Radical formulas are used in many fields of the real world; some examples are in finance, medicine, engineering, and physics. These are just a few. In the finance department they use it to find the interest, depreciation and compound interests. In medicine it can be used to calculate the Body Surface of an adult (BSA), in engineering it can be used to measure voltage. These formulas are vital and important to the people working in these fields of work. Our week 3 assignment requires that we find the capsizing screening value for the Tartan 4100, solve the formula for variable of d, and find the displacement in which the Tartan 4100 is safe for ocean sailing. The problem is broken down into three parts. The problem and work will be on the left hand side and a description will be to the right of the work describing my steps taken to solve the problems.
The assignment requires solving problem 103 on page 605of our reading material. With the information I will solve three different parts and using the information given I will use radical formulas to show the solutions. The first part of the first problem requires us to “Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pound sand a beam of 13.5” (Dugopolski,2012) and determine if it is safe for sailing. The values for the variable of d= 23245 and b= 13.5, I will be using these amounts in my equation.
Part a wants us to find the capsize value for the Tartan 4100 (A) This is our formula; from here I substitute my variables with my amounts for d and b. My new formula is I raise 23245 to the negative 1/3 power and solve
Round to the nearest thousands and use distributive property to multiply and get my answer for C.
Answer for C is 1.89.
The capsize screening value for the Tartan 4100 is 1.89. To be considered for safe sailing the capsize screening must be a less than 2 value, therefore it can be determined that the Tartan 4100 is safe for sailing because its value is less than 2.
Part b of the assignment requires us to solve this formula for d. This formula will be used. Solve for d. 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 as part of the solution.
Rewrite the formula as
Multiply both sides by to get
Divide both sides by C to get
Cube on both sides to get
The radical equation of part b will be used to solve d in part c or Final answer
Part c of the assignment requires finding what displacement is the Tartan 4100 safe for ocean sailing. This will be solved using the radical equation from part b
This formula will be used to solve for our last part and solve d. I substitute the variables with the values 13.5 and 2. The 2 is for the capsize value.
Use order of operations, and follow the quotient rule.
= Follow the power rule, simplify my answer
The Tartan 4100 is safe for ocean sailing at a displacement of 19, 683 pounds. Here on the graph it shows the displacement of 19, 683 pounds is within the region to make for safe sailing.
In this assignment the variable of C represents the capsizing screening value. In this case it has to less than 2 to be considered safe for sailing. The variable of b represents the beaming feet. The variable of d represents the displacement in pounds. As we solved the radical equations we saw the variables were represented as such, Yes, C = 1.89 when d = 23245 and b =13.5. The use of this formula is important for shipbuilders because it can show them if the ship can be considered safe for sailing. Depending on the size of the ship and the width of the ship, they can use the formula above to determine the displacement or the capsizing size a ship can be to be considered safe for sailing. This assignment has let us see the importance of radical expressions by solving this problem. By applying the formulas given we are able to find the capsizing screening value for the Tartan4100, solve the formula for variable of d, and find the displacement in which the Tartan 4100 is safe for ocean sailing.
Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY:McGraw-Hill Publishing