1. Consider a damped spring-mass system with m = 1kg, = 2
kg/s^2 and c = 3 kg/s. Find the general solution. And solve the
initial value problem if y(0) = 1 and y′(0) = 0.

Answers

Answer 1

The general solution of the damped spring-mass system with the given parameters is y(t) = e^(-t/2) [c1cos((√7/2)t) + c2sin((√7/2)t)]. By applying the initial conditions y(0) = 1 and y'(0) = 0, the specific solution can be obtained as y(t) = (2/7)e^(-t/2)cos((√7/2)t) + (3/7)e^(-t/2)sin((√7/2)t).

The equation for the damped spring-mass system can be expressed as my'' + cy' + ky = 0, where m is the mass, c is the damping coefficient, and k is the spring constant. In this case, m = 1 kg, c = 3 kg/s, and k = 2 kg/[tex]s^2[/tex].

To find the general solution, we assume a solution of the form y(t) = e^(rt). By substituting this into the equation and solving for r, we get [tex]r^2[/tex] + 3r + 2 = 0. Solving this quadratic equation gives us the roots r1 = -2 and r2 = -1.

The general solution is then given by y(t) = c1e^(-2t) + c2e^(-t). However, since we have a damped system, the general solution can be rewritten as y(t) = e^(-t/2) [c1cos((√7/2)t) + c2sin((√7/2)t)], where √7/2 = √(3/4).

By applying the initial conditions y(0) = 1 and y'(0) = 0, we can solve for the coefficients c1 and c2. The specific solution is obtained as y(t) = (2/7)e^(-t/2)cos((√7/2)t) + (3/7)e^(-t/2)sin((√7/2)t). This satisfies the given initial value problem.

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Related Questions

Central Airlines claims that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming, is $605. This claim is being challenged by the Association of Travel Agents, who believe the median price is less than $605. A random sample of 25 round-trip tickets from Chicago to Jackson Hole revealed 11 tickets were below $605. None of the tickets was exactly $605. State the null and alternate hypotheses.

Answers

Null hypothesis is that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is $605. Alternative hypothesis is that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is less than $605.

The median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is $605.

The median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is less than $605.As per the given question, Central Airlines claims that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is $605. But, this claim is being challenged by the Association of Travel Agents, who believes that the median price is less than $605. Hence, we need to test whether the median price is less than $605 or not.Hence,Null hypothesis is that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is $605. Alternative hypothesis is that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is less than $605.

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What is the range for the following data?
52, 32, 61, 82, 63

Answers

Answer:

The range would be 50.

Step-by-step explanation:

Range is found by putting a list or set of numbers in order, then subtracting the lowest number from the highest.

32, 61, 63, 52, 82

82 - 32 = 50

44% of what number is 400?

Answers

Answer:

909.09

Step-by-step explanation:

400 divided by 44% is about 909.09.

909 !!!!!!!!!!!!!!!!!!!!!

Isaiah is decorating the outside of a box in the shape of a triangular prism. The figure
below shows a net for the box.
What is the surface area of the box, in square meters, that
Isaiah decorates

Answers

Answer:

389.19 m²

Step-by-step explanation:

The surface area of the box = area of the two equal triangles + area of the 3 different rectangles

✔️Area of the two equal triangles:

Area = 2(½*base*height)

base = 7 m

height = 8 m

Area of the two triangles = 2(½*7*8) = 56 m²

✔️Area of rectangle 1:

Area = Length*Width

L = 13 m

W = 7 m

Area of rectangle 1 = 13*7 = 91 m²

✔️Area of rectangle 2:

L = 13 m

W = 8 m

Area of rectangle 2 = 13*8 = 104 m²

✔️Area of rectangle 3:

L = 13 m

W = 10.63 m

Area of rectangle 3 = 13*10.63 = 138.19 m²

✅Surface Area of the box = 56 + 91 + 104 + 138.19 = 389.19 m²

Sammy counts the number of people in one section of the school auditorium. He counts 18 female students, 16 male students, and 6 teachers. There are 720 people in the auditorium. Consider the probability of selecting one person at random from the auditorium

Answers

Correct Question:

He counts 18 female students, 16 male students, and 6 teachers. There are

720 people in the auditorium. Consider the probability of selecting one person

at random from the auditorium.

