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...

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Mathematical Modelling 1
Mathematical Modelling with Radical Functions
John Q. Student
MAT 222 Week 3 Assignment
Instructor’s Name
Date
Mathematical Modelling 2
Mathematical Modelling with Radical Functions
Introduction
Radical functions are those that have a variable inside a radical. Functions that only have numerals
inside radicals do not count. For e.g. f (h) 2gh= is a radical function. Radical functions can be used to
model a real-world problem. The graphs and the algebraic methods to solve radical functions help us to
model the real-world problems. Algebraic methods involve the various rules that we use for addition and
multiplication of radicals.
Examples
It is stated in problem #103 on page 605 (Dugopolski, 2012) that the capsize screening value C for a
sailing boat in an ocean should be less than 2 for a safe sailing. The formula for capsize screening value C is
given as
( )
( )
1/3C 4d b ----------- (1)
where d = the displcement in pound
b = the beam width in feet
−
=

We know that,
1/3 1/3 1
1/3
1
d = (d ) =
d
− −
, that means -1/3 exponent on the d is solved by taking the cube root of d
first, then taking the reciprocal of the obtained value.
a) The capsize screening value C for Tartan4100 is calculated below. Given that, beam of the boat
=13.5 feet and displacement=23,245 pounds.
Substituting these given values in the above equation, we get
1/3C 4(23245) (13.5)−= According to...