A mass of 5 kg is attached to a spring with spring constant 25N/m. The mass is acted on by an external force of 10 sin(t) Newtons and moves in a medium that imparts a viscous force (i.e. friction) proportional to the velocity with constant 10Ns/m. If the mass is set in motion from its equilibrium position with an initial velocity of 60 cm/s, formulate the initial value problem describing the motion of the mass. Then solve this initial value problem. HINT: watch out for the units! Centimeters are not meters!
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- A particle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field F(x, y, z) = z2i+ 3xyj + 3y2k. Use Stokes' Theorem to find the work done.A photon moving in the +x-direction, scatters off a free stationary electron. The wavelength of the incident photon is 0.0310 nm. After the collision, the electron moves at an angle a below the +x- axis, while the photon moves at an angle = 81.3° above the +x-axis. (For the purpose of this exercise, assume that the electron is traveling slow enough that the non-relativistic relationship between momentum and velocity can be used.) (a) What is the angle a (in degrees)? 47.21 X What is the shift in wavelength of the photon due to the scattering? How can you use momentum conservation in the horizontal and vertical directions to determine the angle? counterclockwise from the +x-axis (b) Determine the speed of the electron (h m/s). m/sConsider two assets with expected return R1=0.22,R2=0.55and variance are s1=0.80, s2=0.88 and r12=0.55 respectively.A portifolio with weights W1=0.25 and W2= 0.65 is formed calculate the expected return and variance of the portifolio
- Expected return and standard deviation. Use the following information to answer the questions: a. What is the expected return of each asset? b. What is the variance of each asset? c. What is the standard deviation of each asset? Hint: Make sure to round all intermediate calculations to at least seven (7) decimal places. The input instructions, phra answers you will type. Data table (Click on the following icon in order to copy its contents into a spreadsheet.) Return on Asset A in State of Economy Boom Normal Recession Probability of State 0.35 0.51 0.14 Print State 0.05 0.05 0.05 Done Return on Asset B in State 0.23 0.08 -0.05 Return on Asset C in State 0.33 0.17 -0.223. Fizen Lures Inc. manufactured fishing lures. Their most popular lure is a Bass plug which uses a hook purchased from another manufacturer and polystyrene for the body of the lure itself. The company uses highly automated injection molding machines to manufacture lures. Because of this direct labor cost are at a minimum because one machine operator can operate three injection molding machines at same time. The company has developed the following standard costs include scrap to manufacture each lure: Material standards: Hook: 1.1 Hooks per lure at $.10 per hook. Polystyrene plastic: 3.5 ounces per lure at $.25 per Labor standards: ounce. Direct labor: .005 hours to produce one lure at $23.50/hr. including all employer payroll taxes and benefits. During month of April the company manufactured 120,000 Bass lures and incurred the following costs: Material costs: Purchased 30,000 pounds (480,000 ounces) of polystyrene for a total cost of $144,000 dollars. Used 418,000 ounces of…If expected level of EBIT is more than the breakeven point, then the EPS will be – a. Infinite b. Negative c. Positive d. Minimum
- Consider the following time series data: Construct a time series plot. What type of pattern exists in the data? Develop a three-week moving average for this time series. Compute MSE and a forecast for week 8. Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 8. Compare the three-week moving average forecast with the exponential smoothing forecast using α = 0.2. Which appears to provide the better forecast based on MSE? Use trial and error to find a value of the exponential smoothing coefficient α that results in a smaller MSE than what you calculated for α = 0.2.The regression analysis is normally depicted as "y = Ax+ B." What does "A" indicate in the equation? A) It is the expected change in the independent variable for a one-unit change in the dependent variable OB) It is the significance level for the test OC) It is the expected change in the dependent variable for a one-unit change in the independent variable OD) The confidence intervalI need to find the slope and the intercept. For the slope round to two decimal places, and for the intercept round to the nearest dollar 
- Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-unit production run in the following situations. a. The process standard deviation is 0.15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects. b. Through process design improvements, the process standard deviation can be reduced to 0.05. Assume that the process control remains the same, with weights less than 9.85 or greater than 10.15 ounces being classified as defects. c. What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?Please include excel formula Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. Input area: Year X Y 1 13% 27% 2 26% 36% 3 7% 11% 4 -5% -29% 5 11% 16% (Use cells A6 to C11 from the given information to complete this question. You must use the built-in Excel function to answers this question. Make sure to use the “sample” Excel formulas.) Output area: Asset X: Average return Variance Standard deviation Asset Y: Average return Variance Standard deviationExplain the following concepts? a. Off-sheet analysis. b. Horizontal analysis. c. Vertical analysis. d. Time-value analysis.