LaddiusMaximus
  • LaddiusMaximus
Find the dimensions of the rectangle of maximum area that can be formed from a 330-in. piece of wire
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
YAY Optimization :)
anonymous
  • anonymous
so we have a rectangle |dw:1334016584546:dw| A = b * h and we know that b + h = 330 inches Follow?
anonymous
  • anonymous
Now we need to solve for one of the variables b = (330 - h) thus A = (330 - h)h How about a little interaction :l

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LaddiusMaximus
  • LaddiusMaximus
so is that a standard formula?
anonymous
  • anonymous
This is normally what you do yes
LaddiusMaximus
  • LaddiusMaximus
Sorry my son is crying.
anonymous
  • anonymous
its fine :)
LaddiusMaximus
  • LaddiusMaximus
is that all there is to it?
anonymous
  • anonymous
So next step we need to take the derivative with A respect to the change in x so (Ad/dx) A = (Ad/dx) 330h - h^(2) A' = 330 - 2h
anonymous
  • anonymous
Now We need to look at the domain of A' = 330 - 2h and see if we can find any places where it violates the domain (as this could be a place where the graph changes) The domain is clearly all real numbers Next We set A'(x) = 0 (write this on your test it looks good and will get you a mark probably) 330 - 2h = 0 Now solve
anonymous
  • anonymous
Do you follow so far?
LaddiusMaximus
  • LaddiusMaximus
165?
anonymous
  • anonymous
btw there is no standard formula but we know: Area of a Square (or Rectangle) = Base * Height We also know that the length of the wire is all sides added up so we get b + h = Length of wire or we could express it as 2b + 2h = Length of wire But really that would give you the same answer its best to keep it simple
anonymous
  • anonymous
h = 165 so we have a point Now we need to use the rules MEMORIZE THESE BTW f'(x) > 0 The function is increasing f'(x) < 0 The function is decreasing Make a Table |dw:1334017324830:dw|
anonymous
  • anonymous
sub a number smaller than 165 and a number larger than 165 into the function A'(x) = 330 - 2h
anonymous
  • anonymous
Do this on your test for more marks :)
anonymous
  • anonymous
then check to see if it is positive or negative and put it in the square of the chart
LaddiusMaximus
  • LaddiusMaximus
so 330-2(164)?
anonymous
  • anonymous
Keep it simple !!! I would go 330 - 2(0)
anonymous
  • anonymous
= 330 this is positive f'(x) > 0 Function is increasing so |dw:1334017519222:dw|
anonymous
  • anonymous
Remember you can use any number smaller (unless it is not defined by the domain) :)
anonymous
  • anonymous
Fill in the next part of the chart :)
LaddiusMaximus
  • LaddiusMaximus
330-2(1)?
LaddiusMaximus
  • LaddiusMaximus
or 330-2(166)?
anonymous
  • anonymous
hell I will do it I should be studying General intermediary metabolism :) FML |dw:1334017660396:dw|
anonymous
  • anonymous
yup you can tell that the function will give you a negative number right 330 - 2(166)
anonymous
  • anonymous
thus you can deduce that your graph looks something like this|dw:1334017724724:dw|
anonymous
  • anonymous
Can you now see the answer? h = 165 So now we know the max size of the height to give optimial area Can you guess how to solve for the base?
anonymous
  • anonymous
do you follow? If you dont understand something ask
LaddiusMaximus
  • LaddiusMaximus
do i use base times heighy?
anonymous
  • anonymous
|dw:1334017945453:dw|
anonymous
  • anonymous
No think about what you are doing, go back to the original formulas Calculus is just measuring change. With these problems we just are measuring how the Area changes when we change the length of h
anonymous
  • anonymous
Area of a rectangle = base * height Length of The wire = Height length + Base length A = b * h and we know that b + h= 330 inches If we know that base length is = 165 and total wire used is = 330 165 + b = 330
anonymous
  • anonymous
solve for b to find the length of the base
LaddiusMaximus
  • LaddiusMaximus
0h 330-165. sorry Im way behind in this class. Its been a rough semester.
anonymous
  • anonymous
Do you see how obvious the answer is :) I hear you, I'm probably going to fail some of my classes :(
anonymous
  • anonymous
Remember when deal with these questions though always take into consideration each side of the object
anonymous
  • anonymous
so what would the actual lengths of h and b, be
LaddiusMaximus
  • LaddiusMaximus
165 isnt right
anonymous
  • anonymous
I even explained how to get the final question earlier on lol. Think about it
anonymous
  • anonymous
you have b= 165 inch and h = 165 inch and you have a 4 sided rectangle
anonymous
  • anonymous
I went a little more of an indirect route because it kept the arithmatic simpler
anonymous
  • anonymous
The actual formula would be 2b + 2h = A you cant make a 4 sided object with only 2 strands of wire
anonymous
  • anonymous
165/2 = 82.5 inches |dw:1334018556160:dw|
anonymous
  • anonymous
for all sides
anonymous
  • anonymous
To get the max area of a rectangle all sides have to be the same length :)
anonymous
  • anonymous
sorry for over complicating it but you would get the same answer if you used 2b + 2h = Area
LaddiusMaximus
  • LaddiusMaximus
82.5 is not right either.
anonymous
  • anonymous
says who
anonymous
  • anonymous
82.5* 4 = 330
LaddiusMaximus
  • LaddiusMaximus
webworks
anonymous
  • anonymous
Webworks is wrong
anonymous
  • anonymous
To maximize the area of a rectangle all sides must be of equal length
LaddiusMaximus
  • LaddiusMaximus
dimension of maximum area? 82.5 in^(2)?
anonymous
  • anonymous
yes you probably forgot units
LaddiusMaximus
  • LaddiusMaximus
it doesnt require me to enter units
anonymous
  • anonymous
well I recommend email the people overseeing your course, but lets ask someone to check first
LaddiusMaximus
  • LaddiusMaximus
like who?
anonymous
  • anonymous
Someone else on the site
anonymous
  • anonymous
The answer I got is h = 82.5 and b = 82.5
anonymous
  • anonymous
thats right
anonymous
  • anonymous
Yeah I know lol
anonymous
  • anonymous
You sadisfied Laddius?
anonymous
  • anonymous
satisfied*
LaddiusMaximus
  • LaddiusMaximus
i suppose
anonymous
  • anonymous
do you understand the process?
anonymous
  • anonymous
Trust me it is right, logically it makes sense
anonymous
  • anonymous
Its easy 1st acquire two formulas from the question 2nd Solve for one of the variables in one of the equations and sub it into the other equation 3rd take the derivative of the new equation you made 4th check domain and points the function is 0 5th look to see if function is increasing or decreasing and at what point it is at its max or min and that will be your answer 6th sub the answer back into the one of the equation to solve for the other variable. 7th check to see if your answer is reasonable
anonymous
  • anonymous
The answer would be 85.5*85.5 or the Max Area sorry
anonymous
  • anonymous
the real answer would be 7310.25
anonymous
  • anonymous
sorry that is the answer I'm not use to using a calculator for these kinds of questions
anonymous
  • anonymous
try it I bet it works
LaddiusMaximus
  • LaddiusMaximus
nope
LaddiusMaximus
  • LaddiusMaximus
6806.25

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