Mathematics Questions and Answers August 14, 2020

explain about this diagram?

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The manager of a downtown Chicago sightseeing tour company is concerned about overbooking for one of his bus tours. The bus has 15 seats but sometimes there are empty seats. His records show that about 20% of ticket holders do not show up for their tour. Tickets cost $10 and are non-refundable. If the manager overbooks the tour and more than 15

The following data shows the results of womens 200m training camp. Each value below is the time (in seconds) taken on a single 200m lap by each athlete. 30.2 30.1 29.8 29.9 30.1 30 30.2 30 30.1 30 29.7 30.4 30.2 29.8 30.2 30.5 29.9 30 29.9 29.7 30.1 30 30.2 30.2 30.2 30.3 29.3 29.7 30.7 29.6 30 29.8 29.4 30.2 29.9 29.9 30 30 29.9 30 29.9 29.8 29.8

The production of wine is a multibilliondollar worldwide industry. In an attempt to develop a model of wine quality as judged by wine experts, data was collected from red wine variants. A sample of 20 wines is provided in the accompanying table. Develop a muitiple linear regression model to predict wine quality, measured on a scale from 0 (very

Calculate p-value for the following conditions and determine whether or not to reject the null hypothesis: (a) one-tail test, zx=1.50zx=1.50 and =0.05=0.05 . (b) one-tail test, zx=2.75zx=2.75 and =0.02=0.02 . (c) two-tail test, zbarx=2.60zbarx=2.60 and =0.05=0.05 . (d) two-tail test, zx=1.26zx=1.26 and =0.10=0.10

Instaleaf, a Canadian clothing merchandiser, made a contract with Raston Clothing of Hong Kong whereby Instaleaf would import jackets from Raston and pay them by letter of credit. The letter of credit provided that shipments were to be made in installments from Taiwan to Montreal and that the foreign supplier could recover payment for each

MusicZ is an independent recording company. MusicZ is facing increasing competition from new entrants to their industry. As a result, MusicZ needs to implement changes in their work units. These changes are likely to disrupt current schedules, employee rosters and work processes significantly. As a consultant for MusicZ, prepares a change

please answer all the questions for me B and C (i, ii)

(b) You are employed as the Quality Control Officer of Guinness Ghana limited, Kumasi. As part of your responsibilities, you are to ensure that the company procures the best of raw materials and other inputs for their day to day productions. The company has just purchased lots (1,000,000 pieces) of bottles and you are to inspect them to ensure the

a) Consider again the chemical reactor example with parameter ? = 0.5. We saw in Section 5.6 that 10% of the particles stay in the vessel no longer than about 12 secondswhile the mean residence time is 2 minutes. Which percentage of the particles stay no longer than 2 minutes in the vessel? b) Compute the median of an Exp(lamnda) distribution. c)

Four different kinds of fertilizers f1, f2, f3 and f4 are used to study the yield of beans. The soil is divided into three blocks each containing four homogeneous plots. The yields in pounds per acre and the corresponding treatments are as follows: Block 1 Block 2 Block 3 f1 = 42.7 f3 = 50.9 f4 = 51.1 f3 = 48.5 f1 = 50.0 f2 = 46.3 f4 = 32.8 f2 =

IA i) Identify a development problem. Describe the context within which the problem exists. and why it is a problem. ii) Develop a conceptual framework that outlines your problem identified in (1) above within its context. Question 2 2A Using the problem you identified in 1A above, develop the following components Problem tree Objective tree ii)

Find z when the area between 0 and z is 0.4750

Rome Petshop uses 3 different ingredients to manufacture 4 types of dog food. These 3 ingredients are protein, fat, and grains. Rome Petshop has 1000 pounds of protein, 750 pounds of fat, and 450 pounds of grains in its inventory for August 2020 production. The four types are dogfood and their specifications are as follows. Puppy-Love: At least

The student performs a second titration using the 0.10 M NAOH(aq) solution again as the titrant, but this time with a 20. mL sample of 0.20 M HCl(aq) instead of 0.10 M HC1(aq). (f) The box below to the left represents ions in a certain volume of 0.10 M HCl(aq). In the box below to the right, draw a representation of ions in the same volume of 0.20

one of the biggest obstacles to empowerment is that employees are given decision-making responsibilities but not the appropriate to implement the decision a). level in the organization b). influence c). compensation d). authority

One study showed that in a certain year, airline fatalities occur at the rate of 0.012 deaths per 100 million miles. Find the probability that, during the next 100 million miles of flight, there will (a) exactly zero deaths. Interpret the results. (b) at least one death. Interpret the results. (c) more than one death. Interpret the results. (a)

Let U is the set of matrix B in M_3(R) and B is orthogonally diagonalizable. also Another set V contains matrix B in M_3(R) and B is lower triangular. and granted that U and V are subspaces of M_3(R). show U is isomorphic to V and through constructing isomorphism from U to V and V to U.

