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Recently Asked Numerical Methods Questions

Expert help when you need it

Q1: 4. To test Ho: = 60 versus H: µ<60, a random sample of size n= 23 is obtained from a population that is known to benormally distributed. Complete parts (a) through (d) below. (a) If x = 57.8 and s = 11:1, compute the test statistic.to =.(Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a = 0.1 level of significance, determine the critical value(s).Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution tablegiven. Critical Value: (c) Draw a t-distribution that depicts the critical region. Choose the correct answer below. OA.O B.С. (d) Will the researcher reject the null hypothesis? A. No, because the test statistic falls in the critical region.B. Yes, because the test statistic falls in the critical region.C. No, because the test statistic does not fall in the critical region.D. Yes, because the test statistic does not fall in the critical region.See Answer
Q2: Find the correct form of the particular solution to the following DE. Do not go on to find the specific numerical values of the undetermined coefficients! y^{\prime \prime}+4 y^{\prime}+3 y=5 e^{-3 t}+\sin (t)+\cos (2 t)-7 t^{2}See Answer
Q3: 3. Determine the t-value in each of the caşes, (a) Find the t-value such that the area in the right tail is 0.20 with 24 degrees of freedom.(Round to three decimal places as needed.) (b) Find the t-value such that the area in the right tail is 0.025 with 24 degrees of freedom.(Round to three decimal places as needed.) (c) Find the t-value such that the area left of the t-value is 0.05 with 14 degrees of freedom. [Hint: Use symmetry.](Round to three decimal places as needed.) (d) Find the critical t-value that corresponds to an area of 0.01 to the left. Assume 19 degrees of freedom. [Hint: Usesymmetry.](Round to three decimal places as needed.)See Answer
Q4: 14.7 The following data were gathered to determine therelationship between pressure and temperature of a fixedvolume of 1 kg of nitrogen. The volume is 10 m. Employ the ideal gas law pV = nRT to determine R on the basis of these data. Note that for the law, T must be expressed in kelvins.See Answer
Q5: 14.25 In water-resources engineering, the sizing of reservoirs depends on accurate estimates of water flow in the river that is being impounded. For some rivers, long-term historical records of such flow data are difficult to obtain .In contrast, meteorological data on precipitation are often available for many years past. Therefore, it is often useful to determine a relationship between flow and precipitation .This relationship can then be used to estimate flows for years when only precipitation measurements were made. The following data are available for a river that is to be dammed: Plot the data. Fit a straight line to the data with linear regression . Superimpose this line on your plot. Use the best-fit line to predict the annual water flow if the precipitation is 120 cm. If the drainage area is 1100 km(2) estimate what fraction of the precipitation is lost via processes such as evaporation, deep groundwater infiltration, and consumptive use. See Answer
Q6: 15.5 For the data from Table P15.5, use polynomial regression to derive a predictive equation for dissolved oxy-gen concentration as a function of temperature for the case where the chloride concentration is equal to zero. Employ a polynomial that is of sufficiently high order that the predictions match the number of significant digits displayed in the table.See Answer
Q7: Fit a cubic polynomial to the following data: Along with the coefficients, determine r^{2} \text { and } s_{y / x^{*}}See Answer
Q8: Solve the following system of two first order ODES over the interval from t = 0 to 0.2 using astep size of 0.1 with a classical Fourth-order Runge-Kutta method. The initial conditions are y(0)= 2 and z(0) =4. \begin{array}{l} \frac{d y}{d t}=-2 y+5 e^{-t} \\ \frac{d z}{d t}=-\frac{y z^{2}}{2} \end{array} Show all the steps of your hand calculations. Box your results.See Answer
