Write an explicit and recursive rule for t(n)=3,3/2,3/4,3/8

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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The expected value of the continuous random variable V is 5. The expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.

To calculate the expected value of a continuous random variable V with a given probability density function (PDF), we integrate the product of V and the PDF over its entire range.

The PDF of V is defined as:

f(v) = 6/24 = 0.25 for 3 ≤ v ≤ 7, and 0 otherwise.

The expected value of V, denoted as E(V), can be calculated as:

E(V) = ∫v * f(v) dv

To find the expected value, we integrate v * f(v) over the range where the PDF is non-zero, which is 3 to 7.

E(V) = ∫v * (0.25) dv, with the limits of integration from 3 to 7.

E(V) = (0.25) * ∫v dv, with the limits of integration from 3 to 7.

E(V) = (0.25) * [(v^2) / 2] evaluated from 3 to 7.

E(V) = (0.25) * [(7^2 / 2) - (3^2 / 2)].

E(V) = (0.25) * [(49 / 2) - (9 / 2)].

E(V) = (0.25) * (40 / 2).

E(V) = (0.25) * 20.

E(V) = 5.

Therefore, the expected value of the continuous random variable V is 5.

The expected value represents the average value or mean of the random variable V. It is the weighted average of all possible values of V, with each value weighted by its corresponding probability. In this case, the expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.

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Answer:

x = - 2

Step-by-step explanation:

using the rules of exponents

\(a^{m}\) ×\(a^{n}\) = \(a^{(m+n)}\)

\(\frac{a^{m} }{a^{n} }\) = \(a^{(m-n)}\)

given

\(\frac{9^{3}(9^{1}) }{9^{6} }\)

= \(\frac{9^{(3+1)} }{9^{6} }\)

= \(\frac{9^{4} }{9^6} }\)

= \(9^{(4-6)}\)

= \(9^{-2}\) = \(9^{x}\)

then equating exponents

x = - 2

Answer:

slope is 2

Step-by-step explanation:

the equation of linear is y=mx+b, where m is the slope

therefore, m=2 which means the slope is 2

Answer:the slope is 2

Step-by-step explanation:

the equation y=mx+b represents m as the slope.

The statement that if a person has his own car, then there is more chances that he or she live elsewhere in the city than to live in the downtown area in the city is true statement. So, the option(a) is right answer for problem.

We have, a sample of sample size, n

= 200

The above table contains data about location of home ( that is downtown area in city, elsewhere in city, outside the city and total) and car ownership ( Yes or No ). Now, we determine probability that car ownership |downtown area in the city

= 10/70

= 1/7

probability that car ownership | elsewhere in the city = 15/70

= 3/14

Probability that car ownership | outside in the city = 35/60 = 7/12

As we see, 1/7 < 3/14 < 7/12

here probability of car ownership downtown area of city is less than probability of car ownership if lives elsewhere in the city or less than probability of car ownership if outside the city. So, statement (a) is true in this case. Also consider,

Probability that no car ownership | downtown area in the city = 60/70 = 6/7

Probability that no car ownership | elsewhere in the city = 55/70 = 11/14

Probability that no car ownership|outside the city = 25/60 = 5/12

As we see probabilities, 5/12 < 11/14 < 6/7

Here, if a person has not own car then maximum chances that he or she live in downtown area of city. So, statement (b) is false.

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Complete question:

The above figure complete the question. A local company is interested in supporting environmentally friendly initiatives such as carpooling among employees. The company surveyed all of the 200 employees at the downtown offices. Employees responded as to whether or not they own a car and to the location of the home where they live. The results are shown in the table above. Which of the following statements about a randomly chosen person from these 200 employees is true? responses

a) if the person owns a car, he or she is more likely to live elsewhere in the city than to live in the downtown area in the city.

b) if the person does not own a car, he or she is more likely to live outside the city than to live in the city (downtown area or elsewhere).

c) the person is more likely to own a car if he or she lives in the city (downtown area or elsewhere) than if he or she lives outside the city.

d) the person is more likely to live in the downtown area in the city than elsewhere in the city.

e) the person is more likely to own a car than not to own a car.

