a
Solve for a.
13
68°
83%
a = [?
Round your final answer
to the nearest tenth.

The laplace transform of f(t) is \(F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}\) and it's values exists for \(s=w\pm\sqrt{3}wi\).

Given,

\(f(t)=sin^2(wt)\\\\\therefore sin^2x=\frac{1-cos2x}{2}\\\\f(t)=\frac{1-cos2wt}{2}\)

applying laplace transform on both sides,

\(L[f(t)]=L[\frac{1-cos2wt}{2}]\\\\F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}\)

The range for values of s for which F(s) exists is when F(s)≥0

\(\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)} \geq0\\\\\frac{1}{2s} \geq\frac{2w}{2(s^2+4w^2)}\\\\2(s^2+4w^2) \geq 2sw\\\\s^2-2sw+4w^2 \geq0\)

using formula to find roots,

\(s=\frac{-(-2w)\pm\sqrt{(-2w^2)-4(4w^2)}}{2}\\\\s=\frac{-(-2w)\pm\sqrt{(12w^2}}{2}\\\\s=w\pm\sqrt{3}wi\)

Thus,  the laplace transform of f(t) is \(F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}\) and it's values exists for \(s=w\pm\sqrt{3}wi\).

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Answer:

SEE BELOW

Step-by-step explanation:

INTERRIOR ANGLES

3.

∠A + ∠B + ∠C = 180

(180 - 103) + (3x - 14) + (3x + 9) = 180

6x = 180 - 77 + 14 - 9

x = 108 / 6

x = 18

m∠ACB = (3x - 14)

             = 3(18) - 14

             = 40

m∠ABC = (3x + 9)

              = 3(18) + 9

              = 63

-------------------------------

INTERRIOR ANGLES

4.

∠A + ∠B + ∠C = 180

(180 - 97) + (2x + 2) + (14x - 1) = 180

16x = 180 - 83 - 2 + 1

x = 96 / 16

x = 6

m∠BCA = 2x + 2

             = 2(6) + 2

             = 14

m∠ABC = 14x - 1

             = 14(6) - 1

             = 83

-------------------------------

EXTERIOR ANGLES

5.

∠B

180 - 15x + 20

15x = 180 + 20

   x = 200/15

   x = 13.33

∠C

180 - 9x + 10  

9x = 190

 x = 190/9

 x = 21.11

∠E

180 - 17x + 2

17x = 182

  x = 182/17

  x = 10.706

m∠BEF = 17x + 2

             = 17 (10.706) + 2

             = 184

m∠ABC = 15x + 20

             = 15(15.33) + 20

             = 220

-------------------------------

EXTERIOR ANGLES

6.

first solve x by adding all the interior angles = 180

∠B + ∠E + ∠C = 180

2x + x + 93 = 180

3x = 180 - 93

x = 87/2

x = 43.5

m∠BEC = 360 - x

             = 360 - 43.5

             = 316.5

m∠ABC = 180 - 2x

             = 180 - 2(43.5)

             = 93

Answer:

x = - \(\frac{4}{5}\)

Step-by-step explanation:

Given

5x - 2 = 25x + 14 ( subtract 25x from both sides )

- 20x - 2 = 14 ( add 2 to both sides )

- 20x = 16 ( divide both sides by - 20 )

x = \(\frac{16}{-20}\) = - \(\frac{4}{5}\)

Answer:

42%

Step-by-step explanation:

The first step is to calculate the difference in the number of fishes from the beginning of the day to the end of the day.

90 -52

= 38 fishes

Therefore the percent decrease can be calculated as follows

= 38/90 × 100

= 0.422 × 100

= 42.2 %

= 42% ( to the nearest cent)

Answer:

-4

Step-by-step explanation:

I hope this helps! if it does please please mark as brainliest!

Answer:

I think 15 I am sure

Step-by-step explanation:

The number of insects consumed by pitcher plants is essential for their survival and growth, and it is fascinating to observe this unique aspect of their carnivorous nature.

Pitcher plants are carnivorous plants that trap and digest insects to obtain nutrients. The exact number of insects consumed by pitcher plants in a month can vary depending on factors such as the species of pitcher plant, its size, and the local environment. However, studies have estimated that a single pitcher plant can consume anywhere from a few dozen to hundreds of insects per month.

The mechanism of the pitcher plant is quite interesting. Insects are lured into the plant by its color and sweet-smelling nectar. Once inside, the insect becomes trapped and is unable to escape due to the slippery inner walls of the pitcher. The plant then secretes digestive enzymes that break down the insect's tissues, allowing the plant to absorb the nutrients.

