Show that the eigenvalue problem (4.75-4.77) has no negative eigenvalues. Hint: Use an energy argument-multiply the ODE by y and integrate from p=0 to r=R; use integration by parts and use the boundedness at r = 0 to get the boundary term to vanish.

Answer:

400

Step-by-step explanation:

480-80=400

Answer

x=6

Step-by-step explanation:

80*x=480

80*6=480

the measures of the angles of the triangle are A = 26.29 degrees, B = 131.45 degrees, and C = 22.29 degrees.

How to solve angles?

To solve for the angles of a triangle, we need to use the fact that the sum of the angles of a triangle is equal to 180 degrees. We can use this fact to set up equations based on the given information.

Let's start by assigning variables to the angles of the triangle. Let A be the measure of angle A, B be the measure of angle B, and C be the measure of angle C.

We are given that angle B is 5 times angle A, which we can express as B = 5A. We are also given that angle C is 4 times less than angle A, which we can express as C = A - 4.

Using the fact that the sum of the angles of a triangle is 180 degrees, we can write the following equation:

A + B + C = 180

Substituting the expressions we found for B and C, we get:

A + 5A + (A-4) = 180

Simplifying the equation, we get:

7A - 4 = 180

Adding 4 to both sides of the equation, we get:

7A = 184

Dividing both sides by 7, we get:

A = 26.29

Now that we know the measure of angle A, we can use the expressions we found for B and C to find their measures:

B = 5A = 131.45

C = A - 4 = 22.29

Therefore, the measures of the angles of the triangle are A = 26.29 degrees, B = 131.45 degrees, and C = 22.29 degrees.

In summary, we used the fact that the sum of the angles of a triangle is 180 degrees and the given information about the relationship between the angles to set up an equation and solve for the measure of angle A. We then used the expressions we found for angles B and C to find their measures.

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Answer:

41.67 kg

72 books

Step-by-step explanation:

mass of 150 books = 150/108 × 30 kg

= 41.67 kg

number of books = 20/30 × 108 books

= 72 books

Answer:

48 calories per (each) minute.

Step-by- Step

=

Answer: NOT CONGRUENT

Step-by-step explanation:

Answer:

They are congruent because of ASA.

Step-by-step explanation:

Since these points are at the same rate, we can safely assume that it is congruent based on these given statements below.  It is also ASA because angle B and angle C are mentioned in the given statements and there is a side explanation which is BC and EF which makes them angle-side-angle.

Answer:

36

Step-by-step explanation:

10+10+8+8=36 you just need to add all sides

To find extrema of the function f(x, y) = 16x^0.7y^0.3 to the constraint 2x + y = 25, we can use Lagrange multipliers. Solving system of equations formed by equating the partial derivatives of the Lagrangian to zero.

We start by setting up the Lagrangian function L(x, y, λ) = f(x, y) - λ(g(x, y) - c), where f(x, y) = 16x^0.7y^0.3, g(x, y) = 2x + y, and c = 25 is the constraint value.

Taking the partial derivatives of L with respect to x, y, and λ, and setting them equal to zero, we obtain the following system of equations:

∂L/∂x = 0: 0.7(16)x^(-0.3)y^0.3 - 2λ = 0

∂L/∂y = 0: 0.3(16)x^0.7y^(-0.7) - λ = 0

∂L/∂λ = 0: 2x + y - 25 = 0

Solving these equations simultaneously will give us the critical points. However, it is important to also check the boundary points, which in this case are the points where the constraint is active. Here, the constraint is 2x + y = 25.

Solving the system of equations, we find the critical point (x, y) = (5, 15) as a potential relative extremum.

To determine if it is a maximum, minimum, or neither, we can use the second partial derivative test or substitute the critical point into the original function and compare it to nearby points.

Comparing the value of f(5, 15) to the values of f at nearby points or using the second partial derivative test will help determine if (5, 15) is a relative maximum, minimum, or neither.

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There is a total of 15 yes/no questions on the test. Hence, 15 is the correct answer.

Let's assume the number of yes/no questions on the test is represented by 'x'. The number of multiple-choice questions would then be '20 - x' since the test consists of a total of 20 questions.

