Use Muller's method to find a solution in [0.1, 1] accurate to within 600x^4−550x^3+200x^2−20x−1=0. Explain how the algorithm works.

a. Prove that y=sin(x) is a subspace of R^2

b. Prove that a set of 2x2 non invertible matrices a subspace of all 2x2 matrices

Write The MATLAB SCRIPT for:

An open-top box is constructed from a rectangular piece of sheet metal measuring 10 by 16 inches. Square of what size (accurate to 10^-9 inch) should be cut from the corners if the volume of the box is to be 100 cubic inches?
Notes: to roughly estimate the locations of the roots of the equation and then approximate the roots to this equation using Newton Iteration method.

Please don't give me the Matlab Commands for this. I need "Matlab Script" as its solution.

In Matlab:

Any complex number z=a+bi can be given by its polar coordinates r and θ, where r=|z|=sqrt(a^2+b^2) is the magnitude and θ= arctan(ba) is the angle. Write a function that will return both the magnitude r and the angle θ of a given complex numberz=a+bi. You should not use the built-in functions abs and angle. You may use the built-in functions real and imag.

Please provide step by step solution and i will give a positive rating. Many thanks

1)Suppose we have a steady fluid flow through a section of a cylindrical pipe with varying area, with control volume.  At the entrance the radius of the pipe r1 = 4m, the flow velocity is U1 = 5 i m/s and at the exit the radius of the pipe is r2 = 2.5 m and the velocity of the flow is U2 = 5 i m/s. Use the integral form of the continuity equation to show that the ratio of the density of the fluid entering the pipe to that exiting the pipe is

ρ1/ ρ2 ≈ 0.4

Explain the result?

Determine whether the polynomial is reducible or irreducible in the given polynomial ring. Justify your answers.

(c) x^4 + 1 in Z5[x]

(e) 2x^3 − 5x^2 + 6x − 2 in Z[x]

(f) x^4 + 4x^3 + 6x^2 + 2x + 1 in Z[x]. Hint: Substitute x − 1 for x.

Consider an infinite sequence of positions 1, 2, 3, . . . and suppose we have a stone at position 1 and another stone at position 2. In each step, we choose one of the stones and move it according to the following rule: Say we decide to move the stone at position i; if the other stone is not at any of the positions i + 1, i + 2, . . . , 2i, then it goes to 2i, otherwise it goes to 2i + 1.

For example, in the first step, if we move the stone at position 1, it will go to 3 and if we move the stone at position 2 it will go to 4. Note that, no matter how we move the stones, they will never be at the same position.

Use induction to prove that, for any given positive integer n, it is possible to move one of the stones to position n. For example, if n = 7 first we move the stone at position 1 to 3. Then, we move the stone at position 2 to 5 Finally, we move the stone at position 3 to 7.

Probabilities

Compute P(X₁ + 2X₂ -2X₃ > 7) , where X₁, X₂, X₃ are iid random variables with common distribution N(1,4). You must give the numerical answer.

Specify and show any formulas used for E, P, and Var

for example Var( X₁ + 2X₂ -2X₃) = 4 + 2²(4) + (-2)²(4) = 35. Please specify how all the individual numbers where obtained and the formula used.

CNY Coffee Inc. uses three types of coffee beans (Columbia, Java, and Brazil) as mixtures to manufacture its two coffee products (Energy, and Everyday). The cost per pound, the availability, and rating information of the coffee beans are as follows.

Coffee product tests are used to provide ratings on a scale of 0-100, with higher ratings indicating higher product performance. Here are the two coffee products and their product information:

Due to the popular demand of the low-price segment, at least 920 pounds of Everyday must be produced.

Set up and list the linear programming model for the above problem. (You do not need to solve the listed model).

**Program needs to be in matlab format**

A bowling match consists of ten frames. Each frame except for the tenth consists of one or two balls, or attempts to knock down the ten pins at the end of the alley. Doing so on the first ball of the frame is called a strike, and the second ball of the frame is not rolled. Knocking down all ten pins with both balls (having left some up with the first ball) is called a spare. If both attempts to knock down the pins leave some standing, the frame is called an open frame. A spare in the tenth frame gives the bowler one extra ball; a strike in the tenth gives him or her two extra balls. A bowling score is computed as follows. A strike counts as 10 points plus the sum of the next two balls. A spare counts as 10 points plus the next ball. Any other balls merely count as themselves, as do any bonus balls rolled as a result of a strike or a spare in the tenth frame. Suppose for example that the sequence of balls was 9 1 0 10 10 10 6 2 7 3 8 2 10 9 0 9 1 10 The score for the ten frames would be Frame score ----- ----- 1 10 2 30 3 56 4 74 5 82 6 100 7 120 8 139 9 148 10 168 Your goal in this project is to write a program to accept from standard input the scores for a sequence of balls and output the scores for the ten frames. The program should ask for input for each frame, asking for a second score if the first roll was not a strike. At most bowling alleys, the computerized scoring machines congratulate bowlers when they are doing a good job. When a bowler achieves consecutive strikes, output the following, according to the number of consecutive strikes: No. of consecutive strikes Output 2 Double! 3 Turkey! 4 Hambone! 5 Yahtzee! 6 Wild Turkey! This is a two week homework. For this homework, you will need to come up with an outline of goals for the project. By the end of the first week, your program should be able to do the following things: -Add up scores for the first nine frames (do NOT worry about the tenth frame yet) for both simple bowls (no strikes or spares) and frames that involve spares You will evaluate each other's code in class with several tests to see if the code does indeed successfully calculate simple games and games that involve spares. The complete checklist that you will be evaluated on is below: -The program runs -The program asks for scores one at a time (not for all of them at once) -The program asks for scores for 9 frames -Test the program for the following easy case: Every frame you bowl zero for both times. --Does the program output a final score? --Is the final score correct (i.e. 0)? --Does the program output the score at the end of every frame? -Next, test the program for the next most difficult case: Every frame you bowl a score of 1. -Is the final score correct (i.e. 18)? -Next, test the program to see if it successfully calculates spares. For the first two frames, the bowler bowls a 5 on the first throw and a 5 on the second throw. For frames 3-9, the bowler throws zeros. -Is the final score correct (i.e. 25)? -Lastly, test the program for a case in which you have many spares. For every frame, the bowler bowls a 5 on the first throw and a 5 on the second throw. -Is the final score correct (i.e. 135)? -The program does not crash (i.e. encounter Octave errors) for any of the test cases.

360 feedback is an example of which type of intervention?

Select one:

a. trans-organizational

b. organizational

c. individual

d. team

Consider the linear transformation T: R^2x2 -> R^2x2 defined by T(A) = A^T - A.

Determine the eigenvalues of this linear transformation and their algebraic and geometric multiplicities.