Answer:

Step-by-step explanation:

The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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Answer:

D is 107 and E is 38

Step-by-step explanation:

20x+40=180

20x=140

X=140/20

x=7

M<A=5(7)+3

38

m<a=m<e

15(7)+2

107

m<b=m<d

Answer:

2 · x² - 20

Step-by-step explanation:

2x - 5 · x + 4

2x · x - 20

2x² - 20

2 · x² - 20

Answer:

18 inches

Step-by-step explanation:

Rick is building a scale model of the Alamo.

We are given a scale that 3 in. = 15 ft.

The length of the Alamo is 90 feet.

What is the length of the scale model in inches?

So we know that for every 15 feet, 3 inches are actually used in the project and we need a total of 90 feet. To solve, we need to find how many times 15 goes into 90, in which the number it multiplies to will apply to the inches.

15 * ? = 90

90 / 15

6

It takes 15 6 times to get to 90, meaning that we need to multiply 3 inches 6 times to find the actual length of the scale model in inches.

3 * 6

18 inches.

A transversal is a straight line that intersects two parallel lines forming four angles at each point of intersection. Thus the required answers to the given question are:

i. Side NM is parallel to side XZ.

ii. Using the corresponding property

iii. <XYZ is congruent to <NYM

iv. ΔXYZ is similar toΔNYM by SAS theorem

Two or more angles are said to be congruent if and only if they have equal measure. This property can be used to relate equal angles.

While a transversal is a straight line that intersects two parallel lines forming four angles at each point of the intersection.

The required answers to the question are as stated below:

i. Side NM is parallel to side XZ.

ii. The corresponding property

iii. <XYZ is congruent to <NYM

iv. ΔXYZ is similar toΔNYM by SAS theorem

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Answer: For the first box it is parallel, for the second box it is the corresponding angles theorem, the third is NYM, and the last one is AA.

Step-by-step explanation: 1.) Since line NM has an arrow on it's line and XZ has an arrow on it's line, that means that those two line are parallel to each other. 2.) Since both triangle contain the same transversal line (NY) and the corresponding angles theorem states that if a transversal intersects parallel lines, the corresponding angles are congruent. From this we can conclude that this means that the angle <YXZ has is congruent to the angle <YNM. Therefore we use the corresponding angles theorem. 3.) Answer 2 basically answers box number three but since we concluded that Angles of <YXZ and <YNM are both congruent <NYM would be your answer its just flipped. 4.) We use the AA theorem, because the AA theorem states that if an angle or angle(s) of one triangle is congruent to another angle/angle(s) of another triangle, then the triangles are similar (congruent). Therefore we would use the AA theorem.

Hope this helps :)

By the way this is the answer for EDGE in 2023

On solving the provided question, we cans ay that Area of the quadrilateral = 1/2*4.8*(5.9+1.1+5.9) =  30.96 cm sq.

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

Area of the quadrilateral = 1/2*4.8*(5.9+1.1+5.9) =  30.96 cm sq.

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Answer:

In Crista’s class, 8 students have blonde hair, 14 have brown hair, 3 have black hair, and 2 have red hair. If one student is chosen at random, it is  

that the student has blonde hair, it is  

that the student has brown hair, it is  

that the student has black hair, and it is  

that the student has red hair.

Answer:

In Crista’s class, 8 students have blonde hair, 14 have brown hair, 3 have black hair, and 2 have red hair. If one student is chosen at random, it is

unlikely

that the student has blonde hair, it is

neither likely nor unlikely

that the student has brown hair, it is

unlikely

that the student has black hair, and it is

unlikely

that the student has red hair.

