In this paper I will be discussing on radical formulas and how to solve for the formula that is given as C = 4d^-1/3b where d is the displacement in pounds and b is the beam width in feet. The exponent of -1/3 means that the cube root of d will be taken and then the reciprocal of the number will be used in the multiplication. These rules include accurately finding the cube and square root for numbers and understanding the application of the solution in sailboat stability (Example, 2013).
In this paper we will need to solve problem #103 on page 605 Sailboat Stability (Dugopolski, 2012). In order to consider safe for ocean sailing the capsize screening value C should be less than 2. For a boat with a beam (width) b in feet and displacement d in pounds, C is determined by the function C=4d-1/3b (Dugopolski, 2012). In the beginning of the problem radicals look difficult at first, but the idea ranges through exponents and order of operations. To start out the problem we have to solve a, b, and c. a)Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam of 13.5. C=4d-1/3b
C= 4(23245)-1/3(13.5)I have plugged in the values into the formula. Allowing the order of operations, the exponents are solved first (exponent computed by calculator). C=4(.035)(13.5)Now it’s just two multiplications.
C=1.89The capsize screening value is less than 2.
b)Solve the formula for d.
4d-1/3 * b = c
d-1/3 = c Divide both sides by 4b
d = ( 4b )3 I then cubed both sides, to invert to get rid of the negative. c
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? d = (4 * 13.5) 3 Using the formula in b I got this formula set.
d = 19683 Pounds displacement for a value of c = 2
Courtney from Study Moose
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