + a) is e^(-at).

Therefore, the inverse Laplace transform of (9s - 8)/(s^2 + 24s) is:

L^-1 {(9s - 8)/(s^2 + 24s)} = (-1/3) * 1 + (10/3) * e^(-24t)

Simplifying, we get:

L^-1 {(9s - 8)/(s^2 + 24s)} = (-1/3) + (10/3) * e^(-24t)

Hence, the inverse Laplace transform of (9s - 8)/(s^2 + 24s) is (-1/3) + (10/3) * e^(-24t).

3. To find the inverse Laplace transform of (3s - 16)/(s^2 - 24s - 69), we need to perform partial fraction decomposition. First, let's factor the denominator:

s^2 - 24s - 69 = (s - 3)(s - 23)

Now, we can express the given expression as:

(3s - 16)/(s^2 - 24s - 69) = A/(s - 3) + B/(s - 23)

To find the values of A and B, we can multiply both sides of the equation by the common denominator (s - 3)(s - 23) and equate the numerators:

3s - 16 = A(s - 23) + B(s - 3)

Expanding and equating coefficients, we get:

3s - 16 = (A + B)s - (23A + 3B)

Equating coefficients of s:

3 = A + B

Equating constant terms:

-16 = -23A + 3B

Solving the above equations, we find A = 5/8 and B = 19/8.

Now, we can express the original expression as:

(3s - 16)/(s^2 - 24s - 69) = (5/8) * 1/(s - 3) + (19/8) * 1/(s - 23)

Using the Laplace transform table, the inverse Laplace transform of 1/(s - a) is e^(at).

Therefore, the inverse Laplace transform of (3s - 16)/(s^2 - 24s - 69) is:

L^-1 {(3s - 16)/(s^2 - 24s - 69)} = (5/8) * e^(3t) + (19/8) * e^(23t)

Simplifying, we get:

L^-1 {(3s - 16)/(s^2 - 24s - 69)} = (5/8) * e^(3t) + (19/8) * e^(23t)

Hence, the inverse Laplace transform of (3s - 16)/(s^2 - 24s - 69) is (5/8) * e^(3t) + (19/8) * e^(23t).

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We get two solutions where x = 22 and y = 20 and x = 42 and

y = 0 with the objective function value being 420.

Here we are given the objective function to be

z=10x+10y

The constraints given are

6x + 6y ≥ 102

14x − 11y ≥ 88

x + y ≤ 42

Now if we plot the points in a graph we will now have to shade the easible region.

Clearly for the constraint 6x + 6y ≥ 102,

the shaded region would be away from the origin.

similarly for the constraint 14x − 11y ≥ 88,

the shaded region will be away from the origin.

and for the last constraint, x + y ≤ 42

this will be similar to the objective function and the shaded region will be towards the origin.

Hence we obtain the blue shaded feasible region.

Marking the corner points as A, B, C and D we get

point           coordinates               objective function value

   A                    (11,6)                             110 + 60 = 170

   B                    (17,0)                             170 + 0 = 170

   C                    (22,20)                          220 + 200 = 420

   D                    (42,0)                             420 + 0 = 420

Hence we get two solutions where x = 22 and y = 20 and x = 42 and

y = 0 with the objective function value being 420.

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The (s - 1)2F(s - 1) - (s - 1) option matches the given function (option B).

Let's go through the options one by one to determine the correct answer.

Option A: s-F(s) - s

This option doesn't match the given function.

Option B: (s - 1)2F(s - 1) - (s - 1)

This option matches the given function.

Option C: (s2 - 1)F(s) - s + 1

This option doesn't match the given function.

Option D: sF(s - 1) - 5 - 1

This option doesn't match the given function.

Option E: (s - 1)F(s - 1) - s

This option doesn't match the given function.

Based on the given function, the correct answer is Option B: (s - 1)2F(s - 1) - (s - 1).

Regarding the second question, the Existence and Uniqueness Theorem guarantees the existence and uniqueness of a solution passing through a given point (x0, y0) only if the function is continuous and satisfies certain conditions. None of the provided options mention the function's continuity or satisfy the conditions for the Existence and Uniqueness Theorem. Therefore, none of the options can be determined as having a unique solution passing through the point (2, 4).

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I think the anwser is c -2 and 9

Answer:

2. 55

3. 125

4. 125

Step-by-step explanation:

Answer : The probability of the given event occurring would be 0.75 or 75%.

Explanation :The given problem states that you ordered eighteen burritos, with nine having hot peppers and nine not having hot peppers. However, the restaurant forgot your order. We are supposed to find the probability of the event happening.

Let the probability of getting a burrito with hot peppers be P(h) and the probability of getting a burrito without hot peppers be P(n).

The total number of burritos ordered is 18.

Thus, P(h) + P(n) = 18. We can assume that all burritos are the same.

Thus, P(h) = 9/18 = 0.5 and P(n) = 9/18 = 0.5.

Therefore, the probability of getting an order that is incorrect would be: 1 - (0.5 * 0.5) = 1 - 0.25 = 0.75 or 75%. Therefore, the probability of the given event occurring would be 0.75 or 75%.