Step-by-step explanation:

Answer:

$51.75

Step-by-step explanation:

Multiply 45.00 by 0.15 and you get 6.75

Once you get that add the 45.00 and the 6.75 to get 51.75 hope this helps

Answer:

A=½bh

20=5x(½)

multiply by reciprocal both sides

40=5x

divide

8=x

Answer:

Step-by-step explanation:

25x+120=35x+80

25x+120 is Country Carpets equation

35x+80 is City carpets equation

x=4

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    25*x+120-(35*x+80)=0

Pull out like factors :

  -10x + 40  =   -10 • (x - 4)

Solve :    -10   =  0

Solve  :    x-4 = 0

Add  4  to both sides of the equation :

                     x = 4

Answer:

36

Step-by-step explanation:

8 x 9 = 72

72 ÷ 2 = 36

Find the measurements of the height and length then multiply them together.

Now, divide the sum by two because a triangle has half the area of a square's area.

The value of x when f(x) of 8 according to the graph is; 4.

In order to determine a point's coordinates in a coordinate system, you must do the opposite. Start at the point and move in a vertical line in either an upwards or downwards direction to the x-axis. Here is the x-coordinate for you. Next, repeat the process while following a horizontal line to determine the y-coordinate.

According to the graph;

To determine the value of x when f(x) = 8.

We must plot a line of the equation; y = 8.

This y = 8 line produces a horizontal line.

The point at which the horizontal line, y = 8 intersects the given graph has an x coordinate.

Ultimately, this point has x coordinates of 4, making 4 the value of x when f(x) = 8.

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Impulse = ∫[0 to 0.800] f(t) dt

The force function f(t), we need more information about the acceleration during the contact time.

To model the force exerted by the woman on the floor, we can use the principles of conservation of energy.

When the woman jumps down to the floor, her initial potential energy is converted into kinetic energy as she accelerates towards the ground. At the moment of contact with the floor, all her initial potential energy is converted into kinetic energy. We can calculate the initial potential energy as:

PE_initial = m×g× h

Where:

m = mass of the woman = 68.0 kg

g = acceleration due to gravity = 9.8 m/s²

h = height from which she jumps = 0.740 m

PE_initial = 68.0 kg × 9.8 m/s² ×0.740 m

Next, when the woman jumps back up, she converts all her kinetic energy into potential energy. At the maximum height, all the kinetic energy is converted into potential energy. We can calculate the maximum height reached using the conservation of energy:

PE_final = KE_initial

Where:

PE_final = potential energy at maximum height (when she jumps back up)

KE_initial = initial kinetic energy (when she jumps down)

PE_final = m×g×h_max

Since her initial kinetic energy is equal to her initial potential energy:

KE_initial = PE_initial

Therefore:

m× g×h_max = m×g ×h

We can solve for h_max:

h_max = h

So, the maximum height reached during her jump back up is equal to the height from which she initially jumped down.

During the time interval when the woman is in contact with the ground (0 < t < 0.800 s), the force she exerts on the floor can be modeled using the function f(t). Since the force is exerted in the opposite direction to her motion, the force will be negative when she jumps back up.

If we assume that the force exerted by the woman on the floor is constant during the contact time (approximation), we can calculate the magnitude of the force using the impulse-momentum principle:

Impulse = Change in momentum

The change in momentum is given by:

Change in momentum = m×(v_final - v_initial)

Since the woman jumps back up to her initial height, the final velocity is zero (v_final = 0). The initial velocity can be calculated using the equation of motion:

v_final² = v_initial²+ 2×a × d

Where:

v_final = final velocity = 0 m/s (when she jumps back up)

v_initial = initial velocity

a = acceleration during contact time

d = distance traveled during contact time = h

Solving for v_initial:

0² = v_initial² + 2×a × h

v_initial² = -2 × a× h

v_initial = √(-2× a×h)

The negative sign indicates that the velocity is in the opposite direction of motion.

