Real World Radical Formulas Essay Example
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 = 18.9 Capsize Screening Value. B.) Solve for D.
C = 4d-1/3 b
4d-1/3 b = c Flipping equation so d is on the left.
4d-13 b = c Divide both sides by 4b. 4b 4b
(d-1/3)3 = c3 Raise all sides to the 3rd power. 4b
D = c3 Formula solved for D. 64b3
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)-2/3 Values plugged into formula.
S = 16(810)(.00122776) Exponent applied first.
S = 12960(.00122776) Multiplication left.
S = 15.9 Formula solved for sail power.
B.) Write d in terms of A and S.
S = 16Ad-2/3
16Ad-2/3 = S Moved d to the left of the equation.
16Ad-2/3 = S Divide both sides by 16A 16A 16A
(d-2/3)3/2 = S3/2 Raise all sides by 3/2.
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 = 18.9 Capsize Screening Value. B.) Solve for D.
C = 4d-1/3 b
4d-1/3 b = c Flipping equation so d is on the left.
4d-13 b = c Divide both sides by 4b. 4b 4b
(d-1/3)3 = c3 Raise all sides to the 3rd power. 4b
D = c3 Formula solved for D. 64b3
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)-2/3 Values plugged into formula.
S = 16(810)(.00122776) Exponent applied first.
S = 12960(.00122776) Multiplication left.
S = 15.9 Formula solved for sail power.
B.) Write d in terms of A and S.
S = 16Ad-2/3
16Ad-2/3 = S Moved d to the left of the equation.
16Ad-2/3 = S Divide both sides by 16A 16A 16A
(d-2/3)3/2 = S3/2 Raise all sides by 3/2.