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Answer:

4) -3

Step-by-step explanation:

The minimum y value of this absolute value function is -3

The degree of precision of a quadrature formula with an error term of 27" (T) is 2.

To understand why the degree of precision is 2, let's first define what the degree of precision means in the context of quadrature formulas. The degree of precision refers to the highest power of x up to which the formula can integrate exactly. In other words, if a quadrature formula has a degree of precision of 2, it means that the formula can integrate exactly all polynomials of degree 2 or lower.

Now, to determine the degree of precision based on the given error term of 27" (T), we need to consider the approximation error. The error term T represents the maximum absolute difference between the exact integral and the approximate integral obtained using the quadrature formula.

In this case, the error term is given as 27" (T). The presence of the quotation mark (") indicates that the error term is measured in arc seconds. This suggests that the error is related to numerical integration over angles or circular arcs.

Since the error term is specified as 27" (T), we can conclude that the error is proportional to the square of the step size used in the quadrature formula. Therefore, the error term is of the order h^2, where h represents the step size.

Since the error term is of order h^2, it implies that the degree of precision is 2. This means that the quadrature formula can provide an exact result for polynomials of degree 2 or lower.

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The product of the two matrices Q₁Q₂ is orthogonal

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. ... {\displaystyle Q^{\mathrm {T} }Q=QQ^{\mathrm {T} }=I,} where QT is the transpose of Q and I is the identity matrix.

It is said to be an orthogonal matrix if its transpose is equal to its inverse matrix, or when the product of a square matrix and its transpose gives an identity matrix of the same order.

If A is an n*n orthogonal matric, then A*A¹ = A¹*A

Therefore A*A¹ = A¹*A  = 1

This implies that the product Q₁O₂ is orthogonal.

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Answer:

B:y=|x+2| -3

The graph shows the points throughout the equation

Answer:

48

Step-by-step explanation:

( it might be wrong pls dont report me just let me kno y its wrong )

Answer:

a.) 200

b.) -56

If I typed out all my work, it would be one LONG answer. I’m just going to include the steps in an attachment. Hope it’s accurate & helpful!

Answer: 390625

The quiz has 5 choices for each question, so there are 5 ^ 8   ways to answer the quiz questions.

In other words, you can calculate the possible numbers of answers = 5x5x5x5x5x5x5x5 = 390625

Answer: Graph A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Correct on khan

Answer:

a = 18.8

Step-by-step explanation:

With it being a right angle, you can use the pythagorean theorem equation.

[tex]a^{2} + b^{2} =c^{2} \\a^{2} + 18^{2} =26^{2} \\a^{2} +324 = 676\\a^{2} = 676 - 324 \\a^{2} = 352\\a = \sqrt{352} \\a = 18.76 = 18.8[/tex]

Answer:

One example of this can be:

P(x) = (3/2)*(x - 4)*(x - 5)*(x - 5)*(x - 6)

Step-by-step explanation:

A quartic equation is a polynomial of degree 4.

Now, remember that for a polynomial of degree n, with leading coefficient A and zeros {x₁, x₂, ..., xₙ}

The polinomial can be written as:

p(x) = A*(x - x₁)*(x - x₂)*...*(x - xₙ)

In this case we know that we have the zeros 4, 5 and 6.

Notice that this is a polynomial of degree 4 but we have 3 zeros, so one of them may be a double one, i will assume that is the 5.

And we have a leading coefficient that we do not know, let's call it A

Then we can write our polynomial as:

P(x) = A*(x - 4)*(x - 5)*(x - 5)*(x - 6)

Now we know that the polynomial passes through the point (7, 18), then:

P(7) = 18 = A*(7 - 4)*(7 - 5)*(7 - 5)*(7 - 6)

With this equation, we can find the value of A.

18 = A*(7 - 4)*(7 - 5)*(7 - 5)*(7 - 6)

18 = A*12

18/12 = A

(3/2) = A

Then our equation can be:

P(x) = (3/2)*(x - 4)*(x - 5)*(x - 5)*(x - 6)

To determine whether the mean or the median would be higher, or if they would be about equal, we need more specific information about the case or dataset in question.

The mean and median are statistical measures used to describe different aspects of a dataset.

Mean: The mean is the average value of a dataset and is calculated by summing all the values and dividing by the total number of values. The mean is sensitive to extreme values or outliers since it takes into account every value in the dataset.

Median: The median is the middle value in a sorted dataset. If the dataset has an odd number of values, the median is the middle value itself. If the dataset has an even number of values, the median is the average of the two middle values. The median is less affected by extreme values or outliers since it only depends on the order of values.

Without specific information about the dataset, it is difficult to determine whether the mean or the median would be higher or if they would be about equal. Different datasets can exhibit different characteristics, such as skewed distributions or symmetric distributions, which can influence the relationship between the mean and the median.

In general terms, if the dataset is symmetrical and does not contain extreme values, the mean and the median are likely to be about equal. However, if the dataset is skewed or contains extreme values, the mean may be influenced more by these outliers, potentially making it higher or lower than the median.

To provide a more accurate assessment, please provide additional details about the case or dataset under consideration.

