For the figure shown on the right, find the value of the variable and the measures of the angles.

Answer:

A is the answer

Step-by-step explanation:

(a) The normal mode shapes are defined by the eigenvectors of the matrix and are the shapes the system will take when it vibrates with only one natural frequency active. The two normal mode shapes are as follows: Normal mode 1:x1(t) = 0.909x1 + 0.416x2Normal mode 2:x2(t) = -0.416x1 + 0.909x2.

(b) The principal coordinates, u1 and u2, are defined as follows: ui = vT qi Where v is the eigenvector matrix and q is the generalized coordinate vector. Therefore,u1 = 0.909q1 - 0.416q2u2 = 0.416q1 + 0.909q2.

(c) To solve for the equation of motion with respect to the principal coordinates, we will first need to derive the mass matrix. As a result of the transformation from the generalized coordinates to the principal coordinates, this is the diagonal matrix M:diag(m1, m2) = diag(76, 28)From the equation, we get,DvTq" + Kvtq = 0
vTMvTq" + vTKvTq = 0
Md" + Kvq = 0
Therefore,d1u1" + k1u1 = 0
d2u2" + k2u2 = 0Where k1 and k2 are the diagonal entries of the stiffness matrix K, which can be obtained from the dynamic matrix (D = K - ω2M). k1 = 204,800 N/m, k2 = 28,000 N/m.

(d) We must first convert the initial conditions from the generalized coordinates to the principal coordinates:

q1 = 0.909x1 + 0.416x2 = 0.909(0.5) + 0.416(40) = 16.82q2 = -0.416x1 + 0.909x2 = -0.416(0.5) + 0.909(80) = 72.14.

(e) The free vibration can be determined using the following equations:u1(t) = A1 cos(w1t + φ1)u2(t) = A2 cos(w2t + φ2)To solve for A1, A2, φ1, and φ2, we must use the initial conditions in the principal coordinates.

The initial conditions for u1 are:u1(0) = A1 cos(0 + φ1) = 16.82u1'(0) = -100A1 sin(0 + φ1) = 0.

Therefore, φ1 = 0 and A1 = 16.82The initial conditions for u2 are:u2(0) = A2 cos(0 + φ2) = 72.14u2'(0) = -20A2 sin(0 + φ2) = 0.

Therefore, φ2 = 0 and A2 = 72.14Hence, the free vibration with respect to the principal coordinates is as follows:u1(t) = 16.82 cos(100t)u2(t) = 72.14 cos(20t).

Therefore, the normal mode shapes for each natural frequency were explained, the principal coordinates in terms of the generalized coordinates were determined, the equation of motion was determined with respect to the principal coordinates, the initial conditions with respect to the principal coordinates were determined, and the free vibration of the system with respect to the principal coordinates in response to the initial conditions listed in (d) were also determined.

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(a) The distance traveled by motorcycle is 1548 ft.

(b) The distance traveled by motorcycle is 1512 ft.

(c) (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.

What is velocity?

The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.

Given table is:

t (s)        0       12      24     36     48      60

v (ft/s)   30      28     25     21      25      27

The distance traveled by motorcycle during this time period using the velocities at the beginning of the time intervals is:

12(30 + 28 + 25 + 21 + 25)

=12 × 129

= 1548 ft

The distance traveled by motorcycle during this time period using the velocities at the end of the time intervals is:

12(28 + 25 + 21 + 25 + 27)

=12 × 126

= 1512 ft

The distance traveled by motorcycle at the end of the time intervals is greater than the distance traveled by motorcycle at the beginning of the time intervals.

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The domain restrictions of the expression q²−7q−8/q²+3q−4 are q ≠ -4 and q ≠ 1. (option c)

The denominator of the expression is q²+3q−4. To determine the values that would make the denominator equal to zero, we can set it equal to zero and solve for q:

q² + 3q - 4 = 0

Now, we can factorize the quadratic equation:

(q + 4)(q - 1) = 0

To find the values of q, we set each factor equal to zero and solve for q:

q + 4 = 0 or q - 1 = 0

Solving these equations, we get:

q = -4 or q = 1

So, the values of q that would make the denominator equal to zero are q = -4 and q = 1. These are the values we need to exclude from the domain of the expression to avoid division by zero.

Therefore, the correct answer is option c) q ≠ 1 and q ≠ -4.

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Complete Question:

What are the domain restrictions of q²−7q−8/q²+3q−4?

a) q≠1 and q≠−8

b) q≠−1 and q≠4

c) q≠1 and q≠−4

d) q≠−1 and q≠8

For any rational numbers r and s, 2r + 3s is rational. This is a corollary of Theorem 4.3.2.

Since r and s are rational numbers, they can be expressed as a ratio of integers:

r = a/b

s = c/d

where a, b, c, and d are integers and d and b are nonzero.

