Find m2 if m3 = 125 and m4 = 23

The percentage change in frequency is 0%.Hence, the natural frequency of torsional vibration of the custen is given by f = 25.7 / L₀^(1/2) and the percentage change in frequency is 0%.

We are given that:

Total moment of inertia of moving parts = I = 1 kgm²

Moment of inertia of air-screw = I = 18 kgm²

Outer diameter of hollow shaft = D₀ = 80 mm

Inner diameter of hollow shaft = Dᵢ = 35 mm

Length of hollow shaft = L = 0.30 m

Stiffness of the crank-throw = K = 2.5 × 10⁴ Nm/rad

Shear modulus of elasticity = G = 83000 N/mm²

We need to calculate the natural frequency of torsional vibration of the custen.

The formula for natural frequency of torsional vibration is: f = (1/2π) [(K/L) (J/GD)]^(1/2)

Where, J = Polar moment of inertia

J = (π/32) (D₀⁴ - Dᵢ⁴)

The formula for equivalent length of hollow shaft is given by:

q₁ = q₁₁ + q₁₂

Where, q₁₁ = (π/32) (D₀⁴ - Dᵢ⁴) / L₁q₁₂ = (π/64) (D₀⁴ - Dᵢ⁴) / L₂

L₁ = length of outer diameter

L₂ = length of inner diameter

For the given shaft, L₁ + L₂ = L

Let L₁ = L₀D₀ = D = 80 mm

Dᵢ = d = 35 mm

So, L₂ = L - L₁= 0.3 - L₀...(1)

For the given crank-throw, q₁ = (π/32) (D⁴ - d⁴) / L, where D = 80 mm and d = 80 mm

Hence, q₁ = (π/32) (80⁴ - 35⁴) / L

Therefore, q₁ = (π/32) (80⁴ - 35⁴) / L₀...(2)

From the formula for natural frequency of torsional vibration, f = (1/2π) [(K/L) (J/GD)]^(1/2)

Substituting the values of K, J, G, D and L from above, f = (1/2π) [(2.5 × 10⁴ Nm/rad) / (L₀) ((π/32) (80⁴ - 35⁴) / (83000 N/mm² (80 mm)³))]^(1/2)f = (1/2π) [(2.5 × 10⁴ Nm/rad) / (L₀) (18.12)]^(1/2)f = 25.7 / L₀^(1/2)...(3)

Now, if we assume that the air-screw mass is infinite, then the moment of inertia of the air-screw is infinite.

Therefore, the formula for natural frequency of torsional vibration in this case is:

f = (1/2π) [(K/L) (J/GD)]^(1/2)Substituting I = ∞ in the above formula, we get:

f = (1/2π) [(K/L) (J/GD + J/∞)]^(1/2)f = (1/2π) [(K/L) (J/GD)]^(1/2)f = 25.7 / L₀^(1/2)

So, in this case also the frequency is the same.

Therefore, the percentage change in frequency is 0%.Hence, the natural frequency of torsional vibration of the custen is given by f = 25.7 / L₀^(1/2) and the percentage change in frequency is 0%.

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Answer:

tan θ = 4.5

Step-by-step explanation:

tan = opposite/adjacent

The opposite of θ is 45 cm long

The adjacent of θ is 10 cm long

tan θ = 45 / 10 = 4.5

The solution is: the value of tan is : tan θ = 4.5.

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

here, we have,

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

Here, we have,

we know,

tan = opposite/adjacent

from the given diagram, we get,

given that,

The opposite of θ is 45 cm long

The adjacent of θ is 10 cm long

so, we get,

tan θ = 45 / 10

        = 4.5

Hence, The solution is: the value of tan is : tan θ = 4.5.

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Answer: 25

Step-by-step explanation: He scored 25 in the game

To find the roots of a third-degree polynomial, also known as a cubic polynomial, we can use a method called factoring or apply the cubic formula.

The first step is to check if there are any common factors that can be factored out. Next, we can use the rational root theorem to determine potential rational roots. By applying synthetic division or long division, we can divide the polynomial by the potential roots to see if they are indeed roots.

If a rational root is found, we can then use synthetic division to factor out the corresponding quadratic equation. Finally, we can solve the quadratic equation using methods like factoring, completing the square, or using the quadratic formula to find the remaining roots.

It's important to note that not all cubic polynomials can be easily factored or solved algebraically. In such cases, numerical methods or approximation techniques may be used to find the roots.

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To find the roots of a third degree polynomial, you can follow these steps: 1) Check for rational roots using the Rational Root Theorem. 2) Use synthetic division to divide the polynomial by a linear factor. 3) Factor the resulting quadratic equation. 4) Solve for the roots by setting each factor equal to zero.

To find the roots of a third degree polynomial, we can follow these steps:

Remember, the Fundamental Theorem of Algebra states that every polynomial equation of degree n has exactly n complex roots, counting multiplicities.

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Answer:

20% - $80

40% - $160

60% - $240

80% - $320

100% - $400

At $360, she will have saved up 90% of her goal.

Answer:

The percent decrease in the price of shirt is 27.78%

Step-by-step explanation:

The percent decrease is the decrease in the price of a product or good.

