Kind of urgent...

[indestructible09]

I don't typically ask for answers, but I just got so backed up with school work last week that I'm rushing to get this big math assignment done tonight. One of the problems I have to solve is just wracking my brain (partly because I'm rushing), and I really need help, because I'm SO close to finishing the assignment. This is the main part of the problem from my text book:

"A homeowner needs to run a new water pipe from his house to a water terminal as shown in the accompanying diagram. The terminal is 30 ft down the 10 ft wide driveway and on the other side. A contractor charges $3/ft alongside the driveway and $4/ft for underneath the driveway."

The picture is basically a 30 ft x 10 ft driveway. What I have to do for the part I'm stuck on is write the cost as a function of x. I'm drawing a blank on what the answer is, here. Can some one help me out? I'm down to mere hours of having to get this assignment in... :/ The only other time "x" was mentioned before was in an earlier part of the assignment:

The contractor claims he can do the job for $120 by going alongside the driveway for some distance and then going under the drive diagonally to the terminal. Find x, the distance alongside the driveway.

I'm not sure if this is the same x I need to write in a function, or if the "write a function of x" part is just meant to be its own thing. Any help is greatly appreciated, I'm running out of time, here...

 

[mmm4444bot]

… the part I'm stuck on is [how to] write the cost as a function of x …

The total cost of the job is the sum of two dollar amounts.

The first dollar amount is the cost for installing the section of pipe along the driveway.

The second dollar amount is the cost for installing the section of pipe diagonally underneath the driveway.

The length of the pipe along the driveway is x feet long. The cost "per foot" for this section of pipe is given. So, multiply the number of feet by the cost per foot, to get an expression for the first dollar amount.

The length of the pipe underneath the driveway is the hypotenuse of a right triangle; use the Pythagorean Theorem to calculate this length. The cost "per foot" for this section of pipe installation is also given. So, multiply the number of feet for this underground section by the cost per foot, to get an expression for the second dollar amount.

The sum of these two dollar-amount expressions defines function f.

You're given a value for f(x), so substitute this value for f(x), and solve the resulting equation for x to finish.

If I wrote anything that you do not understand, then please ask specific questions.

If you need more help, then please show whatever work that you can, and we'll go from there.

 

[soroban]

Hello, indestructible09!

A homeowner needs to run a new water pipe from his house to a water terminal as shown.
The terminal is 30 ft down the 10 ft wide driveway and on the other side.
A contractor charges $3/ft alongside the driveway and $4/ft for underneath the driveway.

The contractor claims he can do the job for $120 by going alongside the driveway for some distance
and then going under the drive diagonally to the terminal.

Find x, the distance alongside the driveway.

               x        P   30-x
    A o - - - - - - - - o - - - - - o B
      |                   *         | 
      |                     *       | 
   10 |                       *     | 10 
      |                         *   | 
      |                           * | 
    D o - - - - - - - - - - - - - - o C 
                    30

\(\displaystyle \text{The pipe will run }x\text{ feet along the driveway from }A\text{ to }P.\)
\(\displaystyle \text{At \$3 per foot, this will cost: }\,3x\text{ dollars.}\)

\(\displaystyle \text{The pipe will run under the driveway from }P\text{ to }C.\)
\(\displaystyle \text{The distance is: }\,\sqrt{(30-x)^2 + 10^2}\,\text{ feet (Pythagorus).}\)
\(\displaystyle \text{At \$4 per foot, this will cost: }\,4\sqrt{(30-x)^2 + 100}\text{ dollars.}\)


\(\displaystyle \text{The total cost is \$120.}\)

\(\displaystyle \text{There is our equation!}\quad\hdots\quad 3x + 4\sqrt{x^2-60x + 1000} \:=\:120\)


\(\displaystyle \text{Now solve for }x\;\hdots\)

 

[kcorbets1]

Hello,
Can someone please elaborate on these questions and answers. I'm leaving for a work trip and need to get this assignment in today. I'm having trouble factoring the equation above. I then need to write the cost as a function of x and find the minimum cost that the job can be done for. Looking for any help you can give me. Thank you.

 

[Deleted member 4993]

\(\displaystyle 3x + \sqrt{x^2-60x+1000} \ = \ 120\)

\(\displaystyle \sqrt{x^2-60x+1000} \ = \ 120 \ - \ 3x\)

Square both sides and continue....