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Answer:

Step-by-step explanation:

y=-5x-13

Since we know the value of y we can substitute it in

6x+6(-5x-13)=-6

6x-30x-78=-6

-24x=72

-x=3

x=-3

Now that we know the value of x we can solve Y

y=-5(-3)-13

y=15-13

y=2

Answer:

No

Step-by-step explanation:

a^2 + b^2 = c^2

Since 78 is the largest it will be c.

26^2 + 76^2 = 78^2

676 + 5776 = 6084

6452 does NOT = 6084

Since c^2 is larger it is an obtuse triangle.

Answer:

Step-by-step explanation:

[tex]10^9 \div 10^7\\=\frac{10^9}{10^7} \\=10^9 \times 10^{-7}\\=10^{9-7}\\=10^2\\=100[/tex]

Answer:

is D

Step-by-step explanation:

because it just makes more sense and my teacher told me the answer

The differential equation describing the relationship between the balance B of Rachel's car loan and time t is given by dB/dt = 0.045B - 375.

The equation represents the change in the balance of Rachel's car loan over time. The term dB/dt represents the rate of change of the balance with respect to time. The right-hand side of the equation consists of two terms. The first term, 0.045B, represents the increase in the balance by 4.5% per month. This term accounts for the growth of the loan balance due to accrued interest.

The second term, -375, represents the decrease in the balance by $375.00 each month, which could be the monthly payment towards the loan principal. By subtracting this payment from the growth, the equation captures the net change in the balance. The equation allows us to model and analyze the behavior of the loan balance as time progresses.

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Answer:

V = 603.19 unit^3

or

V = 192π unit^3

Step-by-step explanation:

V = πr^2 *h

V = π(8)^2 *3

V = 603.19 unit^3

or

V = 192π unit^3

Answer:

603.186^3

Step-by-step explanation:

v =  πR2 · h

π8^2 x 3

= 603.186^3

MJH = 120

Let TJH = x

You’re told MJT is 4 times TJH

So you have 4x + x = 120

Simplify: 5x = 120

Divide both sides by 5:

X = 24

TJH = x = 24 degrees.

JT is a bisector so both TJH and TJA are the same. So TJA is also 24 degrees

So MJA = 120 - 24 - 24 = 72

MJA = 72 degrees

Answer

34MJT

Step-by-step explanation:

did it on edge

Answer: [tex]\$16\dfrac{9}{10}[/tex]

Step-by-step explanation:

Given

Hannah had 30 dollars

Money spent on gift A

[tex]8\ \dfrac{7}{10}=\dfrac{8\times 10+7}{10}=\dfrac{87}{10}[/tex]

money spent on gift B

[tex]4\ \dfrac{2}{5}=\dfrac{22}{5}[/tex]

Money spent on gift C

[tex]\Rightarrow \text{Total-Money spent on (A+B)}\\\\\Rightarrow 30-\dfrac{87}{10}-\dfrac{22}{5}=30-\dfrac{87}{10}-\dfrac{44}{10}\\\\\Rightarrow \dfrac{300-87-44}{10}=\dfrac{169}{10}\\\\\Rightarrow \$16\ \dfrac{9}{10}[/tex]

Answer:

I don't think it is correct.

Step-by-step explanation:

Square root just means half of a number. If you square this number, it just goes back to it's original form, just without the square root sign. But however, You must square the 10 at the end of the equation as well. This solution is not correct.

f1 is neither injective nor surjective.

f2 is bijective (both injective and surjective).

f3 is injective, but not surjective.

The given sets and their functions are f1 = {(a, c), (b, a),(c,d),(d,b)}, f2 = {(a, b), (b, d), (c, d),(d, c)}, and f3 = {(a, b), (b, b), (c, b),(d, b)}. To determine whether each function is injective, surjective, and/or bijective, the following terms are to be kept in mind:

- A function is injective if every element in the domain has a unique pre-image in the range.
- A function is surjective if every element in the range has at least one pre-image in the domain.
- A function is bijective if it is both injective and surjective.

Function f1 = {(a, c), (b, a), (c, d), (d, b)} is neither injective nor surjective. This function is not injective since it maps both b and d to a, thus making two elements in the domain map to one element in the range. Similarly, it is not surjective because neither b nor d has a pre-image in the range. For example, no element in the domain maps to b or d.

Function f2 = {(a, b), (b, d), (c, d), (d, c)} is bijective. It is injective since every element in the domain has a unique pre-image in the range. Also, it is surjective since every element in the range has at least one pre-image in the domain.

Function f3 = {(a, b), (b, b), (c, b), (d, b)} is injective and not surjective. This function is injective since every element in the domain has a unique pre-image in the range. However, it is not surjective since only b has a pre-image in the domain. Hence, the negative answer is because the elements in the domain do not have any other pre-image apart from b.

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Answer:

5

Step-by-step explanation:

Answer:

5 centimeters

Step-by-step explanation:

You have to look at where it says 2 inches, and follow the line up to where the red stops and see how many centimeters it crosses

Answer:

Step-by-step explanation:

-6*p ---> -6*5=-30

23 - 25<---5*5

p is 5

-30 - (-2)=-28