Question 103: Sailboat Stability, help for step b, and c

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internalmemory

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I'm having problems with this math question, the assignment is actually due in around an hour but I'm thinking of holding off unless I can get immediate help within that time. I'm taking an online course (online school) and I emailed the professor but I'm waiting for an email back. The question is:

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:
C = 4d -1/3b

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.
B. Solve this formula for d.
C. 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?

I have done part A easily, and the answer is 1.89 (still under 2 so it's applicable).

Shown Work:

C = 4d -1/3b Original Formula
C = 4(23245) -1/3(13.5) Plugged the values in for the variables. Exponents are first
C = 4(.035)(13.5) Solving d with the exponent first, leaving 2 multiplications
C = .14(13.5) Solving 4 with d for .14
C = 1.89 Resulting in capsizing screening value.

=============================================

Now as for where it says "Solve for d" I have no idea. I am absolutely confused to this point.

I can include the entire example worksheet for this, and the graph for the problem (as asked for in part C).

week3 assignment.jpg

Examples: http://s000.tinyupload.com/?file_id=08142649753430216524

Note that I have seen this question on here before but it wasn't answered fully, and the people got confused between the actual question, and the examples for the question.
 
internalmemory said:
I'm having problems with this math question, the assignment is actually due in around an hour but I'm thinking of holding off unless I can get immediate help within that time. I'm taking an online course (online school) and I emailed the professor but I'm waiting for an email back. The question is:

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:
C = 4d -1/3b

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.
B. Solve this formula for d.
C. 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?

I have done part A easily, and the answer is 1.89 (still under 2 so it's applicable).

Shown Work:

C = 4d -1/3b Original Formula
C = 4(23245) -1/3(13.5) Plugged the values in for the variables. Exponents are first
C = 4(.035)(13.5) Solving d with the exponent first, leaving 2 multiplications
C = .14(13.5) Solving 4 with d for .14
C = 1.89 Resulting in capsizing screening value.

=============================================

Now as for where it says "Solve for d" I have no idea. I am absolutely confused to this point.

I can include the entire example worksheet for this, and the graph for the problem (as asked for in part C).

View attachment 3889

Examples: http://s000.tinyupload.com/?file_id=08142649753430216524

Note that I have seen this question on here before but it wasn't answered fully, and the people got confused between the actual question, and the examples for the question.
Click to expand...

If you are given:

y = 4*x3

Can you express 'x' in terms of y (in other words solve for 'x')?
 
Last edited by a moderator:
Subhotosh Khan said:
If you are given:

y = 4*x3

Can you express 'x' in terms of y (in other words solve for 'x')?
Click to expand...


The instructor says it has to be in the form of
D =

I received an email from her today explaining the situation and that was the only thing she said (a whole lot of help, let me say).

"You want to use the formula given in the problem (not the example)
c=4d^-1/3b
Using the rules of algebra how can you solve this formula so that it is in the form d= "
 
Quaid said:

The graph above does not match the formula shown.

For example, when d = 10000, the graph shows C ≈ 25

However 54(10000)^(-1/3)(13.5) ≈ 33.8
Click to expand...

I have also noticed this. And as the formula I'm supposed to be working isn't 54d but rather 4d. But I didn't bring this up to the instructor since she's about as useful as reciting a poem to a brick..


That symbol needs to be a lower-case d

Are you familiar with the following two Property of Exponents?

x^(-m) = 1/x^m

x^(1/n) = nth root of x
Click to expand...

No, I'm not familiar with that.
 
Last edited:
Denis said:
What poem? :rolleyes:

Go havva glance here; you'll become an "exponent expert":
http://www.mathsisfun.com/algebra/negative-exponents.html
Click to expand...


Lol I have plenty of poems, but trying to recite a poem to her is like opening 1,000 boxes that are empty, and I'm fully aware that they're empty - but I'm going to continue opening them with an extremely excited look on my face just because I can. Lol...

That's actually a really nice link. I admit I think I learned about negative exponents lol which is saying more than what I'm supposed to be learning from this math class that I'm paying over a grand for.
 
internalmemory said:
this math class that I'm paying over a grand for
Click to expand...

Sorry to hear that. (Hope it's not at University of Phoenix.)


Here's a similar example, for you to see whether you understand the properties involved; solve the equation for x:

y = 5*x^(-1/2)*z

The power may be rewritten, using the property for negative exponents.

y = 5z/x^(1/2)

We're trying to solve for x, so we don't want it in a denominator. Multiply both sides by the power of x.

y*x^(1/2) = 5z

Now isolate the power of x, by dividing (both sides) by y.

x^(1/2) = 5z/y

This result tells us that the square root of x equals 5z/y. To find x, we raise both sides to the power of 2

x = 25z^2/y^2

That is, by properties of exponents, [x^(1/2)]^2 = x^(1/2*2) = x^1

and (5z/y)^2 = 5^2*z^2/y^2

Questions about this? :)
 
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