Intermediate Algebra: Algebra 2

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1. Solving for parts a, b, and c of problem 103

Problem 103 explanation and equation below refers.

In the graph here above C which is capsize screening value is a function of d (displacement value) and b (beam or width of a ship). C in the equation is a dependent variable. The capsize screening value C is dependent on independent variables d and b. By manipulating d and b in the equation one is able to get a value for C For example with the capsize screening value with b=13.5 ft in the equation in the graph above i can calculate the capsize screening value C in the table below for various values of b and d as follows using the equation C=54d-1/3b (Genç, 2012)

d 0 10 20 2 30 50

b 10 10 20 50 15 2

C 0 18 18 450 9 0.72

When d=0, b=10, C will be calculated as follows;

C=54*0-1/310= 0

The capsize screening value is less than 2 hence this is safe for ocean sailing since C=0

When d=10 and b=10 C will be as follows

C=54*10-1/3*10

First i solve for the radical or root 10-1/3 which gives us 0.03333333

When I multiply with 54*0.0333333*10 the result is =18. Capsize screening value is more than 2. This means that it is not safe for ocean sailing since the capsize screening value should be less than 2 (Hoag & Benedict, 2010)

When d=20 and b=20 then C will be as follows;

C=54*20-1/3*20=

First I solve for the radical or root 20-1/3 whose answer is 0.01666666

The next step would be C=54*0.0166666*20=18

This capsize screening value of 18 is not safe for ocean sailing since C must be less than 2

When d=2 and b=50 then C will be as calculated below

C=54*2-1/350

Then I calculate for the root or radical 2-1/3=0.16666666

Then C will be given by 54*0.1666666*50=450

The ship with a C of 450 is not safe for ocean sailing since C must be less than 2

When d=30 and b=15 we can calculate for C as follows;

C=54*30-1/3*15

The next step is that I must solve for the radical or root 30-1/3=0.01111111

Then C=54*0.01111111*15=9

This capsize screening value where C is 9 is not also safe for ocean sailing

Lastly when d=50 and b=2 then the value of C is as determined below;

C=54*50-1/3*2

I then solve for the radical 50-1/3=0.0066666

C in this case will be 54*0.006666*2=0.72

In this case capsize screening value C is 0.72 which is less than 2 and this implies that the ship is safe for ocean sailing (Hoag & Benedict, 2010).

From the calculations above the ship will only be safe for ocean sailing when the value of beam or width b is 0 and displacement d is 10 as at that point the capsize screening value will be 0. The other time is when d is 50 and b is 2 since capsize screening value C is 0.72. The other test values of b and d are not viable as shown in the table. It implies that the values of b and d should be inversely proportional to obtain a favorable capsize screening value.

The use of this equation is very important for ship builders because if the capsize screening value C of any ship that they build and sell is more than 2 then it will not be safe for use in the sea. This type of ship will not only endanger the lives of the sailors but will also destroy the reputation of the ship building company. This type of ship will also expose the ship building company to legal action from the ship buyers who suffer loss as a result of a ship with a capsize screening value of more than 2.The ship buyers after getting expert opinion that they bought a ship with an industrial defect of a capsize screening value of more than 2 will most likely file a case in court claiming for damages from the ship builders. The ship builders will be found liable and fined heavily which will most likely lead to loss of reputation, loss of funds and may lead to winding up of the ship builders company.

References

Genç, A.,I. (2012). Distribution of linear functions from ordered bivariate log-normal distribution. Statistical Papers, 53(4), 865-874. doi:http://dx.doi.org/10.1007/s00362-011-0389-y

Hoag, J., & Benedict, M. E. (2010). WHAT INFLUENCE DOES MATHEMATICS PREPARATION AND PERFORMANCE HAVE ON PERFORMANCE IN FIRST ECONOMICS CLASSES?1. Journal of Economics and Economic Education Research, 11(1), 19-42. Retrieved from http://search.proquest.com/docview/521203317?accountid=45049