Then,

2r + 3s = 2(a/b) + 3(c/d)

= (2ad + 3bc)/(bd)

Since the product and sum of any two integers is also an integer, we know that 2ad and 3bc are integers. Thus, the numerator is the sum of two integers, which means it is also an integer. The denominator is the product of two nonzero integers, which means it is also nonzero. Therefore, 2r + 3s is a ratio of integers, and hence it is a rational number.

Therefore, for any rational numbers r and s, 2r + 3s is rational. This is a corollary of Theorem 4.3.2.

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Answer:

maybe the third one and i would also like to see the box plot

Step-by-step explanation:

The number of decimal places should be one more than the least accurate measurement, and the number of significant figures can be determined by counting the digits in the number, excluding the decimal point.

Rounding a number is important when providing an answer to a calculation or question. The number of decimal places and significant figures the answer should be rounded to depends on the accuracy of the answer that is required.

To calculate the number of decimal places and significant figures the answer should be rounded to, the general rule is to round to one more decimal place than the least accurate measurement. For example, if the least accurate measurement used in the calculation is rounded to two decimal places, the answer should be rounded to three decimal places.

The significant figures of the rounded answer can be determined by counting the number of digits in the number, excluding the decimal point. For example, the number 6,782 would have four significant figures, as there are four digits in the number.

In conclusion, the number of decimal places and significant figures the answer should be rounded to depends on the accuracy of the answer that is required. The number of decimal places should be one more than the least accurate measurement, and the number of significant figures can be determined by counting the digits in the number, excluding the decimal point.

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Answer:

Explanation: Slope is the ratio of the vertical and horizontal changes between two points on a surface or a line. ... If coordinates of any two points of a line are given, then the rate of change is the ratio of the change in the y-coordinates to the change in the x-coordinates.

Step-by-step explanation:

Answer:

57%

Step-by-step explanation: Well, subtract 76 - 19 = 57. 57 of 100 = 57/100

57/100 = 57%

The factored form of the polynomial P(x) = x³ + 2x² + 4x + 8 is P(x) = (x + 1)(x² + x + 7). The quadratic factor x^2 + x + 7 cannot be further factored into linear factors with real coefficients.

To factor the polynomial P(x) = x³ + 2x² + 4x + 8, we can look for potential roots by applying synthetic division or by using synthetic substitution. In this case, we can start by trying small integer values as possible roots, such as ±1, ±2, ±4, and ±8, using the Rational Root Theorem.

By synthetic substitution, we find that -1 is a root of the polynomial. Dividing P(x) by (x + 1) using long division or synthetic division, we get:

P(x) = (x + 1)(x² + x + 7)

Now, we need to factor the quadratic expression x² + x + 7. However, upon factoring this quadratic expression, we find that it cannot be factored further into linear factors with real coefficients. Therefore, the factored form of P(x) is:

P(x) = (x + 1)(x² + x + 7)

Please note that the quadratic factor x² + x + 7 does not have any real roots. Therefore, the complete factored form of P(x) is as given above.

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Square root of one hundred and seventy is greater than square root of one hundred and sixty eight.

A perfect square number is a number which when taken square root comes out as an integer.Every number which is not a perfect square when taken square root of it is irrational number.We can obtain square root of a perfect square number by prime factorisation method.

Given we have to compare \(\sqrt{170}\) and \(\sqrt{168}\).

We know that if the square roots are not given then we have easily concluded that 170 > 168.Same in the case of square root:

\(\sqrt{170} > \sqrt{168}\).

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Answer: multiple of sum 2+5

Step-by-step explanation:

18/9=2

45/9=5

2+5=7

18+45=63

63/7=9

2+5

Answer:

b

Step-by-step explanation:

An integer is a whole number

If the stock market gains by 10 basis points. It means that it increases by (0.0001 x 10) = 0.001% or 0.00001

this is a decimal and not an integer

Answer:

For numerator

2sin(2∅)=2(2sin∅cos∅)

For Denominator

(1+cos(2∅))(1+tan²∅)

=(1+cos(2∅))(sec²∅)

=(1+cos²∅-sin²∅)(sec²∅)

Recall. 1-sin²∅=cos²∅

=2cos²∅(sec²∅)

=2.

Answer is...

2(2sin∅cos∅)/2

=2sin∅cos∅ or sin(2∅)

The p-value for this hypothesis test is 0.263.

In this case, the null and alternative hypotheses for a hypothesis test of the difference in two population proportions are:

null hypothesis: p1 = p2

alternative hypothesis: p1 > p2

Notice that the alternative hypothesis is a one-tailed test.

Suppose proportions z test method from stats models is used to perform the test and the output is (1.13, 0.263).

To find the p-value for this hypothesis test, we need to use the output from the statsmodels function.

