RADICAL FORMULAS 2
Real World Radical Formulas (title required on first line)
Though radicals seem complicated at first glance, the concept simply extends what is
already known about exponents and the order of operations. Additionally, manipulating formulas that include radicals is no different than those without, providing appropriate rules are followed. These rules include accurately finding the cube and square root for numbers and understanding the application of the solution in the real world.
It is stated in #103 on page 605 (Dugopolski, 2012) that the capsize screening value C
should be less than 2 if a boat is to be considered safe for ocean sailing. The formula is given as C = 4d(-1/3 power)b where 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.
a) For the first portion of this problem we need to calculate the capsizing screening value for the Tartan 4100 calculated. The boat has a beam of 13.5 ft. and a displacement of 23,245 lbs.
C = 4d-1/3b
C = 4(23,245)-1/3(13.5) Values plugged into the formula.
According to order of operations, the exponents are solved first.
C = 4(.035)(13.5)
C = .14(13.5) Now it is just two multiplications.
C = 1.89 The capsize screening value is less than 2.
b) Here is a formula similar to the capsize screening value. D = 1.1g -1/4H.
The formula will be solved for g.
D = 1.1g -1/4H
No substitution is needed because the formula is being manipulated.
RADICAL FORMULAS 3
D = 1.1g-1/4H Divide both sides by 1.1H.
1.1H 1.1H
D-4 = ( g-1/4
)
-4 Raise all parts of both sides to the -4th power . The (1.1H)
-4
(1.1H)
-4 on the left side becomes its reciprocal to the 4th power.
The right side becomes simply g.
1.4641H4
= g The formula has now been solved for g.
D4
Problem 104...