Given

Original Price = $45

Decreased price = $32.50

Percentage decrease is calculated by using the formula

\(Percentage\ decrease = \frac{decrease}{Original\ price} *100\\\)

And the decrease is calculated as:

\(Decrease = Original\ price - Reduced\ price\)

So,

\(Decrease = 45-32.50 = 12.5\)

Putting the values in the formula for percent decrease

\(Percent\ decrease = \frac{12.50}{45} *100\\=0.2777..*100\\= 27.77..\)

Rounding off to nearest hundredth: 27.78%

Hence

The percent decrease in the price of shirt is 27.78%

Answer:

The ratio of girls to total students is 12:30, which can be simplified to 2:5.

Step-by-step explanation:

You can express the ratio in different ways by using the same numbers, for example, you could say that for every 2 girls, there are 5 total students, or that for every 5 total students, 2 of them are girls.

Calories from 20 grams of fat will be 180 .

Given,

Dinner with 20 grams of fat .

Now,

Carbohydrates provide 4 calories per gram, protein provides 4 calories per gram, and fat provides 9 calories per gram.

So,

1 gram fat ⇒ 9 calories

20 gram fat ⇒ 20*9

Thus 20 gram of fat in dinner will provide 180 calories .

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Answer:

7.5 × 10\( {}^{2} \) (scientific notation)

Step-by-step explanation:

➟ 750 = 7.5 × 10\( {}^{2} \) (scientific notation)

Answer:

See Explanation

Step-by-step explanation:

\(25x + 30y = 340\\y = 2x\\\)

x=number of hours Isaiah worked.

y=number of hours Cooper worked

The matrix of \(t\) relative to the basis \(b'\) is \(A' = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\).

\(\textbf{To find the matrix of } t \textbf{ relative to the basis } b', \textbf{we have to follow some steps. The steps are described below:}\)

First, we have to find the images of basis vectors under the transformation \(t\). \(t(-1,1) = (-9,7)\) and \(t(1,-5) = (-37,43)\).

Represent the image vectors of the basis in the standard basis. We use these vectors as columns in the matrix of \(t\) in the basis \(b'\).

\((-9,7) = -9(1,0) + 7(0,1) = (-9,7) = -9(-1,1) + 7(1,-5)\)

\((-37,43) = -37(1,0) + 43(0,1) = (-37,43) = -37(-1,1) + 43(1,-5)\)

Hence, we can write the following equation: \(A[x]_{b'} = [x]_S\)

Where \(A[x]_{b'}\) is the main answer in the form of a matrix, and \([x]_S\) is the coordinate of \([x]_{b'}\) with respect to the standard basis.

Now, we will write the equations with the coordinates of the basis vectors of \(b'\).

\(A[1,0] = [-9, -37]\) and \(A[0,1] = [7, 43]\)

Now we will write the matrix of \(A\) as follows:

\(A = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\)

Thus, the matrix of \(t\) relative to the basis \(b'\) is \(A' = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\).

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Answer:

3

Step-by-step explanation:

Answer:

55.50

Step-by-step explanation:

Answer:

can you provide the table?

Step-by-step explanation:

Answer:

detailed answer

Step-by-step explanation:

answer detailed

Answer:

uhhh ok

Step-by-step explanation:

Total 241 adult ticket and 220 student ticket are sold.

system of equations, orsimultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.

a + s = 461       or    s = 461 -a

Value of student tickets sold = s × 3   = 3 × (461-a)

Value of adult ticket sold =  4 a              

Summed they total 1624

System of equations :

s = 461-a3 (461-a) + 4a

  = 16241383 -3a +4a

  = 1624a

  = 241    

then  s = 461 -a = 220 ticket

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In the extension field Z₂(α), where α is a zero of the irreducible polynomial p(x) = x³ + x² + 1 over Z₂, every nonzero element can indeed be expressed as a power of α. This is because α satisfies the equation α³ + α² + 1 = 0, which implies that α³ = -α² - 1.

Thus, for any nonzero element β in Z₂(α), we can express β as β = αⁿ, where n is an integer.

To verify that every nonzero element of Z₂(α) can be expressed as a power of α, we first need to find the values of α and the elements of Z₂(α).

Given the irreducible polynomial p(x) = x³ + x² + 1 over Z₂, we are looking for a zero (root) of this polynomial in an extension field of Z₂.

To find the zeros of p(x), we can systematically substitute values of x from Z₂ into the polynomial and check which ones result in p(x) = 0. However, in this case, we can observe that there are no zeros in Z₂ for this polynomial. Therefore, p(x) does not have any roots in Z₂ or its extension fields.

Since p(x) has no roots, it means that α is not defined in Z₂ or its extension fields. Consequently, Z₂(α) is not a valid field, and it is not possible to express nonzero elements of Z₂(α) as powers of α.

In summary, for the irreducible polynomial p(x) = x³ + x² + 1 over Z₂, there are no zeros or roots, and hence, the concept of α and Z₂(α) does not apply.

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Since 3x > 24, we can find the solution by dividing both sides of the inequality by 3, which gives x > 8.

