Real World Radical Formulas

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  • Topic: Problem solving, Expression, Sailing
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Real World Radical Formulas
MAT222 Intermediate Algebra

Real World Radical Formulas
This week’s assignment involved solving real work radicals. We were required to solve two problems on pages 605 and 606. While this assignment was not easy for me, I feel like I most definitely learned something new. The problems involve sailboat stability and speed. I will be looking for the capsize screening value and the sail power of the sailboat.

Page 605 Problem 103
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
A)Find the capsize screening value.
Displacement = 23,245
Beam = 13.5
C = 4(23245)-1/3 (13.5)Values plugged into the formula.
C = 4(.035)(13.5)Applied exponent first.
C = 1.4(13.5)Multiplication left.
C = 18.9Capsize Screening Value.
B.) Solve for D.
C = 4d-1/3 b
4d-1/3 b = cFlipping equation so d is on the left.
4d-13 b = cDivide both sides by 4b.
4b 4b

(d-1/3)3 = c3Raise all sides to the 3rd power.

D = c3 Formula solved for D.

Page 606 Problem 104
Sailboat Speed. The sail area-displacement ratio S provides a measure of the sail power available to drive a boat. For a boat with a displacement of d pounds and a sail area of A square feet S is determined by the function:

A.)S = 16Ad-2/3
Sail Area = 810 Square Feet
Displacement = 23245
S = 16(810)(23245)-2/3Values plugged into formula.
S = 16(810)(.00122776)Exponent applied first.
S = 12960(.00122776)Multiplication left.
S = 15.9Formula solved for sail power.
B.)Write d in terms of A and S.
S = 16Ad-2/3
16Ad-2/3 = SMoved d to the left of the equation.
16Ad-2/3 = SDivide both sides by 16A
16A 16A

(d-2/3)3/2 = S3/2 Raise all sides by 3/2....
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