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You cannot solve all the mathematical problems analytically. Here, a numerical approach is applied. You can approximate a solution using a numerical method. In every area of mathematics where we typically struggle to find an answer, we can apply numerical approaches to solve the problem. In general, this will involve solving linear systems, solving differential equations, and determining the derivative of a function at a specific location. If one looks closely at this subject, one will find it very intricate. As a result, many students find numerical procedures to be complicated. TutorBin, therefore, employs specialists in the field of numerical methods. They offer the best maths numerical methods homework help and can assist you with even the most challenging issues.

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Numerical approaches come in a variety of forms. Our maths methods tutor cover the following in maths numerical methods homework help:

**The bisection technique** divides an interval into two equal halves using a line segment. The procedure then establishes the interval's midpoint and determines whether it falls within the specified range. If so, the interval supplied is the answer. If not, you must create a new two-part interval and repeat the process.
**The Newton-Raphson Method:**This approach determines the equation's root by calculating the slope of a line tangent to a curve at a certain point. It is an improved version of the bisection technique.
**The secant method** divides an interval into two unequal portions using a line segment. The procedure then establishes the interval's midpoint and determines whether it falls within the specified range. If so, the interval supplied is the answer. If not, you must create a new two-part interval and repeat the process.
**The fixed point iteration method**uses a function to locate a function's fixed point. It resolves equation systems.
**The conjugate gradient method:** This technique determines the minimum or maximum of a function using the function's gradient.

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**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:**MotoWin Auto Superstore is thinking about offering a two-year limited warranty for $934 on all new cars of a certain model. The terms of the warranty would be that MotoWin would replace the car free of charge under certain, specified conditions. Replacing the car in this way would cost MotoWin $12,100. Suppose that under the warranty, there is an 8% chance that MotoWin would have to replace the car one time and a 92% chance they wouldn't have to replace the car. If MotoWin knows that it will sell many of these warranties, should it expect to make or lose money from offering them? How much?See Answer**Q3:**2. (20 pts) (Problem 2.18) Piecewise functions are sometimes useful when the relationship between adependent and an independent variable cannot be adequately represented by a single equation. Forexample, the velocity of a rocket might be described by: v(t)=\left\{\begin{array}{cc} 11 t^{2}-5 t & 0 \leq t \leq 10 \\ 1100-5 t & 10 \leq t \leq 20 \\ 50 t+2(t-20)^{2} & 20 \leq t \leq 30 \\ 1520 e^{-0.2(t-30)} & t>30 \\ 0 & \text { otherwise } \end{array}\right. Develop a well-structured function in MATLAB to compute v as a function of t. Then use this function to generate a table of v versus t for t = -5 to 50 at increments of 0.5 and plot a curve of v versus t with clearly labelled axis and legend. Turn in the source code as well as the results.See Answer**Q4:**8 Use multiple linear regression to fitSee Answer**Q5:**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**Q6:**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**Q7:**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**Q8:**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**Q9:**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**Q10:**Fit a cubic polynomial to the following data: Along with the coefficients, determine r^{2} \text { and } s_{y / x^{*}}See Answer**Q11:**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**Q12:**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**Q13:**\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**Q14:**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**Q15:**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**Q16:**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**Q17:**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**Q18:**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**Q19:**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**Q20:**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

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