Which of these statements are true?

Choose all that apply.

A:  The probability of selecting a teacher is 6%.

B : The probability of selecting a student is 85%.

C : The probability of selecting a male student is 32%.

D : The probability of selecting a female student is 45%.

Step-by-step explanation:

Option B  and D are correct because

The total number of people in one cross section = 18 + 16 + 6 = 40.

A = The probability of selecting a teacher is = (6/40)x100 = 15 % not equal to 6 %

B = The probability of selecting a male student is = (34/40)x100 = 85%

C = The probability of selecting a male student is = (16/40)x100 = 40 % not equal to 32 %

D : The probability of selecting a female student is = (18/40)x100= 45%

Point (2.-3) on glx) is transformed by -g[4(x+2)]. What is the new point? Show your work

Answers

After considering the given data we conclude that the new point generated is (2,3), under the condition that g(x) is transformed by [tex]-g[4(x+2)][/tex].

To evaluate the new point after the transformation of point (2,-3) by -g[4(x+2)], we can stage x=2 and g(x)=-3 into the expression [tex]-g[4(x+2)][/tex]and apply  simplification to get the new y-coordinate. Then, we can combine the new x-coordinate x=2 with the new y-coordinate to get the new point.
Stage x=2 and g(x)=-3 into [tex]-g[4(x+2)]:[/tex]
[tex]-g[4(2+2)] = -g = -(-3) = 3[/tex]
The new y-coordinate is 3.
The new point is (2,3).
Hence, the new point after the transformation of point (2,-3) by [tex]-g[4(x+2)][/tex] is (2,3).
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Write a function trapezium_integrator(f, start, end, num_traps) that uses the Trapezium Rule to evaluate the integral ∫endstartf(x)dx where f, start, and end are defined in the formula above, and num_traps is the number of trapeziums that the integration interval should be divided into.

Notes:

You may assume num_traps >= 1
Hint: This should be a simple modification of your code from the last question.
We are still expecting you to compute the width of each trapezium and then use a for loop to solve this problem, iterating over the trapeziums to sum their areas. A more efficient approach, using numpy and avoiding any explicit loops, is the topic of one of the challenge questions.

Answers

The function trapezium_integrator uses the Trapezium Rule to approximate the value of a definite integral. It takes four parameters: f, which represents the function to be integrated, start and end, which specify the interval of integration, and num_traps, the number of trapeziums used to approximate the integral.

In the Trapezium Rule, the interval of integration is divided into multiple trapeziums of equal width. The area of each trapezium is calculated as the sum of the lengths of its parallel sides divided by 2, multiplied by its height (the difference between the function values at the two endpoints of the trapezium). The areas of all trapeziums are then summed to obtain an approximation of the integral.

The function calculates the width of each trapezium by dividing the interval length by the number of trapeziums. It then uses a for loop to iterate over the trapeziums, accumulating their areas. The final result is returned as the approximation of the integral.

By dividing the interval into smaller trapeziums, the Trapezium Rule provides a reasonably accurate estimate of the integral. However, for highly oscillatory or irregular functions, a large number of trapeziums may be required to achieve sufficient accuracy. In such cases, more sophisticated numerical integration methods may be more appropriate.

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Find the zeros of the following quadratic functions.
3) x2 + 5x + 6 = 0

Answers

the zeros are x= -6 & x= 1

Given the definitions of f(x) and g(x) below, find the value of (gof)(1).
f(x) = 2x² – 2x – 4
g(x) = -5x + 14

Answers

Answer:

[tex](g*f)(x) = 34[/tex]

Step-by-step explanation:

For sake of clarity, [tex](g * f)(x) = g(f(x))[/tex]

First, find [tex]f(1)[/tex]

[tex]f(1) = 2(1)^2 - 2(1) - 4\\f(1) = 2-2-4 \\f(1)=-4[/tex]

Then, take what you got for [tex]f(1)[/tex] and plug that into [tex]g(x)[/tex].  In this case, [tex]f(1) = -4[/tex]

[tex]g(-4) = -5(-4) + 14\\g(-4)= 20 + 14\\g(-4) = 34[/tex]

Please make sure to mark brainliest if this satisfies your

How do you turn 5/2 into 10/4?