Now, the impulse can be calculated as:

Impulse = m ×(0 - v_initial) = -m ×v_initial

Since impulse is equal to the integral of force with respect to time, we have:

Impulse = ∫[0 to 0.800] f(t) dt

Therefore:

-m× v_initial = ∫[0 to 0.800] f(t) dt

To find the force function f(t), we need more information about the acceleration during the contact time.

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By controlling variables, we can isolate the impact of a specific variable on the outcome, allowing us to draw accurate conclusions.

The reason it is important to control all variables except one when studying cause-and-effect relationships is to establish a clear understanding of the relationship between the cause and the effect. By controlling variables, we can isolate the impact of a specific variable on the outcome, allowing us to draw accurate conclusions.

Here is a step-by-step explanation of why controlling variables is important:

1. Identifying the cause: When studying cause-and-effect relationships, we are interested in understanding the effect that a particular variable has on the outcome. By controlling all other variables, we can determine the true cause of the effect.

2. Eliminating confounding factors: Confounding factors are variables that can influence the outcome but are not the actual cause. By controlling these variables, we can eliminate their impact and prevent them from clouding the true cause-and-effect relationship.

3. Establishing a clear connection: By controlling all variables except one, we can clearly attribute any changes in the outcome to the specific variable being studied. This allows us to establish a direct cause-and-effect relationship and avoid drawing incorrect conclusions.

4. Replicability and reliability: Controlling variables ensures that the study can be replicated by other researchers. This enhances the reliability of the findings and allows for further investigation and validation of the cause-and-effect relationship.

Example: Let's say we want to study the effect of a new fertilizer on plant growth. If we don't control variables such as sunlight, water, temperature, and soil quality, these factors could potentially impact plant growth and confound the results. By controlling these variables and only changing the fertilizer, we can accurately determine the impact of the fertilizer on plant growth.

In summary, controlling variables except one when studying cause-and-effect relationships is important because it allows us to identify the true cause, eliminate confounding factors, establish a clear connection, and ensure replicability and reliability of the findings.

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Answer:

Step-by-step explanation: ok

Answer:

the answer is cubes curve

Answer:

B.× =158.11

IS THE ANSWER

x=158.11 is the solution to 24•log(2x) = 60, rounded to two decimal places

Answer:

All of the above

Step-by-step explanation:

Answer:4 1/2

Step-by-step explanation:

To figure this out you need to just subtract the amount sold from the amount in the beginning and it will tell you the remainder of the pencils

12-7 1/2=4 1/2

The mean is 4 and the standard deviation is 2.68.

Mean = EF / n

Mean = (1 + 5 + 8 + 5 + 1) / 5

Mean = 20 / 5

Mean = 4.

The differences from the mean for each value are:

Squaring each difference:

\(= (-3)^2\\= 9(1)^2\\= 1(4)^2\\= 16(1)^2\\= 1(-3)^2\\= 9\)

Variance = (9 + 1 + 16 + 1 + 9) / 5

Variance = 36 / 5

Variance = 7.2

Standard Deviation = √Variance

Standard Deviation = √7.2

Standard Deviation = 2.68.

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Answer:

_______the answer is Y=X+1___________

We are given the plane curve C given parametrically by the equations:x(t) = t² - ty(t) = t² + 3t - 4

We have to find the slope of the straight line tangent to the plane curve C at the point on the curve where t = 1.

We know that the slope of the tangent line is given by dy/dx and x is given as a function of t.

So we need to find dy/dt and dx/dt separately and then divide dy/dt by dx/dt to get dy/dx.

We have:x(t) = t² - t

=> dx/dt = 2t - 1y(t)

= t² + 3t - 4

=> dy/dt = 2t + 3At

t = 1,

dx/dt = 1,

dy/dt = 5

Therefore, the slope of the tangent line is:dy/dx = dy/dt ÷ dx/dt

= (2t + 3) / (2t - 1)

= (2(1) + 3) / (2(1) - 1)

= 5/1

= 5

Therefore, the slope of the tangent line is 5.

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