Interestingly, not all insects are consumed by pitcher plants. They tend to prefer smaller insects such as ants and flies, but larger insects such as bees and wasps may occasionally become trapped as well.

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Answer:

Step-by-step explanation:

320000 is your answer

The true statements for all invertible n×n matrices A and B are: B. A+A⁻¹ is invertible, C. (In+A)(In+A⁻¹)=2In+A+A⁻¹, F. AB=BA.

A. (A+B)² = A² + AB + BA + B². This equation is only true for certain matrices, and not all invertible matrices.

B. This statement is true for all invertible matrices A. The sum of an invertible matrix and its inverse is always invertible.

C. This statement is true for all invertible matrices A. It is a special case of the Sherman-Morrison formula.

D. This statement is not true for all invertible matrices A. For example, the matrix A = 0 is invertible, but A⁶ is not invertible.

E. This statement is not true for all invertible matrices A. For example, the matrix A = -1 is invertible, but (A+A⁻¹)⁹ = 2⁹ - 2⁷+ 2⁵ - 2³+ 2 = 506.

F. This statement is true for all invertible matrices A and B. It is known as the commutativity property of invertible matrices.

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Complete Question : Select all statements below which are true for all invertible n×n matrices A and B

A. (A+B)^2=A^2+B^2+2AB

B. A+A^−1 is invertible

C. (In+A)(In+A^−1)=2In+A+A^−1

D. A^6 is invertible

E. (A+A^-1)^9=A^9+A^−9

F. AB=BA

Answer:

\(y = \frac{10x - 1}{45} \\ \)

Step-by-step explanation:

\( \frac{10x - 1}{3y} = 15 \\ 10x - 1 = 15 \times 3y \\ 10x - 1 = 45y \\ \frac{10x - 1}{45} = y \\ \)

Step-by-step explanation:

1x +1 +1 +6x > 3 ( 1x - 4) - 1(1x - 4)

7x +2 > 3x - 12 - 1x +4

7x - 3x +1x > - 2-12+4

5x > - 10

x > - 2

Answer:

y = -2x - 5

Step-by-step explanation:

y = is a standard for any equation, as is the use of x as a variable, unless something else is specified.

-2x is the way to denote a slope of -2, and -5 gives you the y-intercept of 5. One point on this line would be (0, -5).

The equation in terms of x (rs) is rs + 3 * rs = 32. By solving this equation, we found that rs = 8 and st = 24.

To find rs and st, we need to write an equation in terms of x using the given information and then solve for x.

Let's suppose that rs and st are two line segments, and x represents the length of rs. To find the lengths of rs and st, we can set up an equation based on the given information.

From the problem, we know that the length of st is three times the length of rs. This can be expressed as:

st = 3 * rs

Additionally, the total length of rs and st is 32 units. Mathematically, this can be represented as:

rs + st = 32

Now, we can substitute the value of st from the first equation into the second equation:

rs + 3 * rs = 32

Simplifying this equation, we have:

4 * rs = 32

To solve for rs, we divide both sides of the equation by 4:

rs = 32 / 4

rs = 8

Hence, we have found that rs is equal to 8 units.

To find the length of st, we can substitute the value of rs into the first equation:

st = 3 * rs

st = 3 * 8

st = 24

Therefore, the length of st is 24 units.

In summary, the equation in terms of x (rs) is rs + 3 * rs = 32. By solving this equation, we found that rs = 8 and st = 24.

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Answer:

18 units to the right.

Step-by-step explanation:

Hope this helps!

Answer:

There are 6 points on a coordinate plane. The points are (negative 5, 0), (negative 4, 1), (negative 3, 4), (1, negative 2), (2, 4), (5, negative 3).

A domain: {–5, –4, –3, –2, 0, 1, 2, 3, 4, 5}

B domain: {–3, –2, 0, 1, 4}

C domain: {–5, –4, –3, 1, 2, 5}

D domain: {(–5, 0), (–4, 1), (–3, 4), (1, –2), (2, 4), (5, –3)}

Answer:

what can i help u with

Step-by-step explanation:

Option C is correct that is domain is {-5,-4,-3,1,2,5}Explanation:The domain is the values that x will take

Answer:

If the correction of 6 * 6X is accurate then I hope this is the answer.