Answers

That’s easy. To turn 5/2 into 10/4 you multiply by 2. :D Hope this helps!

Answer:

YOU DO IT X 2

Step-by-step explanation:

Find the solution to the linear system of differential equations { 146 +24y 12x + 20y satisfying the initial conditions X(0) = 3 and Y(0) = 3. x(t)=__ y(t)=__

Answers

Therefore, the solution to the given system of differential equations, with the initial conditions x(0) = 3 and y(0) = 3, is:

x_(t) = 146t + 24yt + 3

y_(t) = (876t + 21) / ((-144) - 10t)

To solve the given linear system of differential equations, let's rewrite the system in a more standard form:

dx/dt = 146 + 24y

dy/dt = 12x + 20y

We'll use the initial conditions x_(0) = 3 and y_(0) = 3 to find the specific solution.

To solve the system, we can use the method of integrating factors.

Solve the first equation:

dx/dt = 146 + 24y

Rearrange the equation to isolate dx/dt:

dx = (146 + 24y) dt

Integrate both sides with respect to x:

∫dx = ∫(146 + 24y) dt

x = 146t + 24yt + C_(1) ---(1)

Solve the second equation:

dy/dt = 12x + 20y

Rearrange the equation to isolate dy/dt:

dy = (12x + 20y) dt

Integrate both sides with respect to y:

∫dy = ∫(12x + 20y) dt

y = 6x + 10yt + C_(2) ---(2)

Now, we'll apply the initial conditions x_(0) = 3 and y_(0) = 3 to find the values of C_(1) and C_(2).

From equation (1), when t = 0, x = 3:

3 = 146(0) + 24(3)(0) + C_(1)

C_(1) = 3

From equation (2), when t = 0, y = 3:

3 = 6(0) + 10(3)(0) + C_(2)

C_(2) = 3

Now, substituting the values of C_(1) and C_(2) back into equations (1) and (2), we get:

x = 146t + 24yt + 3

y = 6x + 10yt + 3

Simplifying further:

x = 146t + 24yt + 3

y = 6(146t + 24yt + 3) + 10yt + 3

x = 146t + 24yt + 3

y = 876t + 144y + 18 + 10yt + 3

x = 146t + 24yt + 3

y - 154y - 10yt = 876t + 18 + 3

(-144y) - 10yt = 876t + 21

y = (876t + 21) / (-144 - 10t)

Therefore, the solution to the given system of differential equations, with the initial conditions x(0) = 3 and y(0) = 3, is:

x_(t) = 146t + 24yt + 3

y_(t) = (876t + 21) / ((-144) - 10t)

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i’m lost on this help would be nice

Answers

Answer:

3x - 4 = 14

+4. +4

3x = 18

÷3. ÷3

x = 6

A seventh-grade class raised $380 during a candy sale. They deposited the money in a savings account for 6 months. If the bank pays 5.3% simple interest per year, how much money will be in the account after 6 months?

Answers

Answer: You want to calculate the interest on $380 at 5.3% interest per year after .5 year(s).

The formula we'll use for this is the simple interest formula, or:

Where:

P is the principal amount, $380.00.

r is the interest rate, 5.3% per year, or in decimal form, 5.3/100=0.053.

t is the time involved, 0.5....year(s) time periods.

So, t is 0.5....year time periods.

To find the simple interest, we multiply 380 × 0.053 × 0.5 to get your answer.

Step-by-step explanation:

7. An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Littleton. A random sample of 225 fathers from Littleton, yielded 97 who did not help with child care. Using a .05 level of significance test the claim that the proportion is at least 34%.

Answers

The calculated value of z = 2.80 > the Critical value of z = -1.645, we reject the null hypothesis.

Hence, the claim that the proportion is at least 34% is rejected.

Therefore, the researcher's claim is true that the figure is higher for fathers in Littleton.

Null hypothesis:

H0: p ≥ 0.34

Alternative hypothesis:

Ha: p < 0.34

where:p = proportion of Littleton fathers who do not help with childcare

Here, the level of significance, α = 0.05

Level of significance = α = 0.05

The test statistics for a proportion is given as z-test.  

