Question

Sailboat stability. To be considered safe for ocean sailing, the capsize screening value C should be less than 2 (www.sailing.com). For a boat with a beam (or width) b in feet and displacement d in pounds, C is determined by the function

Answer 1

a) Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam of 13.5 feet.

Answer 2

@nikato @SolomonZelman

Answer 3

@tkhunny @wio

Answer 4

THe\[C = 54 d ^{-\frac{ 1 }{ 3 }}b\] function is :

Answer 5

b) The accompanying graph shows C in terms of d for the Tartan 4100 (b = 13.5). For what displacement is the Tartan 4100 safe for ocean sailing?

Answer 6

I think a is only plug n chuff values, but what about the b) part, please help me out !

Answer 7

,yes. Part a is just pluggin in numbers into the function.
Plug 23245 for d and 13.5 for b and solve for C

Answer 8

Part B is also plug and solve.
In the problem, it states the capsize must be less than 2.

So
Replace C with 2 and write an inequality. And plug in 13.5 for b. and solve for d

2>54d^-1/3 (13.5)

Answer 9

\[C = 4 *d ^{-\frac{ 1 }{ 3 }}* b\]

Answer 10

\[C = 4 * \frac{ 1 }{ d ^{1/3} }* b\]

Answer 11

\[C = 4 * 1/\sqrt[3]{d}*b\]

Answer 12

23,245)pounds *13,5 feet \[C = 4 * \frac{ 1 }{ \sqrt[3]{23,245} } * 13,5\]

Answer 13

b) \[\frac{ C }{ 4b }=\frac{4b * d ^{-\frac{ 1 }{ 3 }} }{ 4b }\]

Answer 14

\[d ^{-\frac{ 1 }{ 3 }} = \frac{ C }{ 4b }\]

Answer 15

\[(d ^{-\frac{ 1 }{ 3 }})^{-3} = (\frac{ C }{ 4b })^{-3}\]

Answer 16

\[d = (\frac{ C }{ 4b })^{-3} = \frac{( C )^{^{-3}}}{ (4b)^{-3} }\]

Answer 17

\[d = \frac{ 1 }{ C ^{3}}*\frac{ (4b)^{3} }{ 1 } \]

Answer 18

\[d = \frac{ (4b)^{3} }{ C ^{3} } = \frac{ 64b ^{3} }{ C ^{3} }\]

Answer 19

\[d = \frac{ 64b ^{3} }{ C ^{3} }\]

Answer 20

2>4 d^-1/3 (13.5)\[2 > 4 (13,5) * d ^{-\frac{ 1 }{ 3 }}\]

Answer 21

\[2 > 54 * d ^{-\frac{ 1 }{ 3 }}\]

Answer 22

\[\frac{ 2 }{ 54 }> \frac{ 54*d ^{-\frac{ 1 }{ 3 }} }{ 54 }\]

Answer 23

\[(\frac{ 1 }{ 27 })^{-3}>(d ^{-\frac{ 1 }{ 3 }})^{-3} \]

Answer 24

\[(27)^{3}> d\]

Answer 25

19683>d