Step-by-step explanation:

6(6x)+3x=3+3x+5

1. First multiply 6 by 6

36x+3x=3+3x+5

2. Then add 36X and 3X

39x=3+3x+5

3. After that add 3 and 5

39x=3x+8

4. Subtract 3x from both sides of the equation.

39x−3x=8

5. Subtract 3x from 39x

36x=8

6. Divide

36X. 8

______. = ______

36. 36

7. 36X and 36 cancel out because they

are common factors

8. The common factor between 8 and 36 is 4.

S you are left with. 2

X= _____

9

_

9. If you would like the decimal, than it is, X = 0.2

the new coordinates of the room are Q(2.3125, 4.125), R(7.3125, 4.125), S(7.3125, 6.125), and T(2.3125, 6.125). the dimensions of the new room on the blueprint are 5.78125 inches by 2 inches and in feet 0.48 feet by 0.17 feet.

To find the new coordinates of the room, we can first calculate the dimensions of the original room and then increase them by 25%. The length of the room is the distance between points R and S, which is:

√(7-2)² + (4-4)² = 5 units

The width of the room is the distance between points Q and T, which is:

√(2-2)² + (6-4)² = 2 units

To increase the dimensions of the room by 25%, we can multiply the length and width by 1.25.

The new length is: 5 × 1.25 = 6.25 units

The new width is: 2 × 1.25 = 2.5 units

To find the new coordinates of the room, we can add half of the increase in each dimension to the original coordinates.

The new coordinates of Q are: (2 + 0.625/2, 4 + 0.25/2) = (2.3125, 4.125)

The new coordinates of R are: (7 + 0.625/2, 4 + 0.25/2) = (7.3125, 4.125)

The new coordinates of S are: (7 + 0.625/2, 6 + 0.25/2) = (7.3125, 6.125)

The new coordinates of T are: (2 + 0.625/2, 6 + 0.25/2) = (2.3125, 6.125)

Therefore, the new coordinates of the room are Q(2.3125, 4.125), R(7.3125, 4.125), S(7.3125, 6.125), and T(2.3125, 6.125).

To find the dimensions of the new room in inches on the blueprint, we can use the Pythagorean theorem: The new length is:

√(7.3125-2.3125)² + (4.125-4.125)² = 5.78125 units

The new width is: √(7.3125-7.3125)² + (6.125-4.125)² = 2 units

Therefore, the dimensions of the new room on the blueprint are 5.78125 inches by 2 inches.

To find the dimensions of the new room in feet in the new house, we can convert the dimensions to feet by dividing by 12:

The new length is: 5.78125 inches / 12 inches/ft = 0.48 ft

The new width is: 2 inches / 12 inches/ft = 0.17 ft

Therefore, the dimensions of the new room in the new house are 0.48 feet by 0.17 feet.

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Complete Question

A rectangular room has coordinates Q (2, 4), R(7, 4), 5 (7, 6), and T(2, 6) on the blueprint. The homeowner wants the dimensions of this room to be 25% larger. What are the coordinates of the new room? What are the dimensions of the new room, in inches, on the blueprint? What will the dimensions of the new room be, in feet, in the new house?

The potential energy of the King Air 200 aircraft is approximately 420,014,400,000 Nm.

To find the potential energy of the King Air 200 aircraft, we need to use the formula:

Potential Energy = Weight * Altitude

Given that the weight of the aircraft is 12,500 lb and the altitude is 25,000 ft, we can calculate the potential energy as follows:

Potential Energy = 12,500 lb * 25,000 ft

Now, let's convert the units to a more suitable form. Since the potential energy is usually measured in joules or foot-pounds, we'll convert the units accordingly.

1 lb = 4.448 N (approximately) 1 ft = 0.3048 m (approximately)

Using these conversion factors, we can convert the units:

Potential Energy = (12,500 lb * 4.448 N/lb) * (25,000 ft * 0.3048 m/ft) Potential Energy ≈ 55,120,000 N * 7,620 m

Finally, we can calculate the potential energy:

Potential Energy ≈ 420,014,400,000 Nm

Therefore, the potential energy of the King Air 200 aircraft is approximately 420,014,400,000 Nm.

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The quantity theory of money is an economic theory that suggests a direct relationship between the money supply (M) and the price level (P) in an economy

According to this theory, the equation MV = PY holds, where V represents the income velocity of money and Y represents real output. This equation states that the total value of money spent in an economy (MV) is equal to the total value of goods and services produced (PY).

The quantity theory of money assumes that the velocity of money (V) and real output (Y) are relatively stable over time and that changes in the money supply (M) primarily affect changes in the price level (P). It implies that an increase in the money supply will lead to inflation, as there is more money chasing the same amount of goods and services.