Dept. Store Deluxe Standard Economy Economy (fate) Up Down,A department store is about to order deluxe, standard, and economy grade DVD players for next year s inventory. The state of the nation s economy (fate) during the year will be a factor on sales for that year. Records over the past 5 years show that if the economy is up, the store will

Adults with epilepsy are recruited into a clinical trial to compare the effect of two classes of anticonvulsant drugsenzyme-inducing and non-enzyme-inducing on serum lipids. The outcome of interest is a new diagnosis of hyperlipidemia. Use the output to answer the following questions. What procedure was used to generate the results in SAS? Is

Data Set Response Variable Number of Response Levels 2 Model Optimization Technique Model Information Number of Observations Read 150 Number of Observations Used 150 Response Profile sex Ordered Total Value hyperlipidemia Frequency 1 No 2 Yes Class Value Class Level Information Female Male hyperlipidemia drug Inducing binary logit Fishers scoring

Figure Q.1 shows the general form of the annual wind speed distribution at a site where the mean wind speed is 5 metres per sec (5 ms). This idealised curve is known as the Rayleigh distribution. i. ii. i. Calculate the percentage of the year during which the site experiences light breezes (4 metres per second), moderate winds (7 metres per

) The optimization problem in Mean Variance Portfolio Optimization (MVO) entails either finding the portfolio w that has the highest expected return for a given level of risk as measured by portfolio variance or finding the portfoliow that has the smallest risk that achieves a target return as shown below min o W wEw s.t. Hp,w w target return w1

Mary Smith, a Level II CFA candidate, was recently hired for an analyst position at the Bank of Ireland. Her first assignment is to examine the competitive strategies employed by various French wineries. Smiths report identifies four wineries that are the major players in the French wine industry. Key characteristics of each are cited in the table

Match the correct terms to the correct definition and in part B correct the bold letters if they are wrong Select the correct term for each of the following descriptions. These are not necessarily complete definitions, but there is only one possible answer for each term. Descriptions Terms The level and nature of risk attributable to a firms

Give your age in days, this calendar year, and the distance to the Sun (this is 1 AU) in km in both standard and scientific notation. Your Age in Days This Calendar Year Distance to Sun Standard Notation Scientific Notation Given the size of the Astronomical Unit (AU) and the fact that Pluto is, on average, 40 AU from the Sun, estimate Plutos

An investigator is interested in the effects of noise on the ability of subjects to concentrate. She assigns subjects randomly to one of three Noise conditions low noise, moderate noise, and loud noise. She administers a test of concentration while the noise is present. She predicts that there will be an overall effect of noise on the ability to

Donny Tee (the Donny) was an unemployed tour guide when lady luck showed up and blessed him with a tax-free Lotto 6/49 winnings of $2 million. After prudently paying off the $500,000 mortgage on his home, he went crazy and spent $300,000 on a used Ferrari Testa Rosa and took a year-long lavish world cruise family vacation for $200,000. Realizing

8. (a) Make a Markov chain model for a rat wandering through the fol lowing maze if, at the end of each period, the rat is equally likely to leave its current room through any of the doorways. (It never stays where it is.) 4 (b) What is the stable distribution 3.

The company that currently you are working with, Dherbalicious has made a strategic decision to provide a fine chemical C, that has been extracted from an algae fermentation broth to the cosmetics industry. You have been assigned to an established extraction plant in North Johor. Feed of 1200 kgh containing 55wt of fine chemicals in aqueous

84. 1) If B and C are subfields of a field E, then their compositum BVC is the intersection of all the subfields of E containing B and C. Prove that if a1,..., an E E, then F(a1) Vv F(an) F(a1,...,an). (ii) Prove that any splitting field KF containing B (as in Exercise 83) has the form K B1v...VB,, where each B is isomorphic to B via an

Cindy has 9000 to invest in a portfolio. Her investment alternatives and their expected returns are Description Expected Return 4.1 Investment RRSP (retirement) Employers retirement plan 1 2 6.2 3 Mutual Fund 5.7 She will put at least 1500 into each investment, and cannot invest more than 9000 in total. In addition, she has three goals which may

