(Chapter 12) The vector <3, -1, 2> is parallel to the plane 6x-2y +4z = 1

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.

Learn more about coordinate  from the given link

https://brainly.com/question/17206319

#SPJ11

The given statement, "The nullspace of a nonzero 4 x 4 matrix cannot contain a set of four linearly independent vectors" is False.

Explanation: Null space is a linear algebra term used to refer to the set of all vectors that are mapped to the null vector. The solution of Ax=0 is also referred to as the null space or kernel of A. Since the matrix is of size 4x4 and non-zero, it must have at least one non-zero eigenvalue. Any non-zero vector multiplied by this non-zero eigenvalue will result in a non-zero vector, even if it is in the nullspace of the matrix. Because of this, a non-zero 4 x 4 matrix's nullspace can have four or fewer linearly independent vectors.

Hence, the statement "The nullspace of a nonzero 4 x 4 matrix cannot contain a set of four linearly independent vectors" is false.

Learn more about nullspace visit:

brainly.com/question/31745967

#SPJ11

Assuming that the standard deviation remains 0.12 ounces, so 16.251 ounces mean weight should Buckley Farms use.

The total weight of each bag follows an approximately normal distribution with a mean of 16.15 ounces and a standard deviation of 0.12 ounces.

Mean (μ) = 16.15

Standard deviation, (σ) = 0.12

n = 6

Buckley Farms decides to increase the mean weight of each bag of chips so that only 5%(0.05) of the bags have weights that are less than 16 ounces. So

P(X > x) = 0.05

P[(X - μ)/(σ/√n) > (x - μ)/(σ/√n)] = 0.05

1 - P(Z ≤ z) = 0.05

Subtract 1 on both side , we get

P(Z ≤ z) = 0.95

z = 1.96

(x' - μ)/(σ/√n) = 1.645

Now putting the value

(x' - 16.15)/(0.15/√6) = 1.645

(x' - 16.15)/(0.15/2.45) = 1.645

(x' - 16.15)/(0.0612) = 1.645

Multiply by 0.0612 on both side, we get

x' - 16.15 = 0.100674

Add 16.15 on both side, we get

x' = 16.251

To learn more about standard deviation link is here

brainly.com/question/23907081

#SPJ4

The complete question is:

Buckley Farms produces homemade potato chips that it sells in bags labeled 16 ounces. The total weight of each bag follows an approximately normal distribution with a mean of 16.15 ounces and a standard deviation of 0.12 ounces. Buckley Farms ships its chips in boxes that contain 6 bags. Buckley Farms decides to increase the mean weight of each bag of chips so that only 5% of the bags have weights that are less than 16 ounces. Assuming that the standard deviation remains 0.12 ounces what mean weight should Buckley Farms use?

Answer:

\(tan 56 = \frac{26}{x}\)

Step-by-step explanation:

\(tangent = \frac{opposite}{adjacent}\)

Side z is the hypotenuse, since it is opposite the right angle.

Side x is the adjacent, since it is next to the angle you are solving for.

The side measuring 26 is the opposite, since it is opposite the angle you are solving for.

Answer:

2602.142857 (you can simplify if you want)

Step-by-step explanation:

just act like the fraction sign is a division sign and then divide the two number.

Hope this helped!

Answer:

-96%

Step-by-step explanation:

Answer: 96%

Step-by-step explanation: There's not much work to show besides a few punches in the calculator.

The maximum S-wave amplitude of the earthquake in Fresno, CA with an epicentral distance of \(340\) km is approximately \(1.049\).

In conclusion, the maximum S-wave amplitude of the earthquake in Fresno, CA with an epicentral distance of \(340\) km is approximately \(1.049\)(without any further context or analysis).

For more such questions on amplitude:

https://brainly.com/question/3613222

#SPJ8

Answer:

1049

Step-by-step explanation:

The maximum S-wave amplitude of an earthquake in Fresno, CA, with an epicentral distance of km can be calculated using the equation: , where represents the amplitude of the S-wave, is the magnitude of the earthquake, and is the epicentral distance in kilometers.

Given the epicentral distance of km, we need to determine the magnitude of the earthquake to compute the S-wave amplitude.

By substituting into the equation, we can solve for $M$, yielding . Substituting this magnitude into the initial equation, we find , resulting in . Therefore, the maximum S-wave amplitude of the earthquake in Fresno, CA, at an epicentral distance of km is approximately .

For a triangle with base of 10 inches and altitude of 16 inches, its area will be 80 in² (third option).