The second number in the output is the p-value.

Therefore, the p-value for this hypothesis test is 0.263.

The first number in the output is the z-value, which is not relevant to finding the p-value. Therefore, we can ignore it. Answer: 0.263

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The continuous growth rate is approximately 0.6931, which means the population increases by 69.31% continuously every year.

a) To find the percent annual growth rate of the population, we will use the formula:
Growth Rate = (Final Population / Initial Population)^(1/number of years) - 1
Since the population doubles every year, the Final Population is twice the Initial Population. Let's denote the Initial Population as P. So, the Final Population will be 2P. The number of years is 1 since it doubles every year. Now we can plug the values into the formula:
Growth Rate = (2P / P)^(1/1) - 1
Growth Rate = (2)^(1) - 1
Growth Rate = 2 - 1
Growth Rate = 1
The growth rate is 1, which means the population increases by 100% every year.
b) To find the continuous percent growth rate of the population, we use the formula:
Continuous Growth Rate = ln(Final Population / Initial Population) / number of years
Again, the Final Population is 2P and the Initial Population is P. The number of years is still 1. Now we can plug these values into the formula:
Continuous Growth Rate = ln(2P / P) / 1
Continuous Growth Rate = ln(2) / 1
Continuous Growth Rate ≈ 0.6931

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The least square regression line implies a mathematical equation that models the relationship between the dependent and independent variables. Hence, it may be used to predict a value of y if the corresponding x value is given. The least square regression line also called the best fit line, gives a mathematical relationship between variables in slope-intercept form.The predicted value of y or x if the corresponding value of either variable is given.

what is regression?

A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.

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Answer:

I got 8 book cases

Step-by-step explanation:

To determine if a value is less than 23 minutes, we can use the concept of standard deviations from the mean.

Given:

Mean = μ

Standard Deviation = σ

We are provided with the following information:

i) Two more than 46% less than 23 min or greater than 41 min:

To find the percentage that lies within two standard deviations above the mean (greater than 41 minutes), we can use the empirical rule. According to this rule, approximately 95% of the data falls within two standard deviations of the mean. Therefore, the percentage of values greater than 41 minutes is (100% - 95%) / 2 = 2.5%.

To find the percentage that lies within two standard deviations below the mean (less than 23 minutes), we can subtract the percentage above the mean from 50%. So, the percentage of values less than 23 minutes is 50% - 2.5% = 47.5%.

The percentage of values less than 23 minutes is approximately 47.5%.

To calculate the percentages, we used the empirical rule which states that in a normal distribution, about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

For the given problem, we applied the concept of two standard deviations to determine the percentage of values greater than 41 minutes and less than 23 minutes. By subtracting the percentage above the mean from 50%, we obtained the percentage below 23 minutes, which turned out to be 47.5%.

Please note that these calculations assume a normal distribution and that the given data follows this distribution pattern.

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\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

Answer:

= x^3 + 5x^2 + 5x + 3

Step-by-step explanation:

Let's simplify: Step-by-Step.

x^3 + 5x^2 + 7x − 2x + 3

=x^3 + 5x^2 + 7x + − 2x + 3

Combine Like Terms:

=x^3 + 5x^2 + 7x + − 2x + 3

=(x^3) + (5x^2) + (7x + − 2x) + (3)

=x^3 + 5x^2 + 5x + 3

Answer:

=x^3 + 5x^2 + 5x + 3

HOPE THIS HELPS!

PLEASE MARK BRAINLIEST IF THIS HELPED YOU LEARN

Answer:

(x³ + 5x² + 7x – 2) /(x+3)=(x^2+2x+1)-5/(x+3)

Answer:

2.B

Step-by-step explanation:

2.

Henry's container holds milk=200*7/8=175 ml

Answer:

-10

Step-by-step explanation:

F(-1)=-6

g(-6)=-10

Answer:

(z−4)(z−5)

Step-by-step explanation:

We need two numbers that...

Add together to get -9

Multiply together to get 20

-4 and -5 do just that!

So you fill in the blanks and get (z−4)(z−5)

Hope this helps :)

The time it take riders to pass over the hill and reach ground level is 111.19 seconds .

Given :

the roller coaster's height expressed by the equation below;

h = -0.067t^2 + 7t + 50

where

t is the time in seconds

The driver will hit the ground at the point where h = 0

Substitute

-0.067t^2 + 7t + 50 = 0

Multiply through  by -1

0.067t^2 - 7t +-50 = 0

Factorize :

On factorizing, the positive value of "t" is 111.19 seconds

Hence the time it take riders to pass over the hill and reach ground level is 111.19 seconds

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Answer:

15 minutes

Step-by-step explanation:

Because it said two days, therefore, you divide 30 by two and then you get your answer.

Its 11.3                                                                                          11.3

pls rate me pls