The formula for calculating z-score for a proportion is: z = (p - P) / sqrt[P(1 - P) / n]

where:

P = Population proportion

p = Sample proportion

n = Sample size

The calculated value of z-statistics can be compared with the critical value of z-score from the standard normal distribution table at a particular level of significance.

If the calculated value of z is greater than the critical value of z, then we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

Calculating the z-statistic:

Here, Sample size n = 225

Sample proportion

p = 97/225

= 0.4311

Population proportion

P = 0.34z

= (p - P) / sqrt[P(1 - P) / n]z

= (0.4311 - 0.34) / sqrt[(0.34)(0.66) / 225]z

= 2.80

Since the alternative hypothesis is one-tailed (Ha: p < 0.34), the critical value of z at α = 0.05 can be found as follows:

The critical value of z = zα

= -1.645

Since the calculated value of z = 2.80 > the Critical value of z = -1.645, we reject the null hypothesis.

Hence, the claim that the proportion is at least 34% is rejected.

Therefore, the researcher's claim is true that the figure is higher for fathers in Littleton.

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ht
Which of the following is an equivalent expression to the expressione,
А
B
D
ANSWER QUICK PLZ

Answers

Answer A is your correct answer

Can someone help me on this

Answers

Answer:

Y = 10 I believe

Step-by-step explanation:

To solve this we need to find what number, times 6, equals 18 - it's fairly easy to find the answer is three.

So what, minus seven, equals 3?

A circle is inscribed in an isosceles trapezoid with bases of 8 cm and 2 cm. Find the probability that a randomly selected point inside the trapezoid lies on the circle

Answers

Given that a circle is inscribed in an isosceles trapezoid with bases of 8 cm and 2 cm. We need to find the probability that a randomly selected point inside the trapezoid lies on the circle.

The isosceles trapezoid is shown below: [asy] draw((0,0)--(8,0)--(3,5)--(1,5)--cycle); draw((1,5)--(1,0)); draw((3,5)--(3,0)); draw((0,0)--(1,5)); draw((8,0)--(3,5)); draw(circle((2.88,2.38),2.38)); label("$8$",(4,0),S); label("$2$",(1.5,5),N); [/asy]Let ABCD be the isosceles trapezoid,

where AB = 8 cm, DC = 2 cm, and AD = BC.

Since the circle is inscribed in the trapezoid, we can use the following formula:2s = AB + DC = 8 + 2 = 10 cm

Where s is the semi-perimeter of the trapezoid. Also, let O be the center of the circle. We can draw lines OA, OB, OC, and OD as shown below: [asy] draw((0,0)--(8,0)--(3,5)--(1,5)--cycle); draw((1,5)--(1,0)); draw((3,5)--(3,0)); draw((0,0)--(1,5)); draw((8,0)--(3,5)); draw(circle((2.88,2.38),2.38)); label("$A$",(0,0),SW); label("$B$",(8,0),SE); label("$C$",(3,5),N); label("$D$",(1,5),N); label("$O$",(2.88,2.38),N); label("$8$",(4,0),S); label("$2$",(1.5,5),N); draw((0,0)--(2.88,2.38)--(8,0)--cycle); label("$s$",(3,0),S); label("$s$",(1.44,2.38),E); [/asy]Since O is the center of the circle, we have:OA = OB = OC = OD = rwhere r is the radius of the circle.

Also, we have:s = OA + OB + AB/2 + DC/2s = 2r + 2s/2s = r + 5 cmWe can solve for r:r + 5 cm = 10 cmr = 5 cmNow that we know the radius of the circle, we can find the area of the trapezoid and the area of the circle.

Then, we can find the probability that a randomly selected point inside the trapezoid lies on the circle as follows:Area of trapezoid = (AB + DC)/2 × height= (8 + 2)/2 × 5= 25 cm²Area of circle = πr²= π(5)²= 25π cm²Therefore, the probability that a randomly selected point inside the trapezoid lies on the circle is:

Area of circle/Area of trapezoid= 25π/25= π/1= π

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The probability that a randomly selected point inside the trapezoid lies on the circle is 0.399 or 39.9%. Therefore, option (A) is the correct answer.