A portfolio manager has a bond portfolio of 50 million. The duration of the portfolio is 6.8 years. The front month Tbond futures price is currently at 9717. The cheapesttodeliver bond has a duration of 7.1 years. How should the portfolio manager immunize the portfolio against changes in interest rates in the near term How many contracts are

ING (20 pts) Alberto is a farmer in Nepal. He is deciding whether to plant rice (x), tea (y), lentis (u), coconut (v) or avocado (r). She has 125 acres of land, she only has 150,000 on hand, a storage capacity of 5,000 tons, and a labor of 4,500 hours. Her wife (Betty) says he needs to plant at least 40 acres of avocado which is a requirement from

Spinneys Supermarket at Emaar Residence has three clerks (cashiers) serving customers. On average, 30 customers are being served by a clerk every 10 minutes. For Spinneyss normal working period, customers arrive at the rate of 2 customers per minute. Assume arrivals follow the Poisson distribution and service times follow the exponential

Let U be a universal set and let A and B be two subsets of U. Draw a Venn diagram for each of thefollowing sets. (a) AUB (b) ANB (c) ANB (d) AUB. What can you say about parts (a) and (b) parts (C) and (d)

Let o A, nEN. where An for n1.2.3... Then N A, n1

explain true or false

Let A a,b Then its Power Set is P(A) 3D

Solve : (2x + y + 5) dy - (x + 2y + 8) dx = 0

Find the differential equation of the following equation of circle : x^2 + y^2 - 2Ax - 2By + c = 0

A tank contains 4lb of salt dissolved in 95 gal of water suppose that brine containing 2lb of salt per gallon of brine is allowed to enter the tank at a rate of 2t gal/min and that the mixed solution is drained from the tank at the same rate. Find the amount of salt in the tank after 60 minutes.

A circuit has in series an electromotive force given by E(t) = 5sin(71)t V , a resister of 10 and inductor of 0.1H and a capacitor of 2x10^-4 farads. If the initial current is zero and the initial charge on the capacitor is 0.01 coulombs, find the charge at time t>0

Solve the differential equation da tang (1t) et seaq9 1t

Solve the following imitial valve problem dy dx 2 9 3y dy coS x 2 with initial conditions y (0) 23 and y(0) 10

Solve the boundary valve problem 2 che3 2y x 2y x with boundary conditions y(0) 6, y(4) 8 and y(2) 12 dx2 3D

da Solve (1t 2q 4t2

Evaluate items a and b using the given tables of values. Then, answer the items that follow. a. (lim x) b. lim x 2 2 2 2 f(x) f(x) f(x) f(r) 1.5 2.5 1.5 2.5 1.9 2.1 1.9 2.1 1.99 2.01 1.99 2.01 1.999 2.001 1.999 2.001 1.9999 2.0001 1.9999 2.0001 c. How do you read the expression (lim x) What about lim x d. What do you obscrve about the limits in a

Consider the following complex function f (z) 2e Where z x iy E C A. Which of the following is true Of (2) eey f (z) e ey Of(2) V Re(f (2)) Im(f (2)) eiy B. If f (z) 3 4i, what is the value of x C. If f (z) 4i, what is the value of y (Ignore the multiplicity)

Let Z = 1 + i and C = 1 i . Our goal is to obtain Z^ C . (Only consider the principle value)

D. If ZC V(2)ewhat is the value of Q E. What is Arg (zC)

Let z = 2 i and = 1 i . For the first four subquestions (A to D), you need to have z . Remember that whenever you evaluate z , at that time, work with the principle value only. The last subquestion (E) is a problem dealing with single-valued functions.

D. What is the value of z E. Suppose G (z) ewhere z 2i This G (z)is a single valued function. Now evaluate ln (Re (G) Im (G)) which is denoting a Real logarithm.

c). In polar coordinates, a polar function exists by the name of strophoid, with equation r sec 02 cos 0. Consider the equation of this strophoid that is bounded as ). Plot the strophoid. (ii). Convert the strophoid equation to rectangular coordinates. (iii). Find the area enclosed by the loop.

