# Mat221 Essay

434 Words2 Pages
A. Find the cap size screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam of 13.5 feet. C=4d-1/3b C= 4(23,245)-1/3(13.5) We will plug in the values into the formula and use the order of operations, doing the exponents first. C = 4(.035)(13.5) Multiply them together C = 1.89 The capsize screening value is less than 2. B. Solve this formula for d. Here is the formula and I’m going to solve for d C=4d-1/3b C = 4d-1/3b I am going to divide both sides by 4b in order to isolate d 4b 4b C-3 = (d-1/3)-3 Raise both sides by -3rd power 4b-3 (4b/c)^3 = d Flip the base on the left side since it’s negative 43b3 = d C3 D = 64b3 The formula has now been solved for d. C3 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 S = 16Ad-2/3 A. Find S to the nearest tenth for the Tartan 4100, which has a sail area of 810 square feet and displacement of 23,245. S = 16(810)(23,245)-2/3 Plug the values in and solve the exponent first. S = 16(810)(.0012) Multiply S = 15.552 This is the amount of sail power to this boat. B. Write d in terms of A and S. Here is the formula to the sail area-displacement ratio. S = 16Ad-2/3 S = 16Ad-2/3 Divide both sides by 16a to isolate d 16a 16a - 3/2 ( S/16a) = (d-2/3)-3/2 Raise both sides by -3/2 power 163/2a3/2 = d d is isolated and we will flip left side since it’s negative S3/2 64a3/2 = d The formula has now been solved for d. s 3/2 Overall, we applied the concept of