The points obtained from yes/no questions can be calculated as 3 times the number of yes/no questions, which is 3x.

Similarly, the points obtained from multiple-choice questions can be calculated as 11 times the number of multiple-choice questions, which is 11(20 - x).

Since the total points for the test are 100, we can set up the equation:

     \(3x + 11(20 - x) = 100\)

or, \(3x + 220 - 20x = 100\)

or, \(8x = 120\)

or, \(x = 15\)

Therefore, the total number of yes/no questions on the test is 15.

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1.  Algebraic rules= (y, -x), (-x, -y), (-y, x) respectively, 2. (0,0), (3,1), and (2,3), 3. (0,0), (1,-3) and (3,2), 4. (0,0), (-3,-1), and (2,-3) 5. would be identical to the original triangle.

Rotation in mathematics refers to the transformation of a figure around a fixed point or axis. The fixed point or axis is called the center of rotation, and the figure is rotated by a certain angle, either clockwise or counterclockwise.

There are different types of rotations, including 2D and 3D rotations. In 2D geometry, a figure can be rotated by an angle about a point or the origin. In 3D geometry, a figure can be rotated about an axis, such as the x-axis, y-axis, or z-axis.

1.The algebraic rules for each kind of rotation are:

90° clockwise about the origin: (x, y) → (y, -x)

180° about the origin: (x, y) → (-x, -y)

270° clockwise about the origin: (x, y) → (-y, x)

2. To draw the image of ΔDEF after a 90° clockwise rotation, we apply the algebraic rule for a 90° rotation to each vertex of the triangle.

D(0,0) → (0,0)

E(-1,3) → (3,1)

F(-3,-2) → (2,3)

So, the image of ΔDEF after a 90° clockwise rotation is a new triangle with vertices (0,0), (3,1), and (2,3).

3. To draw the image of ΔDEF after a 180° rotation, we apply the algebraic rule for a 180° rotation to each vertex of the triangle.

D(0,0) → (0,0)

E(-1,3) → (1,-3)

F(-3,-2) → (3,2)

So, the image of ΔDEF after a 180° rotation is a new triangle with vertices (0,0), (1,-3), and (3,2).

4. To draw the image of ΔDEF after a 270° clockwise rotation, we apply the algebraic rule for a 270° rotation to each vertex of the triangle.

D(0,0) → (0,0)

E(-1,3) → (-3,-1)

F(-3,-2) → (2,-3)

So, the image of ΔDEF after a 270° clockwise rotation is a new triangle with vertices (0,0), (-3,-1), and (2,-3).

5. A 360° rotation would result in the triangle returning to its original position. In other words, the image of the triangle after a 360° rotation would be identical to the original triangle.

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Step-by-step explanation:

perimeter of a sector =r+r+angle/360×2πr

12+12+(40/360×2×22/7×12)

24+8.378

32.378cm

The formula to calculate the confidence interval is given by: \(CI = X \pm Z^* \cdot \frac{\sigma}{\sqrt{n}}\) Here, X = sample mean, σ = population standard deviation, n = sample size, and Z = z-value corresponding to the level of confidence.

Constructing the 99% confidence interval:We have X = $62,000, σ = $23,000, and n = 65.The z-value for a 99% confidence interval can be found using a standard normal distribution table or a calculator.Using the calculator, we get: Z = 2.576 (rounded off to three decimal places)Now, we can substitute these values in the formula:

\(CI = X \pm Z^* \cdot \frac{\sigma}{\sqrt{n}}\)

= $62,000 ± 2.576*($23,000/√65)CI

= $62,000 ± $7,999.16

The lower limit of the interval is given by:

$62,000 - $7,999.16

= $54,000.84T

he upper limit of the interval is given by:

$62,000 + $7,999.16

= $69,000.16

Therefore, the 99% confidence interval for the average bonus that all employees working for financial companies in New York City received last year is ($54,000.84, $69,000.16).

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Answer:

The area is twice the circumference

Area = 2 * circumference

Step-by-step explanation:

Proof:

r = 2

Circumference = 2\(\pi\)r

Circumference = 12.566

Area = \(\pi\)r^2

Area = 25.132

25.132/12.566 ≈ 2

Answer:

the (area) is (1/2) times the (radius) times the circumference.

