A man wishes to run a power cable from the shore to....

N

Nigell

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Jun 20, 2006
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I own the following website so i have scanned and uploaded all the relevant information about the question. Here is the link to the information and questions.
http://www.theeasycash.com/Info4QS.bmp
http://www.theeasycash.com/Questions.bmp

I have done question 1, it was easy. I am stuck on question 2, a,b,c, and d. I have done some parts of these questions and get most of it but i am still having trouble. Please assist me in solving it.

This is what ive done so far.
To find an expression for XP i first found XQ.
From now on z is the same as theta.
It says RX=8-5tan(z)
XQ=8-RX
Using pythagores theorem i got this.
XP=SQRT(25+(8-RX)^2)
In the above equation RX=8-5TAN(Z)
I dont get what it means by show that RX=8-5TAN(Z), it just gave me that info and i presumed it was true.
Then to find an expression for C in terms of theta on question 2B) i done the following.
2500(RX)+5000(XP). You must remember what XP AND RX EQUAL in this equation.
But i dont get how to find the domain. In question 2C) ive tried to graph the equation but my graphics calculator shows nothing, why? Maybe coz when z=1 c=a very big number. How do i get around this.
And i dont get what to do to find the approximate value of z to minimizes c.
And i dont understand question D where it asks find the exact value of z that minimizes C. Also when question D asks state the minimum cost of X I DONT GET THAT QUESTION EITHER. how can x cost something its just a point. can someone please solve this question so i can learn how to do it. Thank you.Actually i bet its too complicated for you to even answer.
I posted this question in a few categories coz i didnt really know which one to put it in.
 
happy said:
Um, is this spam? :roll:
Click to expand...
The site does appear to be, or recently have been, a spammer site. But the links, located outside the cgi-bin folder, are apparently math exercises.

To the original poster: Please type out the exercise here in this thread, rather than requiring the tutors to go elsewhere and transfer the information for you. Please also open the graphic in your graphics program and "save as" either a JPEG or a GIF, so that it may be posted here as well, using the "IMG" tags.

Thank you.

Eliz.
 
Hello, Nigell!

I suppose we're expected to use the trig approach that was suggested.
But that is not the way I would solve the problem.
Code: 
      R       8-x       X     x     Q
      * - - - - - - - - * - - - - - *
                          \         |
                            \       |
                              \     | 5
                                \   |
                                  \ |
                                    *
                                    P
Let \(\displaystyle x \,=\,XQ.\;\) Then \(\displaystyle 8\,-\,x\:=\:RX\)

Using Pythagorus: \(\displaystyle \,XP \:=\:\sqrt{x^2\,+\,25}\)
At $5000/km, the underwater portion will cost: \(\displaystyle \,5000\sqrt{x^2\,+\,25}\) dollars.

The shoreline portion is \(\displaystyle 8\,-\,x\) km.
At $2500/km, the shoreline portion will cost: \(\displaystyle \,2500(8\,-\,x)\)

Hence, the total cost is: \(\displaystyle C\;=\;5000\sqrt{x^2\,+\,25}\,+\,2500(8\,-\,x)\)

We wish to minimize: \(\displaystyle \:C\;=\;5000(x^2\,+\,25)^{\frac{1}{2}}\,+\,20,000\,-\,2500x\)

So we solve: \(\displaystyle C'\,=\,0\;\;\Rightarrow\;\;5000\cdot\frac{1}{2}(x^2\,+\,25)^{-\frac{1}{2}}\cdot2x\,-\,2500\;=\;0\)

\(\displaystyle \;\;\)and we have: \(\displaystyle \:\frac{5000x}{\sqrt{x^2\,+\,25}} - 2500\;=\;0\)

which can be solved with mere algebra . . . no trigonometry.
 
Actually i bet its too complicated for you to even answer
Click to expand...

If you think this is bad, try solving the Riemann Hypothesis.


Soroban's method is the best. You can use that information to find the angle. But, if you must have it in terms of theta

Try \(\displaystyle \L\\2500(8-5tan({\theta}))+5000(5sec({\theta}))\)

Differentiate:

\(\displaystyle \L\\2500(8-5tan({\theta}))d{\theta}=-12500sec^{2}({\theta})\)

\(\displaystyle \L\\5000(5sec({\theta}))d{\theta}=25000sec({\theta})tan({\theta})\)

You have:\(\displaystyle \L\\25000sec({\theta})tan({\theta})-12500sec^{2}({\theta})=12500sec({\theta})(2tan{\theta}-sec{\theta})\)

Now, set to 0 and solve for theta.

What makes \(\displaystyle \L\\2tan{\theta}-sec{\theta}=0?\)

Wasn't Soroban's method easier?. Actually, that's the first time I have seen this sort of problem in terms of theta.
 
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