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Sailboat Stability

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Sailboat Stability

MAT222
Ms. Scarf
July 29, 2014

Sailboat Stability
This weeks assignment is found on page 605 of our math book, question number 103. Focus is solving formulas and using a vocabulary that describes the steps in the equations in mathmatical terms. This weeks focus is radical equations/formulas. The specific problem assigned gives real world value in understanding sailboats and the mathematical understanding of when the stability could be compromised or ideal. The problem is as follows:
Sailboat stability. To be considered safe for ocean sailing, the capsize screening value C should be less than 2. For a boat with a beam (or width) b in feet and displacement d in pounds, C is determined by the function. C=4d-1/3 b (Dugopolski,2012) There are three parts to this problem a, b, and c. Each one will be worked out.
a)Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam 13.5ft.
Using the formula and substituting the values given for the variables of d and b:
C=4(23245)-1/3(13.5) First work the exponent by using the reciprocal due to the negative value
C=4(.035)(13.5) Multiply all
C=1.89 This is the capsize screening value(notice it is below 2 as needed)
b) Solve for d of the formula
C=4d-1/3b Start isolating d by dividing both sides by 4b
C/4b=d-1/3 Now resolve the exponent by raising all sides by the power of 3. Notice that 4 is the cube root of 64.
C3/64b3=d Flip so that d is on the left side
Answer is: d=C3/64b3
C) The accompanying graph shows C in terms of d for the Tartan 4100 (b=13.5). For what displacement is the Tartan 4100 safe for ocean sailing?
I know this is a cop out, but honestly, I don't know. I know that I will lose points for not finishing the last part of this problem, but I am honestly clueless. When I went to solve it I got 273 which equals 19,683 lbs./
I did this by equation 2(which is the safe displacement)=4d-1/3(13.5) multiplied 4 and 13.5 to get 54 then divided both sideds by 54
2/54=d-1/3 then removed the exponent
(54/2)3=d then solved to 19,683
I have no clue how to add the last vocab term for this assignment as I am sure that I haven't shown how to use a radical in this equation.
In conclusion, this formula is vital for sailors around the world. Without knowing the displacement value then they would be putting their lives at risk out to sea. They add the weight of the boat, passangers, cargo, ect. and use it to input to the formula. The is a maximum and it has to be known.

References:
Dugopolski,M. (2012) Elementary and Intermediate Algebra 4th Ed. NY,NY McGraw Hill Publishing.

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