Let f(x, y), where x g(t) and y h(t). dz dx, z dy and az dx, oz dy xy dt Oy dt d ( dz (). Show that dt ox x dt Oyx dt dt y dz (ii). Find dt

du b). Len u(x,y) and v(x, y). The CauchyRiemann differential equations are given as and dx dy du dv dy ox (1). Verify that the CauchyRiemann differential equations can be written in polar coordinate form as du 1 dv dv 1 du and dr rde dr rde (ii). Using the functions uInx y and v tan (). verify the two forms of the Cauchy Riemann differential

A circuit has in series an electromotive force given by A circuit has in series an electromotive force given by E(t) = 5sin(91)t V , a resister of 7 and inductor of 0.1H and a capacitor of 2x10^-4 farads. If the initial current is zero and the initial charge on the capacitor is 0.01 coulombs, find the charge at time t>0

Let e^ w = z , where z = 2 . (Remember, whenever you solve this equation. Also, remember that there is a difference between log z and Log z ).

InLog(2) D. Find tfrom t Here, the numerator denotes a real logarithm. E. What is the branch point of log (2) z 1 D1 z 0 Z z Z 2 2 log (2)has no branch point

As a result of the water crisis in Lasa, the Lasa Department of Water, with the assistance of their engineers and accountants decided to build a water line that has to be cost effective. The water line will be built from point A to D, as shown in Figure 2. The cost differs, given as such 3k from A to B, 2k from B to C, and k from C to D, where the

Use a double integral to find the volume in the first ocyant bounded by the coordinate planes, the plane y 4, and the plane 1. 3 5 b). Find the area in the first quadrant that is inside the circle r4 sin 0 and outside the lemniscate r 8cos 20.

Q1 Consider the massspring oscillator without friction y y 0. Suppose we add a force which corresponds to push (to the left) of the mass as it oscillates. We suppose that push is described by f(t) h(t 2n) u(t (2n a)) For some a 2n which are allowed to vary. Solve the problem by Laplace y y f(t),y(0) 1, y(0) 0.

Refrence Book:Mathematical Physics,

25 48 44 42 02 04

Consider the following complex function f (2) 2e Where z x iy EC ,D. 1 (In 0) f (In 0) . arg (f (In 0) (n 1 0)) 4 (Consider the principle argument only)

Determine the following limits. Write your answer in the form lim f(x) L. If the limit does not exist, express your answer in the form lim f(x) DNE. 1) lim f(x) x3 4) lim f(x) x5 2) lim f(x) x2 5) lim f(x) x2 3) lim f (x) x1 The graph of f(x) is given by 3 1 6 5 4 2 1 1 6. 1 2 3 3, 2.

On a Cartesian Plane, sketch the graph of the function f (x) x. Then, answer the items that follow. a. Describe the graph of f. b. Use the graph to evaluate each. lim f(x) lim f(x) x1 x3 (x) lim f (x) lim f(x) lim x1.5 lim f(x) x0 c. What do you observe about the cvalue and the limit off as x approaches that value d. What inference about limit

4b. Evaluate items a and b using the given tables of values. Then, answer the items that follow. a. lim x x2 b. lim Vx 2 x2 2 2 2 2 f(x) f(x) f(x) f(x) 1.5 2.5 1.5 2.5 1.9 2.1 1.9 2.1 1.99 2.01 1.99 2.01 1.999 2.001 1.999 2.001 1.9999 2.0001 1.9999 2.0001 c. Is it true that lim (x Vx 2) lim x lim vx 2 Explain your answer. x2 x2 x2 d. Is the

Evaluate items a, b, c, and d using the given tables of values. Then, answer the items that follow. a. lim x2 x2 b. lim 3x x2 2 2 2 2 f(x) f(x) f(x) f(x) 1.5 2.5 1.5 2.5 1.9 2.1 1.9 2.1 1.99 2.01 1.99 2.01 1.999 2.001 1.999 2.001 1.9999 2.0001 1.9999 2.0001 c. lim (x2 3x) d. lim (x2 3x) X2 x2 2 f(x) 2 2 2 f(x) f(x) f(x) 1.5 2.5 1.5 2.5 1.9 2.1

The graph of f(x) is given by 3 1 6 5 4 2 1 0 1 3 5 6 1 2 3 2. ,Determine the following limits. Write your answer in the form lim f (x) L. If the limit c does not exist, express your answer in the form lim f (x) DNE. 1) lim f(x) 4) lim f(x) x3 x5 2) lim f(x) 5) lim f(x) x2 x2 3) lim f (x) x1

Let z = 2 i and = 1 i . For the first four subquestions (A to D), you need to have z^ . Remember that whenever you evaluate z^ , at that time, work with the principle value only. The last subquestion (E) is a problem dealing with single-valued functions.