The circle is inscribed in an isosceles trapezoid with bases of 8 cm and 2 cm.

Inscribed Circle of an Isosceles Trapezoid

Therefore, the length of the parallel sides (AB and CD) is equal.

Let the length of the parallel sides be ‘a’. Then, OB = OD = r (let)

It is also given that the lengths of the parallel sides of the trapezoid are 8 cm and 2 cm.

Then, its height is given by:

h = AB - CD / 2 = (8 - 2) / 2 = 3 cm

Therefore, the length of the base BC of the right-angled triangle is equal to ‘3’.

Then, the length of the other side (AC) can be given as:

AC = sqrt((AB - BC)² + h²) = sqrt((8 - 3)² + 3²) = sqrt(34) cm

The area of the trapezoid can be calculated as follows:

Area of the trapezoid = 1/2 (sum of the parallel sides) x (height)A = 1/2 (8 + 2) x 3A = 15 sq. cm.

The area of the circle can be given by:

Area of the circle = πr²πr² = A / 2πr² = 15 / (2 x π)

Therefore, r² = 2.39

r = sqrt(2.39) sq. cm.

Now, the probability that a randomly selected point inside the trapezoid lies on the circle can be calculated by dividing the area of the circle by the area of the trapezoid:

P (point inside the trapezoid lies on the circle) = Area of the circle / Area of the trapezoid

P = πr² / 15

P = π (2.39) / 15

P = 0.399 or 39.9%

The probability that a randomly selected point inside the trapezoid lies on the circle is 0.399 or 39.9%.

Therefore, option (A) is the correct answer.

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Bases are 6 and 10 the height is 4 whats the area of the trapszoid

Answers

Answer:

here,hope this helps : )

Step-by-step explanation:

Answer: A= 32

a (Base) 6

b (Base) 10

h (Height) 4

Step-by-step explanation: A=a+b

2h=6+10

2·4=32    I really hoped this helped

Find the value of X for which the following fraction is undefined
2x²+x-15
________
2/3x²-6

Answers

Answer: ±√2

Step-by-step explanation: A fraction is undefined when its denominator is =0 or undefined. so we need to get 2/3x²-6=0 or undefined. so we can also do 3x^2-6=0. Solving yields ±√2!

Find the median of the data.

93,81,94,71,89,92,94,99

Answers

Answer: 92.5

So to find median all we have to do is rearange it from low - high and get the middle number

71  81  89  92  93  94  94  99

So take this and you know the middle is right in between 92 and 93

71  81  89  92      |      93  94  94  99

All you have to do then is take the mean of 92 and 93 (so do [92+93]/2)

Answer is 92.5

What is the simplified form of the following expression? Assume x>0. 4 square root 3 over 2x

Answers

Answer:

the answer is B)

4√24x^3/2x

Solution:

The answer is B

Step-by-step explanation:

I just took the test.

Can someone state the range of this function pleaseee?

Answers

Answer:

Range = [0, ∞)

Step-by-step explanation:

Range is the y-values

For this question y starts at 0 and just continually goes up so:

Range = [0, ∞)

According to a 2014 poll by the American Academy of Ophthalmology, Americans break down like this when it comes to eye color:

• Brown eyes: 45 %

• Blue eyes: 27 %

• Hazel eyes: 18%

• Green eyes: 9%

• Other: 1%

Consider a random group of 20 American people. Let a random variable X be the number of Americans in this group with green eyes.

(a) Argue that this is a binomial experiment.

(b) Find the probability that

i. None have green eyes

ii. Nine have green eyes

iii. At most three have green eyes

iv. At least four have green eyes

v. If four people out of twenty have green eyes. Is it unusual?

(c) What is the mean and standard deviation of this distribution?

Answers

This is a binomial experiment because it meets all the necessary conditions: a fixed number of trials (20 people in the group), independence of each trial (assuming eye color is independent), two possible outcomes (green eyes or not), a constant probability of success (9% for having green eyes), and the random variable representing the count of successes (number of Americans in the group with green eyes, denoted as X).