Step-by-step explanation:

i dont know how to explain it exactly but i found the cerect answer.

Answer:

a

Step-by-step explanation:

the radial form is, 6 times the eight root of x to the fifth power.

Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.

here, given that,

6x^5/8

now,

the radial form is,

6 times the eight root of x to the fifth power.

Hence, the radical form is, 6 times the eight root of x to the fifth power.

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The probability of selecting a sample of 5 lightbulbs without any defective bulbs is then given by p^5, where p is the probability of not having a defective bulb.

In this situation, the probability of selecting a sample of 5 lightbulbs without any defective bulbs is calculated using the binomial distribution. The probability of success, p, is the probability that a single lightbulb is not defective, and the probability of failure, q, is the probability that a single lightbulb is defective. The probability of selecting 5 lightbulbs with no defective bulbs is then given by the equation:

P(x=0) = (p^5)*(q^0) = p^5

In this case, p is the probability of not having a defective bulb, and q is the probability of having a defective bulb. The probability of selecting 5 lightbulbs without any defective bulbs is then given by p^5.

For example, if the probability of not having a defective bulb is 0.95 and the probability of having a defective bulb is 0.05, then the probability of selecting a sample of 5 lightbulbs without any defective bulbs is 0.95^5 = 0.7737. This means that there is a 77.37% chance of selecting a sample of 5 lightbulbs without any defective bulbs.

To sum up, the probability of selecting a sample of 5 lightbulbs without any defective bulbs is calculated using the binomial distribution. The probability of success is the probability of not having a defective bulb, and the probability of failure is the probability of having a defective bulb. The probability of selecting a sample of 5 lightbulbs without any defective bulbs is then given by p^5, where p is the probability of not having a defective bulb.

The correct question is:

A box contains 100 bulbs, out of which 10 are defective. If a sample of 5 lightbulbs is selected, find the probability that none in the sample are defective

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Answer:

Refer to explanation..

Step-by-step explanation:

Since x represent same number when if it is used multiple times..

40 - 3 - 3 = 34 (Find out how many is 4 x)

4x = 34

X = 34 ÷ 4 = 8.5

I don't know what the question is finding for, if it's breadth then it's 8.5, if it is finding length..

Length = 8.5 + 3 = 11.5

Therefore, the range of the relation 2x + y = 3 for the given domain {-3, 0, 6} is {9, 3, -9}.

To determine the range of the relation 2x + y = 3 for the given domain {-3, 0, 6}, we need to find the corresponding range values when we substitute each value from the domain into the equation.

Substituting -3 into the equation, we have 2(-3) + y = 3, which simplifies to -6 + y = 3. Solving for y, we get y = 9.

Substituting 0 into the equation, we have 2(0) + y = 3, which simplifies to y = 3.

Substituting 6 into the equation, we have 2(6) + y = 3, which simplifies to 12 + y = 3. Solving for y, we get y = -9.

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By using the unitary method , the cost of one shotgun shell to determine that the cost of shooting the last 6 ducks would be $6.86.

The unitary method involves finding the value of one unit and then using that value to find the value of a given number of units. In this problem, we can use the number of shotgun shells as the unit of measurement. Let's say Bill used x shotgun shells to shoot 8 ducks on his previous hunting trip. Therefore, the cost of shooting 8 ducks would be the cost of x shotgun shells.

Now, we know that Bill shot 14 ducks using the same amount of shotgun shells he used on his previous trip. Therefore, the cost of shooting 14 ducks would be the cost of x shotgun shells. We can use a proportion to find the value of x.

8 ducks can be shot using x shotgun shells, so 14 ducks can be shot using (14/8) x x shotgun shells.

Simplifying this expression, we get:

(14/8) x x = 14 ducks

x = (8/14) x 14 ducks

x = 8/7 ducks

So, Bill used 8/7 shotgun shells to shoot 1 duck on his previous hunting trip.

Now, to find the cost of shooting the last 6 ducks, we need to determine how many shotgun shells he would need. Using the unitary method again, we can say:

1 duck can be shot using 8/7 shotgun shells, so 6 ducks can be shot using 6 * (8/7) shotgun shells.

