My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Thanks Tree3Thanks
  • 1 Post By soroban
  • 2 Post By Math Message Board tutor
Reply
 
LinkBack Thread Tools Display Modes
August 17th, 2014, 06:39 AM   #1
Newbie
 
Joined: Jul 2014
From: australia

Posts: 16
Thanks: 0

quadratics

Question is attached:

don't understand part c.

Answer for part c is:

100m by 112.5m

Solutions would be much appreciated!
Attached Images
File Type: jpg Untitled picture.jpg (19.9 KB, 10 views)

Last edited by skipjack; August 17th, 2014 at 07:23 AM.
jessjans11 is offline  
 
August 17th, 2014, 07:28 AM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 19,888
Thanks: 1836

You need to assume that all of the available fencing is used. For part (c), they want you to calculate x and y.
skipjack is offline  
August 17th, 2014, 09:57 PM   #3
Math Team
 
Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 407

Hello, jessjans11!

Quote:
5. 1800 m of fencing is available to
enclose 6 identical pig pens.

Code:
      * - - * - - * - - *
      |      |       |      | y
      * - - * - - * - - *
      |      |       |      | y
      * - - * - - * - - *
         x      x       x
(a) Explain why $9x+8y \:=\:1800.$

There are 9 lengths of fencing which are $x$ m each.
There are 8 lengths of fencing which are $y$ m each.

The total fencing is 1800 m: $\:9x + 8y \:=\:1800\;\;[1]$




Quote:
(b) Show that the area of each pen
$\quad$is given by: $\,A \:=\:-\tfrac{9}{8}x^2 + 225x$

Solve equation [1] for $y$.
$\quad y \;=\;\dfrac{1800-9x}{8} \quad\Rightarrow\quad y \;=\;225 - \tfrac{9}{8}x\;\;[2]$

The area of a pen is: $\:A \;=\;xy \;=\;x\left(225-\frac{9}{8}x\right)$

Therefore: $\:A \;=\;-\frac{9}{8}x^2 + 225$




Quote:
(c) If the enclosed area is to be a maximum,
$\quad$what are the dimensions of each pen?

We want to maximize $A$.

The equation is a down-opening parabola.
Its maximum is at its vertex.

The vertex is: $\:x \:=\:\dfrac{\text{-}b}{2a} \:=\:\dfrac{\text{-}225}{2(\text{-}\frac{9}{8})} \:=\:100 $

Substitute into [2]: $\:y \:=\:225 - \frac{9}{8}(100) \:=\: \dfrac{225}{2}$

Therefore, the dimensions are: $\:100\text{m} \times 112.5\text{m}$.

Thanks from jessjans11
soroban is offline  
August 18th, 2014, 07:19 AM   #4
Banned Camp
 
Joined: Jun 2014
From: Earth

Posts: 945
Thanks: 191

Quote:
Originally Posted by soroban View Post





$\quad y \;=\;\dfrac{1800-9x}{8} \quad\Rightarrow\quad y \;=\;225 - \tfrac{9}{8}x\;\;[2]$

The area of a pen is: $\:A \;=\;xy \;=\;x\left(225-\frac{9}{8}x\right)$

Therefore: $\:A \;=\;-\frac{9}{8}x^2 + 225$






Substitute into [2]: $\:y \:=\:225 - \frac{9}{8}(100) \:=\: \dfrac{225}{2}$

Therefore, the dimensions are: $\:100\text{m} \times 112.5\text{m}$.

Your A expression is incorrect. You left the x off of "225x."

And then when you substituted, you substituted into the wrong expression.

You should have substituted the x-value into

A = 225x - (9/8)x^2.
Thanks from soroban and jessjans11
Math Message Board tutor is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
quadratics



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
quadratics grangeeducation Algebra 1 April 10th, 2014 10:12 AM
Factoring quadratics help 2x^2+20x+50 NeverForgetVivistee Algebra 3 November 21st, 2011 05:35 PM
Ho Do I Factorising Quadratics manich44 Algebra 7 November 5th, 2011 03:21 AM
Quadratics sallyyy Algebra 3 June 4th, 2011 02:58 AM
Quadratics Help maria186 Algebra 1 February 10th, 2010 06:34 PM





Copyright © 2018 My Math Forum. All rights reserved.