MAT222: Intermediate Algebra (AWP1234E)
Instructor Their Name
March 9, 2012
Real World Radical Formulas
Our assignment is to solve problem 103 on page 605, parts a and b, and problem 104 on page 606, both a and b, of our text book, Elementary and Intermediate Algebra. The assignment revolves around sail boat stability and speed. The formulas we will use can give you a good starting point in planning your craft and journey if used wisely. Knowing the restrictions of a ship’s stability and maximum speed is important in real world applications. It can be applied to the design of everyday sail boats and racing boats to ensure the safety of these craft. A formula along these lines can also be used for pleasure yachts, cruise ships, and cargo craft. Knowing the stability and speed of your craft is important to safety as you will know if the sea is rough if you can navigate it safely. This also applies to the aforementioned larger craft as they can decide whether to plot a course around heavy seas or proceed as originally scheduled. The speed of the craft can be used to determine how long it will take to reach your destination. Of course there will be many other variables that would need to be taken into account, like weight of cargo or anything else you may be carrying, but it will give you a good starting point for your journey.
Problem number 103 on page 605 is regarding a Tartan 4100 sail boat. It states that the capsize screening value should be less than two to be considered safe for sailing in the ocean. The formula given is C=4d-1/3b. C is the screening value, 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 that number will be used in the multiplication. This will be shown in the steps below. a)
C = 4d-1/3bThe given radical formula.
C = 4(23,245)-1/3(13.5)Here is the formula with the values plugged in. According to the
order of operations the exponent is the first equation to accomplish C=4(.0350394125548527)(13.5) This leaves only two multiplications left to accomplish. C=.1402(13.5)Still multiply in order.
C=1.8927This craft has a capsize screening value of 1.8927 which is less than two, therefore the Tartan 4100 is safe for ocean sailing.
We are asked to solve the formula for d. As we have already solved for d in the above equation, I am going to assume we are to use the formula given to us as an example from the teacher. D=1.1g-1/4HThe given formula.
g = 1.4641H4 The given solution for g plugged into the formula. d4
D = 1.4641H4 * HMultiply by H
D = 1.4641H5The formula has now been solved for D.
Problem number 104 on page 606 is regarding the speed of a sail boat. It gives us a formula for computing sail power based on the area of sail in square feet, and displacement of pounds. The formula given is S = 16Ad-2/3. S is the speed, A is square feet of sail, and d is pounds of displacement. The exponent of -2/3 on the d means that the cube root of d will be taken and then the result squared. Lastly the last result will divide 16A, (sent to the denominator). This will be shown in the steps below.
We are asked to find S to the nearest tenth for the Tartan 4100. The sail area is 810 square feet and the displacement is 23,245 pounds.
S = 16(810)(23,245)-2/3The equation with the values of A and d inserted. S = 16(810)(.0012)Exponent computed first per order of operations. S = 12960(.0012)First multiplication accomplished.
S = 15.552S is solved and the speed of the sail boat is 15.6 rounded to the nearest 10th.
We are asked to write d in terms of A and S. In the equation, d must be solved for before you can use the givens of A and S. The true value of d is the pounds, (23,245), with an exponent of -2/3. I will now show how I...