achiever test 2, QR ques #14

[bxs023100]

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A 120 m trapping net stretched out into a 3-sided rectangular corral is used to front a flowing river. What value of widths (w), being parallel to the riverbanks, will provide the corral with largest capturing area?


Solution:
Note that this is a 3-sided rectangular corral. {Two widths and one length}

Length of corral, l = 120 – 2w
Capturing area, A = l w = (120 – 2w)w = 120w – 2w2


A = -2(w2 - 60w) = -2(w2 - 60w + 302 -302) = -2(w - 30)2 + 1800
Since A is less than or equal to 1800, it will max out when:
(w - 30) = 0 w = 30 m


what i dont understand is the stuff that is in bold lettering. i understand everything up to that point. can someone please help me!!!

 

[whoaaitzkyle]

A 120 m trapping net stretched out into a 3-sided rectangular corral is used to front a flowing river. What value of widths (w), being parallel to the riverbanks, will provide the corral with largest capturing area?


Solution:
Note that this is a 3-sided rectangular corral. {Two widths and one length}

Length of corral, l = 120 – 2w
Capturing area, A = l w = (120 – 2w)w = 120w – 2w2


A = -2(w2 - 60w) = -2(w2 - 60w + 302 -302) = -2(w - 30)2 + 1800
Since A is less than or equal to 1800, it will max out when:
(w - 30) = 0 w = 30 m


what i dont understand is the stuff that is in bold lettering. i understand everything up to that point. can someone please help me!!!

They are completing the square.

You can also just take the derivative of it and solve for w. It's a lot faster and you end up with the same answer.

 

[bxs023100]

thanks so much for answering all my posts!!!