Calculation For the Area of the Triangle:

It is given that,

The base of the triangle, B = 10 inches

The altitude from the base of the triangle or height, H = 16 inches

Now, the formula used for finding the area of a triangle is given as follows,

Area, A = (1/2) × B × H

Substituting the given values of B and H in the above formula for area, we get,

A = (1/2) × (10 inches) × (16 inches)

A = 5 × 16 inches²

A = 80 inches²

Thus, the area of the triangle have base 10 inches and altitude 16 inches is 80 square inches.

Learn more about area here:

https://brainly.com/question/19305981

#SPJ4

The collection of current NFL players is well defined and is a set

Step-by-step explanation:

For a collection to be termed as a set, it is necessary that it has distinct objects that are defined.

For example, a set of first 10 natural numbers is

A= [1,2,3,4,5,6,7,8,9,10]

It is well defined and therefore called as set which has first 10 natural numbers as its elements.

Same is the case with the collection of current NFL players.

The collection contains defined number of players. Therefore, this collection is called a set.

The members of the collection or team will be known as the elements of the set.

You can learn more about a set collection from

https://brainly.com/question/8053622
#SPJ4

Answer:

1.6

Step-by-step explanation:

Answer:

1.6 degrees

Step-by-step explanation:

Rashid spent a total of 1 hour and 30 minutes on homework for these three subjects.

If Rashid spent 30 minutes on each piece of homework for three subjects, we can calculate the total time he spent by multiplying the time spent per subject (30 minutes) by the number of subjects (3).

30 minutes * 3 = 90 minutes.

To convert this into hours and minutes, we divide 90 minutes by 60 since there are 60 minutes in an hour.

90 minutes ÷ 60 = 1 hour and 30 minutes.

Therefore, Rashid spent a total of 1 hour and 30 minutes on homework for these three subjects.

for such more question on minutes

https://brainly.com/question/25279049

#SPJ8

If a bloodstain has measurements of 30 cm and 15 cm, the angle of impact is going to be 30 degrees.

The angle of impact can be defined as the angle formed when a blood droplet hits the surface of any object. It is usually an acute or right angle.  It is important since it becomes a useful factor in many criminal investigations.  

It is used using the formula = arcsin(w/l) (i)

Here, it has been mentioned that the width, w is = 15 cm (ii)

The length of the blood stain is = 30 cm (iii)

Using the values of (ii) and (iii) in (i), we get -

= arcsin(15/30)

= 30 degrees

Hence, using the formula we know that the angle of impact is 30 degrees.

Learn to know more about Bloodstains on

https://brainly.com/question/15700076?referrer=searchResults

#SPJ4

John needs to make an annual beginning-of-the-year payment of approximately $369,238.68 to fund the estimated college costs of $196,000 in 10 years, given the after-tax rate of return of 8.65% compounded annually.

To compute the annual beginning-of-the-year payment necessary to fund the estimated college costs, we can use the present value of an annuity formula.

The present value of an annuity formula is given by:

P = A * [(1 - (1 + r)^(-n)) / r],

where P is the present value, A is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, John wants to accumulate $196,000 in 10 years, and the interest rate he can earn is 8.65% compounded annually. Therefore, we can substitute the given values into the formula and solve for A:

196,000 = A * [(1 - (1 + 0.0865)^(-10)) / 0.0865].

Simplifying the expression inside the brackets:

196,000 = A * (1 - 0.469091).

196,000 = A * 0.530909.

Dividing both sides by 0.530909:

A = 196,000 / 0.530909.

A ≈ 369,238.68.

Learn more about after-tax rate of return  here:-

https://brainly.com/question/31825431?referrer=searchResults

#SPJ11

The probability of getting a number < 9 is 28/37.

What is probability?

The ratio of good outcomes to all possible outcomes of an event is known as the probability. It has a range from 0 to 1.

Probability(Event) = Favorable Outcomes / Total Outcomes

Main Body:

Total numbers on the spinner greater than 9  = 37 - 10 + 1 = 28

(we are subtracting 10 because we need number that is greater than 10.)

and adding 1 because both the ends of interval is counted.

total numbers on spinner =37

P( x>9) = 28/37.

Hence the probability of getting a number greater than 9 on spinning is 28/37.

to learn more about probability click on the link below

brainly.com/question/24756209

#SPJ4

The coefficient of x^9∙y^16 in〖(2x – 4y)〗^25is (25 × 24 × 23 × 22 × 21 × 20 × 19 × 18 × 17) / (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) (2^9 x^9) (-4^16 y^16).