A. Which of the following is true 20 xp ((1 i) (In 2 i 3) z i exp (In 4) cos (In 2 4) i sin (In 2 ) za exp ((1 i) Log 2i) Oza exp (In 2 5) cos (In 2 ) i sin (In 2 5) za 5.9054 9.7505 i B. If za f (z), then evaluate Re (f (z)) Im (f (z)). C. If za w then what is the value of Im (w) Re (w)

1 The following table gives the seven most common first names among girls born in the United States during 2010 along with their frequencies (in thousands). 332 Number of girls Name (in thousands) Isabella 22.7 Sophia 20.5 Emma 17.2 Olivia 16.9 Ava 15.3 Emily 14.2 Abigail 14.1 Source U.S. Social Security Administration, www.ssa.gov. Draw two bar

The following data give the 2009 estimates of crude oil reserves (in billions of barrels) of Saudi Arabia, Iran, Iraq, Kuwait, Venezuela, the United Arab Emirates, Russia, Libya, Nigeria, Canada, the United States, China, Brazil, and Mexico (source www.eia.gov). 3. 266.7 136.2 115.0 107.0 99.4 97.8 60.0 43.7 36.2 27.7 21.3 16.0 12.6 10.5 Prepare a

4. The television game show The Price Is Right has a game called the Shell Game. The game has four shells, and one of these four shells has a ball under it. The contestant chooses one shell. If this shell con tains the ball, the contestant wins. If a contestant chooses one shell randomly, what is the probability of each of the following outcomes

6. There are a total of 160 practicing physicians in a city. Of them, 75 are female and 25 are pediatri cians. Of the 75 females, 20 are pediatricians. Are the events female and pediatrician independent Are they mutually exclusive Explain why or why not. 212

5. Two thousand randomly selected adults were asked if they are in favor of or against cloning. The following table gives the responses. In Favor Against No Opinion Male 395 405 100 Female 300 680 120 a. If one person is selected at random from these 2000 adults, find the probability that this person i. in favor of cloning ii. against cloning iii.

In a political science class of 35 students, 21 favor abolishing the electoral college and thus electing the President of the United States by popular vote. If two students are selected at random from this class, what is the probability that both of them favor abolition of the electoral college Draw a tree diagram for this problem. 7. 00

8. According to the Recording Industry Association of America, only 37 of music files downloaded from Web sites in 2009 were paid for. Suppose that this percentage holds true for such files downloaded this year. Three downloaded music files are selected at random. What is the probability that all three were paid for What is the probability that

The following table gives a twoway classification of all basketball players at a state university who began their college careers between 2004 and 2008, based on gender and whether or not they graduated. 9. Graduated Did Not Graduate Male 126 55 Female 133 32 If one of these players is selected at random, find the following probabilities. a.

How many home runs would Homer need to hit next season to have a 12-year mean of 60?

13. Verify the following conservation laws (Lamb, 1971) for equation (11.9.1) 0, (1cos u), 0, (1cosu), 3D 3D 4 U. COsu 0, 8. 3D 2 2 u, Un 6. 6. ttt 2 (u cosu). 0. 3D

14. Using the Lagrangian density 1 where V(u) sin u, derive the sineGordon equation 3D u sin u. 15. Show that the bilinear form of the sineGordon equation in Exercise 14 is the pair of equations 3D (D D 1)(w)0 and (D D)(0 w w) 0, (). where u 4 tan

9. (a) Use the Bcklund transformation (11.9.2ab) to show that four solutions u, (r1,2,3,4) satisfy the relation tan ( ( ) (22) (4,2) tan aa where a and 92 are nonzero constants. (b) Apply the relation in Exercise 9(a) to obtain a soliton solution of the sineGordon equation by setting u, 0, and u, different soliton solutions. 10. Examine

4. If V(u) involved in the KleinGordon equation (11.5.1) is given (Whitham, 1974) by Uxx v(u) zo 1 V(u) . ubu .., ,11.13 Exercises 497 derive the result a cos 0ab cos 30 ..., 8. as a0, where the nonlinear dispersion relation is given by o 1k 3abo(a), as a0, and the nonlinear amplitude is 1 9. A a abo(a) as a 0.

Show that the energy integral associated with the KleinGordon equation in Exercise 1 is given by E(1) (1, f cVuf d uf) dr. Show that E(t) is independent of t.