To argue that this is a binomial experiment, we need to check if the following conditions are met:

1. The experiment consists of a fixed number of trials: In this case, we are considering a fixed number of trials equal to 20, as we have a random group of 20 American people.

2. Each trial is independent: We assume that the eye color of each person in the group is independent of the others.

3. There are only two possible outcomes for each trial: The outcomes are either having green eyes or not having green eyes.

4. The probability of success is constant for each trial: The probability of an American having green eyes is fixed at 9% for each individual in the population.

5. The random variable X represents the count of successes: In this case, X represents the number of Americans in the group with green eyes.

Since all these conditions are satisfied, we can conclude that this is a binomial experiment.

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QUICK! Giving brainliest to correct answer

Answers

Answer:

Dominos is the better deal.

In this situation dominos is the better deal.

In 3^6, 6 is called ___.



base


exponent

Answers

The answer is B, Exponent

Step-by-step explanation:

the correct answer is exponent because 6 is its power.

hope this answer will help u.

have a great time.

Rewrite the expression using a DIVISION SYMBOL: "The quotient of m and 7."

Answers

Answer:

m ÷ 7

Step-by-step explanation:

"Quotient" means you're dividing, so this just means you're dividing m by 7.

Which point on the graph represents the y-intercept?


Answers

W . The point was placed on the Y-intercept

HELP



4(x-2+y)=???????

Answers

Answer:

4+4−8

Step-by-step explanation:

A type of origami paper comes in 15 cm by 15 cm
square sheets. Hilary used two sheets to make the
origami dog. What is the total area of the origami
paper that Hilary used to make the dog?

Answers

Answer:

150 cm squared

Step-by-step explanation:

I guess that's the answer if I'm wrong you can tell me right away so that I can try another method thank you.

how do you solve for the x ?

Answers

Answer:

x = -8

Step-by-step explanation:

