Question 662171: Sailboat Races The speed that a sailboat is capable of sailing is determined by three factors: its total length L, the surface area A of its sails, and its displacement V (the volume of water it displaces), as shown in the sketch.
In general, a sailboat is capable of greater speed if it is longer, has a larger sail area, or displaces less water. To make sailing races fair, only boats in the same “class” can qualify to race together. For certain race, a boat is considered to qualify if
0.30L + 0.38A1/2 - 3V1/3 ≤ 16
Where L is measured in feet, A in square feet , and V in cubic feet. Use this inequality to answer the following questions.
(a) A sailboat has length 60ft, a sail area 3400ft2, and displacement 650ft3. Does this boat qualify for the race?
(b) A sailboat has length 65ft and displaces 600ft3. What is the largest possible sail area that could be used and still allow the boat to qualify for this race?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Sailboat Races The speed that a sailboat is capable of sailing is determined by three factors: its total length L, the surface area A of its sails, and its displacement V (the volume of water it displaces), as shown in the sketch.
In general, a sailboat is capable of greater speed if it is longer, has a larger sail area, or displaces less water. To make sailing races fair, only boats in the same “class” can qualify to race together. For certain race, a boat is considered to qualify if
0.30L + 0.38A1/2 - 3V1/3 ≤ 16
Where L is measured in feet, A in square feet , and V in cubic feet. Use this inequality to answer the following questions.
:
The formula:  =< 16
:
(a) A sailboat has length 60ft, a sail area 3400ft2, and displacement 650ft3. Does this boat qualify for the race?
 =< 16
do the math
18 + 22.2 - 26 = 14.2, less than 16, would qualify
:
(b) A sailboat has length 65ft and displaces 600ft3. What is the largest possible sail area that could be used and still allow the boat to qualify for this race?
 =< 16
19.5 + .38A^(1/2) - 25.3 =< 16
 - 5.8 =<16
=< 16 + 5.8
=< 21.8
Divide both sides by .38
 = 57.4
Find the square of both sides
A = 3291 sq/ft of sail area should qualify
:
Check that
.3(65) + .38(3291^(1/2)) - 3(600^(1/3) =< 16
19.5 + 21.8 - 25.3 = 16; just qualifies
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