Simplifying this expression, we get:

6 x (8/7) = 48/7 shotgun shells

Therefore, to shoot the last 6 ducks, Bill would need 48/7 shotgun shells. To determine the cost, we need to know the cost of one shotgun shell. Let's say the cost of one shotgun shell is $1. Then the cost of shooting the last 6 ducks would be:

(48/7) x $1 = $6.86 (rounded to the nearest cent)

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El precio resultante con descuento de 12 % es igual a 342.32 pesos.

En este problema tenemos que determinar el precio resultante, el cual es igual al precio inicial menos el descuento. A continuación, se presenta la siguiente expresión:

x = 389 · (1 - 12/100)

x = 389 - 46.68

x = 342.32

El precio resultante con descuento de 12 % es igual a 342.32 pesos.

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The value of x = 16, y = 172 and z = 2.

x - 4z = 12x - y - 6z = 42x + 3y - 2z = 8

let x - 4z = 8 be equation (1), 12x - y - 6z = 8 be equation (2) and 42x + 3y - 2z = 8 be equation (3)

x - 4z = 8

x = 8 + 4z

12x - y - 6z = 8

12(8 + 4z) -y - 6z =8

96 + 48z - y - 6z = 8

42z - y = -88

y = 42z + 88

42x + 3y - 2z = 8

42(8+4z) + 3(42z + 88) - 2z = 8

336 + 168z + 126z + 264 - 2z = 8

168z + 126z + 2z = 336+264 - 8

296z= 592

z = 2

substituting the value of z

x = 8 + 4z

= 8 + 4(2)

8+8 = 16

y = 42z + 88

42(2) + 88

84 + 88= 172

The value of x = 16, y = 172 and z = 2.

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The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, & The mass-normalised mode shapes can be  normalising the mode shape vectors f1, f2, and f3.

Part (a)

In Equation Q2, the spectral matrix, undamped natural frequencies, damping ratios, and fundamental frequency need to be calculated.

The mass matrix is given by [85.16400 083.3770 0046.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The stiffness matrix is given by [0.16400 00.3770 000.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The damping matrix is given by [0 0 0; 0 0 0; 0 0 0].The undamped natural frequencies, damping ratios, and fundamental frequency for the system in Equation Q2 can be calculated from the spectral matrix.

The characteristic equation can be written as det(K-mω^2M)=0.where K is the stiffness matrix, M is the mass matrix, ω is the angular frequency, and m is the mass-normalised mode shape.

The roots of this equation are the undamped natural frequencies, and the damping ratios can be calculated from the undamped natural frequencies and mode shapes.

The mass-normalised mode shapes can be calculated by normalising the mode shape vectors f1, f2, and f3.

Part (b)

The mass-normalised mode shapes can be calculated using the mode shape vectors f1, f2, and f3.Part (c)The response of the system for the first physical coordinate y1 can be calculated using the mode superposition method. The initial modal displacements and velocities are given in terms of the modal coordinates.

The response is then calculated using the equation y(t)= Σ ai φi(t), where ai are the modal amplitudes, and φi(t) are the modal shapes given by the mode shape vectors f1, f2, and f3.

The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, where Y is the vector of physical coordinates. The modal amplitudes can be calculated from the initial modal displacements and velocities.

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A vector is a mathematical object that represents both magnitude and direction. It is commonly used to represent physical quantities such as displacement, velocity, and force. In simple terms, a vector is an arrow that has a length (magnitude) and points in a specific direction.

To add vectors, we can use the "tip-to-tail" method. This involves placing the tail of the second vector at the tip of the first vector and drawing a new vector from the tail of the first vector to the tip of the second vector. The resulting vector, called the sum or resultant, is the vector that connects the tail of the first vector to the tip of the second vector.

Component styles are two common methods used to represent vectors: the Cartesian coordinate system and the polar coordinate system. In the Cartesian coordinate system, vectors are represented by their horizontal and vertical components. The polar coordinate system represents vectors using their magnitude and angle from a reference axis.

To decompose a vector into components, we use trigonometry. For example, in the Cartesian coordinate system, we can find the horizontal and vertical components of a vector by using the cosine and sine functions, respectively, along with the magnitude and angle of the vector.