Therefore, the correct answer is "static quantity theory of money," which refers to the idea that the relationship between money, velocity, price level, and real output is static and can be represented by the equation MV = PY.

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Answer:

Last one

Step-by-step explanation:

The slope intercept form is: y=mx +b

m=the slope and b is the y intercept

so it would be the last one

Answer:

Length: 12.39313902 cm

Width: 10.89313102 cm

Step-by-step explanation:

Check the attachment.

Answer:

Casey Bought 6 bags of chips

Step-by-step explanation:

If each sandwich costs 3 times the amount of a bag of chips and the sandwich is 6 dollars, the chips are 2 dollars. Casey bought 5 sandwiches and spent $30 dollars on sandwiches. Since the total was $42 dollars you have $12 dollars left to get your total of $42. 2x6 = 12 so therefore Casey bought 6 bags of chips.

Answer:

4

Step-by-step explanation:

Answer:

4 7/12

Step-by-step explanation:

A set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

What is a combination of reflections?

Combination of Two Reflections. A point or object once reflected can further be reflected to form a new image. The axes of these reflections may be parallel to each other or they intersect each other at a point.

Given the coordinates of hexagon ABCDEF, it can be determined that a set of reflections that would carry the hexagon onto itself would be a combination of reflections over the x-axis and y-axis.

One possibility would be to reflect over the x-axis, then reflect over the y=x line, and finally reflect over the x-axis again.

This would take the hexagon from its original position to itself.

Another possibility would be to reflect over the y = x line, then reflect over the x-axis, and finally reflect over the y-axis.

This would also take the hexagon from its original position to itself.

Hence, a set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

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Barton should use a luggage scale to get the most accurate and appropriate measurement of his packed suitcase before he leaves to catch a flight. A luggage scale is a compact and portable device that is designed specifically to weigh luggage. Using a luggage scale is easy and convenient as it allows travelers to weigh their bags accurately, ensuring that they are within the airline's weight limit. To use a luggage scale, Barton should follow these simple steps:

Step 1: Attach the luggage strap Barton should attach the luggage strap to the handle of his suitcase.The strap should be attached in such a way that it can support the weight of the suitcase without slipping or coming off.

Step 2: Turn on the luggage scale Barton should turn on the luggage scale and wait for it to calibrate. This usually takes a few seconds. Once the scale is calibrated, it will display a zero reading.

Step 3: Lift the suitcase Barton should lift the suitcase by the luggage strap until it is off the ground. The luggage scale will display the weight of the suitcase on its digital display. This reading is the weight of the suitcase including all the contents inside.

Step 4: Check the weight If the weight of the suitcase is less than 50 pounds, Barton can go ahead and catch his flight without worrying about any extra charges. If the weight of the suitcase is more than 50 pounds, Barton will have to remove some items from the suitcase or pay the extra fee charged by the airline.

Therefore, using a luggage scale is the most accurate and appropriate method for travelers like Barton to measure their suitcase weight before boarding their flight.

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Answer:

use a standard digital bathroom scale.

Step-by-step explanation:

Answer: $1.25 Per Roll

Step-by-step explanation:

(14,17.50) and (16,20)

True, it is possible for an integer linear program to have more than one optimal solution.

In an integer linear program, the objective is to optimize a linear objective function subject to linear constraints and integer variable restrictions. While it is common for linear programs to have a unique optimal solution, in the case of integer linear programs, it is possible to have multiple optimal solutions.

This occurs when there are multiple feasible solutions that achieve the same optimal objective value. In such cases, any of the feasible solutions that satisfy the optimality conditions can be considered optimal. Therefore, it is true that an integer linear program can have more than one optimal solution.


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Answer:

Lateral surface area=perimeter×Height

Total surface area=Perimeter (p)×Height(h)+2×Area of cross section

Hey there! I'm happy to help!

Let's write this equation out.

2/3+1/3x=2x

We want to get all of the variables on the left side and all the numbers on the right side so we can see what number x is equal to. First, Let's subtract 2/x from both sides.

2/3+1/3x-2x=0

We subtract 2/3 from both sides.

1/3x-2x=-2/3

We combine our x values.

-5/3x=-2/3

We divide both sides by -5/3.

x=-5

Have a wonderful day and keep on learning! :D

Answer:

for the m = -1

b= -3

Type of slope= negative

Step-by-step explanation:

hope this helps