these angles are vertical, therefore they are equal

x + 78 = 70

x = -8

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following the audit report release date, auditors became aware of facts existing at the report date that would have affected the reports had auditors then been aware of such facts. what is the most appropriate initial course of action that auditors should take Select each of the terms with the best description of its purpose. Terms Definitions 1. A report that shows predicted revenues and expenses for a budgeting period. 2. Employees affected by a budget help in preparing it 3. Planning future business actions and expressing them as formal plans, 4. A comprehensive business plan that includes operating, investing, and financing budgets. 5. Summarizes the effects of investing activities on cash 6. Shows expected cash inflows and outflows and helps determine financing needs. 7. An approach that requires all expenses to be justified for each new budget. 8. A formal statement of future plans, usually expressed in monetary termsBudgeted income statement Participatory budgeting Budgeting Master budget Capital expenditures budget Cash budoet g needs. et. Prey 2 of 2 Zero-based budget Budget Sketch the region whose area is given by the integral and evaluate the integral---/int from pi/4 to 3pi/4 /int from 1 to 2 r dr d(theta) Given the demand and cost function shown below, calculate the profit maximizing quantity Q(P)=960-15P C(Q)=8Q+2675 QUESTION 5 Given the demand and cost function shown below, calculate the profit maxim Common ways to reduce a perceived inequity include all the following, except:A.change work effortB.change outcomesC.change perceptions of equityD.leave the job entirelyE.All of these choices are common ways to reduce a perceived inequity. EconomicsStrategy Cost ($ million) Turtles saved (thousands) A. Beach conservation 20 25 B. Turtle excluder equipment on 55 40 trawling nets C. A tax per shrimp caught 20 10 1. If you want to save 10,000 turtl Bill Murray and Rick Moranis get into a debate on the bestGhostbuster Movie. Bill shoves Rick into a a store window displayand Rick sues for battery. In court RIck must proveThat Bill intende Let 5UR5 be the subspace generated by (1,1,1,0,1)(1,1,1,0,1), (2,1,0,0,1)(2,1,0,0,1), and (0,0,1,0,0)(0,0,1,0,0). Let 5VR5 be the subspace generated by (1,1,0,0,1)(1,1,0,0,1), (3,2,0,0,2)(3,2,0,0,2), and (0,1,1,1,1)(0,1,1,1,1).(a) Determine a basis of UV.(b) Determine the dimension of +U+V. Which one of the correlation coefficient (t) values between two variables suggest high multicolinearity? 0.59 -0.80 0.62 -0.20 Change in daughter's height in inches given a 1 inch increase in the mother's height. (m*2+b) - (m*1+b) # essentially the slope. material 1 has an index of refraction of 1.15.material 2 has an index of refraction of 2.30.if light passes from air into each of these materials at the same angle of incidence, how will the angle of refraction in material 1 compare to the angle of refraction in material 2? Consider a perfectly-competitive industry where each firm has the following long run cost functionC(q) = q3 11q2 + 111q,where q is the firms output. What is the long-run equilibrium price in this market?Round your final answer to two decimal places, if necessary A factory has production function Q = f(L, K). In year 1: 212 = f(78, 144) In year 5: 309 = f(117, 216) This production function displays increasing returns to scale.TrueFalse why the server, rent and marketing cost is most expensive sourceto create a digital bank? Give three examples Which was the last of the indian wars to occur in california or oregon? Problem 15.73. Give a combinatorial proof for this identity: n m (0)(...)-("") (" *) k-r r=0 The shifter tool Another manipulable graph object The shifter tool is designed to let you answer questions by shifting entire lines or points along a line (or both) from one position to another. You can select any part of the line and drag it to the left or to the right. Once you have moved the point or line far enough, it will snap into one of a few possible positions. Shift the blue demand line (labeled D) to the right. Then position the point along the line so that it reflects the same price as the point along the original line. Note: Select and drag the curve to the desired position. The curve will snap into position, so if you try to move a curve and it snaps back to its original position, just drag it a little farther. ? 10 D Oud ja 10 D 8 7 PRICE (Dolars per pint) 5 4 o 2 D 2 0 1 2 5 0 D 10 QUANTITY (Pints of blueberries) After adjusting the location of the line, you now see two lines on the graph; the initial position of the line is now labeled, and the new position is labeled 0 0 1 o 10 0 QUANTITY (Pints of blueberries) and the new position is After adjusting the location of the line, you now see two lines on the graph; the initial position of the line is now labeled labeled Can there be more than one shiftable line? Sometimes you will be given two shiftable lines, in which case you may be required to shift just one, both, or neither of these lines, depending on the instructions. Each graph object with its own separate palette icon will be graded individually. Note: When you are given two lines, the point representing their intersection does not have a palette icon, and this point cannot be moved independently of the lines. Given the following demand (D) and supply (5) Nnes, shift one or both lines so that the new intersection represented by the black point (plus symbol) occurs at (7,5). Note: Select and drag one or both of the curves to the desired position. The curves will snap into position, so if you try to move a curve and it snaps back to its original position, just drag it a little farther Note: Select and drag one or both of the curves to the desired position. The curves will snap into position, so if you try to move a curve and it snaps back to its original position, just drag it a little farther. 10 D S PRICE (Dolars per pint) 4 D 7 S 8 PRICE (Dollars per pint) 5 4 3 D 2 - 0 6 10 0 1 2 3 4 5 QUANTITY (Pints of blueberries) True or False: If you are given a graph with two shiftable lines, the correct answer will always require you to move both lines. O True False Predict which of the following two compounds will undergo an E2 reaction more rapidly:O The cis isomer is faster because the Cl predominantly occupies an equatorial position.O The cis isomer is faster because the Cl predominantly occupies an axial position.O The trans isomer is faster because the CI predominantly occupies an axial position.O The trans isomer is faster because the CI predominantly occupies an equatorial position. Assume that a competitive firm has the total cost function:TC=1q340q2+840q+1800TC=1q3-40q2+840q+1800Suppose the price of the firm's output (sold in integer units) is $750 per unit.Using tables (but not calculus) to find a solution, what is the total profit at the optimal output level?Please specify your answer as an integer. The company's internal auditors and the Ethics Officer should report:Day-to-day to the CEODay-to-day to the Audit Committee of the Board of DirectorsRegularly to the Audit Committee of the Board of Directors without management beingpresent(a) and (c)(a) and (b)