Q9: Problem 3:Consider the following 2nd order ODE: \frac{d^{2} y}{d t^{2}}-\left(1-y^{2}\right) \frac{d y}{d t}+y=0 with the initial conditions given by y(t=0)=1, \quad \frac{d y}{d t}(t=0)=1 (a) Convert this into a system of two 1 st order ODES. (b) Solve this system of ODES for t = 0 to 10 in Matlab by writing a script that uses the M-file function rk4sys.m, which is based on the classical fourth order Runge-Kutta method,posted in Canvas under Lecture 25 with two different time steps h= 0.25 and 0.125. Plotthe results of the two dependent variables as a function of time. (c) Solve this system of ODES for t = 0 to 10 in Matlab by writing a script that invokes the Matlab built-in function ode45, which uses adaptive time steps, i.e., determines the time step needed automatically. Plot the results of the two dependent variables as a function of time.Note: The syntax for this built-in function is [t, y] = ode45(odefun, tspan, y0), where odefun is the name of the function that contains the right side of the system of differential equations and tspan contains the initial and final values of the independent variables.See Answer
Q10: \frac{d y}{d x}=(1+4 x) \sqrt{y} (a) Using Euler's method (b) Using the Midpoint (2"d order Runge-Kutta) method (c) Using the classical Fourth-order Runge-Kutta method The exact solution of this ODE can also be derived by using calculus as y exact (x) =1(x2 +x + 1)². Using this result, obtain the true relative error at the end of each step for all the methods. Problem 1:Solve the following problem over the interval from x = 0 to 0.5 using a step size of 0.25, wherey(0) = 1:See Answer
Q11: Q-3: Write a program to find out positive values from the matrix below: Hints: [m,n]=size(A); for i=1:m for j=1:n if A(i,j).......See Answer
Q12: 5. Jack is paddling up a river to the cove and back again. The cove is 11 km away. The current is 5 km/h. The total trip takes him 12 hours. Algebraically determine the speed of the boat in still water.See Answer
Q13: In the thermos shown in figure 4, the innermost compartment is separated from the middle container by a vacuum. There is a final shell around the thermos. This final shell is separated from the middle layer by a thin layer of air. The outside of the final shell comes in contact with room air. Heat transfer from the inner compartment to the next layer q, is by radiation only (assume the space is evacuated). Heat transfer between the middle layer and outside shell q2 is by convection in a small space. Heat transfer from outside shell to the air g3 is by natural convection. The heat flux from each region of the thermos must be equal at steady state (that is q1 = q2 = 93).Find the temperatures T1 and T2 at steady state. To = 500°C and T3 = 25°C. \begin{array}{l} q_{1}=10^{-9}\left[\left(T_{0}+273\right)^{4}-\left(T_{1}+273\right)^{4}\right] \\ q_{2}=4\left(T_{1}-T_{2}\right) \\ q_{3}=1.3\left(T_{2}-T_{3}\right)^{4 / 3} \end{array} See Answer
Q14: A manufacturer provides specialized microchips. During the next 3 months, its sales, costs, and available time are There are no chips in stock at the beginning of the first month. It takes 1.5 hr of production toproduce a chip. The cost to store a chip starts from the beginning of one month to the next (i.e., if a chip is produced in month 1, regardless the date of the month, storage fee will be charged from beginning of month 1). Determine a production schedule and the total cost that meets the demand requirements, does not exceed the monthly production time limitations, and minimizes cost. Note that no chips should be in stock at the end of the 3 months.See Answer
Q15: Q-5: Using if...elseif else structure, write a program for the following grading policy of a University. A (Excellent) = 90 to 100. B+ (Very Good) = 85 to <90. B (Good) = 80 to <85. Fail = <80 Note: If there is a negative value as an input, it will show an error message“ negative value is not allowed ".See Answer
Q16: Q-1: Modify If.. Structure as used in exercise 3.3.1 by input and disp function. Test the code by changing the variable grade'See Answer
Q17: Q-2: Write a program using for loop to compute factorial. Suppose 5!=1 x 2 x 3 x 4 x 5. Hints: x=1; for i=1:n X=x*i;See Answer
Q18: Q-6: Using the script function file of quadratic equation, find the roots of the following equations: 3 x^{2}+6 x=-4 7 x^{2}-5 x=3 Find the roots of above Q-6 using fplotf command .Use @ function.See Answer
Q19: Q-8 Determine the roots of f(x) = -13 +18x? by using Part (a) Built-in Matlab function fzero Part (b) Using graphical method (fplot).See Answer
Q20: Q-4: Calculate value of k2-50 for all integers in [-10, 10] domain but only until k2-50 becomes negative. Use while----break structure and fprintf for displaying results.See Answer

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