Solve using MOSS a) Positive root for x2x8 0 b) T, 150 9,000 200 44 0.0057, T,

16. A chemical engineer is assigned to the section market analysis for their plant design, with a study period of 20 years. Help him calculate the payback period if these are the data from their design Total Cost of the Project P1,350,000,024.75 Annual Expenses P101,250,333.12 Annual Revenues P727,857,491.68 Replacement Costs P1,500,000 (done

(a) Show that the sineGordon equation sin u 3D is invariant under the transformations m(x Ut) and im(x Ut) where m 3(1U) and 1

A hardware store in a regional city is well known for its range of gardening tools and building supplies particularly timber. One year, there is an over-supply of timber, which means that the hardware store must reduce the price of its timber to clear excess stock. For a limited time, the hardware store manager decides to have a timber sale,

Equilibrium quantity Equilibrium price Percentage of GST saving passed onto customers Revenue hardware store receives Revenue hardware store receives if it passes on ALL of GST saving Before GST removal LEAVE THIS CELL BLANK After GST removal Difference 7. Summarise your findings in 300 words. In your conclusion a. Discuss the effect of the

For the given Loploce funetion, s us16 a) F(s) 3D s9s gs 72 25s b) Fls) 3D (S8) (s11)

You are planning to take out a 5 hundred thousand dollar fixedrate mortgage with a 30year term and a stated annual mortgage rate of 5.7 percent. Your lender offers to lower your stated annual interest rate by onequarter of a percentage point for each discount point you buy. What will your monthly payment be if you buy 3 discount points Round your

You are planning to take out a 5 hundred thousand dollar fixedrate mortgage with a 30year term and a stated annual mortgage rate of 5.7 percent. Your lender offers to lower your stated annual interest rate by onequarter of a percentage point for each discount point you buy. What will your monthly payment be if you buy 3 discount points Round your

The VAV1 factorization of a matrix leads to expressing A as a sum of rank one matrices, i.e. A VAV R1 R2 Rn 3D 3D ... Calculate the rankone matrix resulting from the dominant eigen value and its associated vector given the matrix A. 6 8 A 2

Two thousand randomly selected adults were asked if they are in favor of or against cloning. The following table gives the responses. In Favor Against No Opinion Male 395 405 100 Female 300 680 120 a. If one person is selected at random from these 2000 adults, find the probability that this person is i. in favor of cloning ii. against cloning iii.

solve for 0(t) and r(t) separately )( )( (x y 1) Hint You can write this in polar coordinates and then solve for 0(t) and r (t) separately

1 The following data give the 2009 estimates of crude oil reserves (in billions of barrels) of Saudi Arabia, Iran, Iraq, Kuwait, Venezuela, the United Arab Emirates, Russia, Libya, Nigeria, Canada, the United States, China, Brazil, and Mexico ( source: www.eia.gov ). 266.7 136.2 1 15.0 107.0 99.4 97.8 60.0 43.7 36.2 27.7 21.3 16.0 12.6 10.5

x2y Evaluate dV, where D is the region enclosed by the spherical surface D 2x48y2z x2 y z 1. Correct the result to 4 decimal places.

4. The corners of the square used as centers of the four quadrants or arcs of the sectors are dra side of the square is 10 cm determine the area of the shaded portion.

Let f(x) 1, g(x) 7x 2 and h(x) 5x. 3D 3D Consider the inner product (P, 4) P p(x)q(x) dr in the vector space P(R) of polynomials. Use the GramSchmidt process to determine an orthonormal basis for the subspace spanned by the functions f(x), g(x), and h(x). 12 .

A string is stretched between two points (0,0) and (2,0), if it is dis placed into the curve 4 sin() and released from rest in that position at time t 0. Employ the Fourier transform approach to find the displacement at any time t 0 and at any point 0

Implement perturbation technique to the following BVP Uz uyy u 1 x y 1, u(x, y) 1, x y 1. 3D 3D

Use steepest decent method to solve the following system 3r yz 1, x 3y z 7, x y 3z 7.

Apply RayleighRitz method to solve y y x, 0

Solve using the quadratic formula.0= 4x + 11x + 4

Solve using the quadratic formula. List your answers, separated by commas. Give exact answers or decimals accurate to at least 3 decimal places.

Express the following equations in logarithmic form:(a) 4 = 256 is equivalent to the logarithmic equation:(b) 10-2 = 0.01 is equivalent to the logarithmic equation:

Two separate samples, each with n = 9 individuals, receive different treatments. After treatment, the first sample has SS = 546 and the second has SS = 606. a. Find the pooled variance for the two samples.

Condense the following expressions into a single logarithm by applying the properties of logarithms.Make sure your final answer is written as a single logarithm.a. 2 log(x) - 5 log(y) + 9 log(z) =b. -2 log(z) + 5log(x) - 9 log(y) =