Question 199141
L 1.25+ radical symbol over S- 9.8 radical symbol with 3on the side
 and D under the sign this < underline, and 16.296 after underline < sign
where L is the boat’s length in meters (m), S is the sail area
in square meters, and D is the displacement in cubic meters
(www.sailing.com).Ateam of naval architects is planning to
build a boat with a displacement of 21.44 cubic meters (m3),
a sail area of 320.13 square meters (m2), and a length of
21.22 m. Does this boat satisfy the inequality? If the length
and displacement of this boat cannot be changed, then how
many square meters of sail area must be removed so that the
boat satisfies the inequality?
:
I think the formula should be
{{{L + 1.25sqrt(S) - 9.8(D^(1/3)) <= 16.296}}}
Substituting for L, S, D
{{{21.22 + 1.25sqrt(320.13) - 9.8(21.44^(1/3))}}} = 
21.22 + 1.25(17.892) - 9.8(2.778) =
:
21.22 + 22.365 - 27.225 = 16.36, slightly above 16.296
:
:
If the length and displacement of this boat cannot be changed,
 then how many square meters of sail area must be removed so that the
boat satisfies the inequality?
16.36 - 16.296 = .064; the amt that it is over specs
:
Find the reduced sail area:
{{{((22.296 -.064)/1.25)^2}}} = 316.3 sq/ft to meet the rule formula
That's a removal of 3.83 sq/ft
:
:
Check using this sail area
{{{21.22 + 1.25sqrt(316.3) - 9.8(21.44^(1/3))}}} = 
21.22 + 1.25(17.785) - 9.8(2.778) =
:
21.22 + 22.231 - 27.225 = 16.226, which is less than 16.296