Write your own routine to solve a system of n linear equations and n unknowns using the LU decomposition. Input should take an augmented matrix and the number of equations n. Output should be the augmented matrix. L and U matrices and the solution. Also compare your results to those of Matlab’s built in LU decomposition. Use your code to solve the systems given as (a) and (b) below: a) 3a − 2b + c = −3, a − 4b + 2c + 2d = 6, a + 3b = 5, −3a + 7b + 9c + d = 5
In: Advanced Math
Your company's stock sells for $50 per share, its last dividend (D0) was $2.00, its growth rate is a constant 5 percent, and the company would incur a flotation cost of 15 percent if it sold new common stock. Net income for the coming year is expected to be $500,000, the firm's payout ratio is 60 percent, and its common equity ratio is 30 percent. If the firm has a capital budget of $1,000,000, what component cost of common equity will be built into the WACC for the last dollar of capital the company raises?
In: Finance
The figure represents an insect caught at the midpoint of a spider-web thread. The thread breaks under a stress of 9.2 × 108 N/m2 and a strain of 2.00. Initially, it was horizontal and had a length of 3.5 cm and a cross-sectional area of 9.5 × 10-12 m2. As the thread was stretched under the weight of the insect, its volume remained constant. If the weight of the insect puts the thread on the verge of breaking, what is the insect's mass? (A spider's web is built to break if a potentially harmful insect, such as a bumble bee, becomes snared in the web.)
In: Physics
In: Statistics and Probability
A. A disk of radius 0.15 m spins at a rate of 18 rad/s. What is the linear speed of a point on its outer rim? How long does it take that point to make a complete revolution? What would be given as the frequency in hertz of this motion?
B. A mass and spring system is built with a spring constant of 5.0 N/m and a mass of 2 kg. What is its period of oscillation? What length would a simple pendulum have to have to make an identical mass oscillate with that same period?
In: Physics
A contractor builds two types of homes. The Carolina requires one lot, $160,000 capital, and 160 worker-days of labor, whereas the Savannah requires one lot, $240,000 capital, and 160 worker-days of labor. The contractor owns 300 lots and has $48,000,000 available capital and 43,200 worker-days of labor. The profit on the Carolina is $60,000 and the profit on the Savannah is $70,000.
1)Find how many of each type of home should be built to maximize profit.
aCarolina homes
bSavannah homes
2Find the maximum possible profit.
In: Advanced Math
If you were a senior executive at Alibaba, would you have made the same decision? Which of the following would you recommend for taking the company's stock public?
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In: Economics
Deb lives in a jurisdiction where all residential swimming pools are required by law to be enclosed by a fence that is at least six feet tall in order to prevent accidental drowning. Deb built a pool in her backyard a couple of months ago, but she hasn't had the extra money with which to build the fence. Unfortunately, one of the neighborhood children goes swimming in the pool and drowns. The parents of the child sue Deb. Discuss how the parents would likely go about proving their case and the elements that would be required.
In: Operations Management
Construct a finite-state machine, using combinational logic for an apple vending machine that only accepts nickels (5 cents). When 15 cents is deposited the user can push a button to receive an apple and the machine resets. If the user inserts more than 15 cents no money will be returned.
In: Computer Science
In: Accounting