The formula for the coefficient of a term in a binomial expansion is:

nCr a^(n-r) b^r

where n is the exponent of the binomial, r is the exponent of the variable we are interested in (in this case, y), and a and b are the coefficients of the terms in the binomial expansion (in this case, 2x and -4y).

So, to find the coefficient of x^9 y^16 in (2x - 4y)^25, we can use the formula:

nCr a^(n-r) b^r

where n = 25, r = 16, a = 2x, and b = -4y.

The value of nCr can be calculated using the binomial coefficient formula:

nCr = n! / r! (n-r)!

where n! means factorial of n, which is the product of all positive integers from 1 to n.

So, the coefficient of x^9 y^16 in (2x - 4y)^25 is:

nCr a^(n-r) b^r = 25C16 (2x)^(25-16) (-4y)^16

= 25! / (16! 9!) (2^(9) x^9) (-4^(16) y^16)

= (25 × 24 × 23 × 22 × 21 × 20 × 19 × 18 × 17) / (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) (2^9 x^9) (-4^16 y^16)

Know more about coefficient here:

https://brainly.com/question/1038771

#SPJ11

Based on the linear pair theorem, the value of x is: 42°.

A linear pair is a pair of two angles that are formed adjacent to each other on a straight line. These two angles, according to the linear pair theorem, have a sum of 180d degrees when their measures are added together.

From the image, we see that x° and 138° are a linear pair as they lie on a straight line.

Therefore:

x + 138 = 180 [linear pair theorem]

Subtract 138 from both sides of the equation

x + 138 - 138 = 180 - 138

x = 42°

Therefore, based on the linear pair theorem, the value of x is: 42°.

Learn more about linear pair theorem on:

https://brainly.com/question/5598970

#SPJ1

Of the following statements regarding time-series methods, the statement that is false is a simple moving average of three periods is identical to exponential smoothing with an alpha equal to 0.33. (Option D)

In mathematics, a time series refers to a series of data points indexed or listed or graphed based on the time order. Generally, a time series is a sequence captured at successive equally spaced points in time and hence is a sequence of discrete-time data. Time-series methods are used in forecasting. It comprises of analytical methods in order to obtain meaningful statistics and other characteristics of the data. Time series forecasting is a model used to predict future values based on previously observed values. From the given options, the time-series methods that is false is is a simple moving average of three periods is identical to exponential smoothing with an alpha equal to 0.33.

Learn more about Time-series methods:

https://brainly.com/question/28481953

#SPJ4

Answer:

14

Step-by-step explanation:

sum of three angles of a triangle is 180

(x-4) + (11x-11) + (x+13) = 180

13x -2 = 180

13x = 182

x=14

The probability that the lifetime of at least one component exceeds 2 is 0.135.

Given that the joint pdf is f(x,y)=xe^(-x(1+y)) for x≥0, y≥0 and 0 otherwise as shown in attached image.

We want to find the probability that the lifetime of at least one component exceeds 2.

The probability that the lifetime of at least one component exceeds 2 is P(X>2).

\(\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\int_{y=0}^{\infty}f(x,y)dydx\end\)

Now, we will substitute the given function, we get

\(\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\int_{y=0}^{\infty}xe^{-x(1+y)}dydx\end\)

Further, we will simplify this, we get

\(\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\left[-e^{-x(1+y)\right]_{0}^{\infty}dx\\ &=\int_{x=2}^{\infty}e^{-x}dx\\ &=\left[-e^{-x}\right]_{2}^{\infty}\\ &=e^{-2}\\ &=0.135\end\)

Hence, the probability that the lifetime of at least one component exceeds 2 for the joint pdf is f(x,y)=xe^(-x(1+y)) for x≥0, y≥0 and 0 otherwise as shown in attached image is 0.135.

Learn more about the joint pdf from here brainly.com/question/15109814

#SPJ4

Answer:

2

Explanation:

You have to calculate the rise over run. See how many times it rises from the bottom. Then see how many times it takes horizontally to get to the next corner. Not sure if this helped but I tried sorry lol (but dw the answer is correct)

Answer:

Step-by-step explanation:

If you mean 3x^3 - 42x^2 - 4x + 5 = 0 you can graph it manually or with technology

The roots are 14.09, 0.30 and -0.39 to nearest hundredth.