When a vector is multiplied by a scalar (a real number), the vector's magnitude is scaled by the scalar value, and its direction remains unchanged. If the scalar is negative, the vector will reverse direction.

Graphically, we can arrange vectors by placing their tails at the origin of a coordinate system and drawing the vectors as arrows with their tips pointing to the desired location. Vector addition is represented by placing the tail of the second vector at the tip of the first vector, while vector subtraction is represented by placing the tail of the subtracted vector at the tip of the original vector, pointing in the opposite direction.

Overall, vectors provide a powerful mathematical tool for representing and manipulating quantities with both magnitude and direction. They are essential in many areas of science, engineering, and mathematics.

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Given that profits decrease by 13.8% when the degree of operating leverage (DOL) is 3.8.

The decrease in sales is: We have to determine the percentage decrease in sales Let the percentage decrease in sales be x.

Degree of Operating Leverage (DOL) = % change in Profit / % change in Sales3.8

= -13.8% / x Thus, we have: x

= -13.8% / 3.8

= -3.63%Therefore, the decrease in sales is 3.63%.Hence, the correct option is C) 3.63%. Percentage decrease in sales = % change in profit / degree of operating leverage

= 13.8 / 3.8

= 3.63% The percentage decrease in sales is 3.63%.

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Answer:

\(P (Yes | Nebraska) = 0.10\)

Step-by-step explanation:

Given

See attachment for contingency table

Required

\(P (Yes | Nebraska)\)

From the contingency table, we have:

\(P (Yes\ n\ Nebraska) = 0.044\)

\(P (No\ n\ Nebraska) = 0.400\)

The required can be represented as:

\(P (Yes | Nebraska) = \frac{P(Yes\ n\ Nebraska)}{P(Nebraska)}\)

Where

\(P (Nebraska) = P (No\ n\ Nebraska) +P (Yes\ n\ Nebraska)\)

So, we have:

\(P (Nebraska) = 0.400 + 0.044\)

\(P (Nebraska) = 0.444\)

So, we have:

\(P (Yes | Nebraska) = \frac{P(Yes\ n\ Nebraska)}{P(Nebraska)}\)

\(P (Yes | Nebraska) = \frac{0.044}{0.444}\)

\(P (Yes | Nebraska) = 0.10\) --- approximated

Answer:

The given expression is not a complete equation or function. It seems like a linear function, but it is missing an input variable and an equal sign.

A linear function in the form of y = mx + b, where y is the output, x is the input, m is the slope, and b is the y-intercept.

Without the input variable, we cannot evaluate the function. Can you please check if you have provided the complete equation or function?

Step-by-step explanation:

Answer:

282.6 ft

Step-by-step explanation:

First you must figure out how far the elevator drops in three seconds.

To do so you multiply how far it falls per second (5.8 ft) by how long it falls for (3 seconds). 5.8 * 3 = 17.4

now you subtract 17.4 from 300 to get 282.6 ft

The test results of the study's subjects serve as the sample.

The portion of the population from which data was actually gathered is known as a sample.

Sample = Hours of sleep and maths test score of the volunteers that were included in the study.

A population is the total group about which you want to draw conclusions. A sample is the specific group from which you will collect data. Always, the sample size is less than the whole population.

A population in research doesn't usually refer to humans. It can refer to a collection of whatever you desire to study, including things, occasions, groups, nations, species, and animals.

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.

The time it takes to deposit a coating on a decorative drawer handle through a solution depends on various factors, such as the type and concentration of the solution used, the size and shape of the handle, and the method of deposition.

The time it takes to deposit a coating on a decorative drawer handle through a solution depends on various factors, such as the type and concentration of the solution used, the size and shape of the handle, and the method of deposition. In general, the process of depositing a coating through a solution involves immersing the handle in the solution, allowing the coating to adhere to the surface, and then removing the handle and allowing it to dry. This process can take anywhere from a few seconds to several minutes, depending on the variables mentioned above.
To get a more accurate answer to your question, you may need to provide more specific details about the type of solution and coating you are using and the method of deposition. Additionally, you may want to consult with an expert in the field of surface coatings or material science to get a more precise estimate.

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