On the number line, we can represent this solution as a shaded region to the right of 8, since any value of x greater than 8 would satisfy the inequality. The number 8 itself is not included in the solution because the inequality is strict (i.e., "greater than" rather than "greater than or equal to").

The number line would look like:

<----[=======o------------------------)---->

8 infinity

The open circle at 8 indicates that 8 is not included in the solution, while the shaded region to the right of 8 indicates all values of x that satisfy the inequality. The symbol "infinity" indicates that the solution continues indefinitely to the right.

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To calculate a three-month moving average for monthly forecasting, you need to follow these steps: Gather the historical data, Determine the time period, Calculate the moving average, Repeat the process.

Gather the historical data: Collect the monthly data for the specific variable you want to forecast. For example, if you want to forecast sales, gather the sales data for the past several months.

Determine the time period: Decide on the time period for your moving average. In this case, it is three months.

Calculate the moving average: Add up the values for the variable you are analyzing over the past three months and divide the sum by three to get the average. This will be your moving average value for the third month.

Repeat the process: Shift the time period by one month and calculate the moving average for the new three-month period. Continue this process for each subsequent month, updating the time period and calculating the moving average accordingly.

For example, let's say you have the following sales data for the past six months:

Month 1: 100 units

Month 2: 120 units

Month 3: 110 units

Month 4: 130 units

Month 5: 140 units

Month 6: 150 units

To calculate the three-month moving average for Month 4, you would add up the sales values for Month 2, Month 3, and Month 4 (120 + 110 + 130 = 360) and divide it by three to get an average of 120 units. Repeat this process for each subsequent month to obtain the moving average values for your forecast.

Note that the number of data points you include in the moving average calculation and the frequency of the data (monthly in this case) can be adjusted based on your specific needs and the nature of the data.

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The value of y in the triangle is 64.

What is Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices.

We need to find the value of y,

The other two angles of triangle are 79⁰ and 37⁰

We have to use angle sum property of triangle

The sum of three angles of a triangle is 180⁰

y+ 79⁰+37⁰=180⁰

y+116⁰=180⁰

Subtract 116⁰ from both sides

y=180⁰- 116⁰

y=64⁰

Hence, the value of y in the triangle is 64.

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Answer:

z is -2

Step-by-step explanation:

x = -5 y = 4

<----------------------------------------->

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Z is between x and y but is 3 times the lenght of x&z

so jumb from -5 to -3 thats one, however jumb from -2 to 0 that is 1, and form 0 to 2 that is 2, and from 2 to 4 that is 3.

Answer:

Marie Skłodowska Curie (born Maria Salomea Skłodowska (Polish: [ 7 November 1867 – 4 July 1934), was a Polish and naturalized-French physicist and chemist who conducted pioneering research on radioactivity. As the first of the Curie family legacy of five Nobel Prizes, she was the first woman to win a Nobel Prize, the first and the only woman to win the Nobel Prize twice, and the only person to win the Nobel Prize in two scientific fields. She was the first woman to become a professor at the University of Paris in 1906.[4]

Step-by-step explanation:

Answer:

  2

Step-by-step explanation:

The average rate of change from x=a to x=b is found from ...

  m = (f(b) -f(a))/(b -a)

For the points (x, f(x)) = (2, -3) and (3, -1), the average rate of change from x=2 to x=3 is ...

  m = (-1 -(-3))/(3 -2) = 2/1 = 2

The average rate of change on the interval is 2.

Answer:

86 degrees

Step-by-step explanation:

180-135=45

49+45=94

180-94=86

The formula distance = speed x time must be used to calculate the duration of a marathon as a function of the runner's average speed.

 1: List the known data. For example, a marathon is 13.1 miles long, and an average runner moves at s miles per hour.

2 :Rearrange the equation to solve for time in Step 2: Time = Speed/Distance

3: Enter the known numbers for distance and speed into the equation: time = 13.1 miles per second.

4: If necessary, simplify the equation. The units of miles will cancel out because the time is measured in hours and the speed in miles per hour, therefore the ultimate unit of time will be hours.

  The final answer  is t = 13.1/s, which expresses the duration of a marathon (in hours) as a function of the runner's average speed (in miles per hour).

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Answer:20%

Step-by-step explanation:Based on the given conditions, formulate:( 35 - 28 ) divided by 35

Calculate the sum or difference: 7/ 35

Cross out the common factor: 1/5

Multiply a number to both the numerator and the denominator: 1/5 x 20/20

Write as a single fraction: 20/5x20

Calculate the product or quotient:20/100

The percent error of Hector’s guess will be 25%.

A relative number reflecting the hundredth part of any amount. One percent (symbolised 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Hector's prediction is 35 stuffed animals. There are a total of 28 stuffed animals.

The percent error is calculated as,

P = [(35 - 28) / 28] x 100

P = (7 / 25) x 100

P = 0.25 x 100

P = 25%

The percent error of Hector’s guess will be 25%.

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Step-by-step explanation:

it helps to draw a picture

use pythagorean thm

x =

\(x = \sqrt{ {12}^{2} + {35}^{2} } \)