Answer: who knows what the answers is bruh

Step-by-step explanation:

Answer:

27 1/2 cm^2

Step-by-step explanation:

The area of a parallelogram is

A = bh

A = 5 * 5 1/2

Change to an improper fraction

A = 5 * (2*5+1)/2

A = 5*11/2

A = 55/2

Change back to a mixed number

A = 27 1/2

Answer:

-1

Step-by-step explanation:

so -x-6 and x-4 are both = to y so that means they are both = to each

other so -x-6=x-4 add x to both sides -6=2x-4 add 4 to both sides 2x = -2 simplify by divide by 2 so x=-1

Answer:

Take the second equation and add 4 to both sides, this gives you x=y+4. The plug in y+4 on the first equation, so y=-(y+4)-6, distribute the negative to everything inside the parentheses, and you get y=-y-4-6. Combine like terms and you get y=-y-10, then add y to both sides, you get 2y=-10, divide both sides by 2 and you get y=-5.

Then plug -5 into the second equation and you get -5=x-4, add 4 to both sides and you get -1=x.

If you want to check your answer, just plug in x and y to either of the equations and see if it makes a true statement.

(a) The expected number of board-feet of timber next year is 102.9. (b) The interest rate at the bank matters in deciding to cut the trees down now or in the future due to the opportunity cost of waiting and potential earnings from investing the proceeds. (c) In order for cutting the trees down next year to be a better choice than cutting them down now, the interest rate at the bank has to be lower.

(a) To calculate the expected number of board-feet of timber next year, we multiply the probabilities of each outcome by the corresponding timber quantity and sum them. With a 98% probability of growth and a 5% increase in timber, and a 2% probability of fire and no timber, the expected number of board-feet of timber next year would be: (0.98 * 100 * 1.05) + (0.02 * 0) = 102.9 board-feet.

(b) The interest rate at the bank matters in deciding to cut the trees down now or in the future because it represents the opportunity cost of waiting. By cutting the trees down now and selling the timber, you can invest the proceeds in the bank and earn interest over time. If the interest rate is high, the present value of the future timber may be lower compared to the immediate cash flow from selling the timber now, making it more favorable to cut the trees down earlier.

(c) In order for cutting the trees down next year to be a better choice than cutting them down now, the interest rate at the bank has to be lower. A lower interest rate implies that the present value of future cash flows (from selling the timber next year) is higher relative to the immediate cash flow (from selling the timber now). Therefore, a lower interest rate makes it more advantageous to delay cutting the trees and wait for them to grow, maximizing the forester's profit.

To know more about interest rate,

https://brainly.com/question/16270250

#SPJ11

The probability that at least one of the ten random numbers drawn from a uniform distribution on [0, 4.62] will exceed 4.62 is approximately 0.450.

In a uniform distribution, the probability of a value falling within a specific range is proportional to the length of that range. Since the range of the uniform distribution is [0, 4.62], the probability of drawing a number less than or equal to 4.62 from this distribution is 1.

Therefore, the probability that at least one number will exceed 4.62 is equal to 1 minus the probability that all ten numbers drawn are less than or equal to 4.62. Since the draws are independent, we can calculate this probability as (1 - 1)^10 = 1^10 = 1.

Rounded to three decimal places, the probability that at least one number will exceed 4.62 is approximately 0.450.

To learn more about probability click here: brainly.com/question/31120123
#SPJ11

Based on the given probabilities:

Events A and B are independent.

Events B and C are mutually exclusive.

Events C and A are independent.

To determine whether pairs of events are independent or mutually exclusive, we need to analyze their conditional probabilities.

Pair A and B:

P(A) = 0.26, P(B) = 0.5, and P(A|B) = 0.26. The fact that P(A|B) is equal to P(A) suggests that events A and B are independent. This means that knowing the occurrence of event B does not affect the probability of event A.

Pair B and C:

P(B) = 0.5, P(C) = 0.45, and P(B|C) = 0. The fact that P(B|C) is equal to 0 implies that events B and C are mutually exclusive. This means that if event C occurs, event B cannot occur, and vice versa.

Pair C and A:

P(C) = 0.45, P(A) = 0.26, and P(C|A) = 0.26. The fact that P(C|A) is equal to P(C) suggests that events C and A are independent.

To learn more about probabilities click on,

https://brainly.com/question/30708861

#SPJ4

Complete question is:

Given the following information about events A, B, and C, determine which pairs of events, if any, are independent and which pairs are mutually exclusive.

P(A)= 0.26

P(B)= 0.5

P(C)= 0.45

P(A|B)= 0.26

P(B|C)=0

P(C|A)=0.26

Answer:

X=17

Step-by-step explanation:

They are verticals angles so 4x+1=69

Answer:

Acute / interior angle pair x = 17

Step-by-step explanation:

Using basic Algebra, you can set up an equation such as this:

69 = -1 + 4x

68/4 = 4x/4

17 = x or x = 17

Acute/interior angle pair

Answer:

57

Step-by-step explanation:

6 X 9.50