Real World Radical Formulas
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Real World Radical Formulas
Shameeza Persaud
MAT222: Intermediate Algebra (GSQ1344C)
Instructor: Ami Gates
November 18, 2013
Real World Radical Formulas
A rational exponent is an exponent in the form of a portion. Any expression that contains the square root of a number is a radical expression. However, both have real world problems. A radical expression is any expression or equation that contains a square root. The square root sign specifies the number inside is a radical. The number inside the square root is called the radicand. Also, a variable numbers can also be radical expressions.
Question number 103 on page 605 (Dugopolski, 2012), states that the capsize screening on value C should be less than 2 if about is to be consider safe for sailing. The given formula is C=4d-â…“b where d is the displacement in pounds and b is the beam width in feet. Also, the exponent of -â…“ means the cube root of d will be taken and the reciprocal of that number will then be used in multiplication.
In the first example, a 4100 Tartan sailboat capsize screening value will be calculated. The sailboat has a beam of 13.5 and a displacement of 23,245 pounds. The inches value will be then converted into a decimal division.
C=4d-â…“b
Values are plugged into the formula.
C=4(23245)-â…“ (13.5)
Applied exponent first.
C=4(0.35)(13.5)
Multiplication is being executed.
C=.14(13.5)
Simplify
C=1.89
The capsize of screening value is less than 2.
Now, we need to solve for D.
C/4b=d-â…“
Divide by 4 and b.
(C / 4b)‾³ = d
multiply both sides by the “cube root of d”. Since the -1/3 is an exponent, I canceled it by raising each side to the -3/1 power.
(4b / C)Âł = d
exponent on the left side is negative, I made it positive by flipping the fraction C/4b over.
d = (4Âł)CÂł / bÂł
I applied the exponent of 3 to each part of the equation.
d = 64CÂł / bÂł
Finale answer.
In conclusion, knowing the restrictions of a ships stability and maximum speed is important in real world situations. It can be applied to the design of everyday sail boats and activities to ensure the safety of machines. Using radical equations can also help us find the moving force towards the center of a person ride in an amusement park. Overall, itt is very important to remember to use radical equations to solve real life problems,