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Find the dimensions of the rectangle of maximum area that can be formed from a 330in. piece of wire
 2 years ago
 2 years ago
Find the dimensions of the rectangle of maximum area that can be formed from a 330in. piece of wire
 2 years ago
 2 years ago

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cuddleponyBest ResponseYou've already chosen the best response.2
so we have a rectangle dw:1334016584546:dw A = b * h and we know that b + h = 330 inches Follow?
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
Now we need to solve for one of the variables b = (330  h) thus A = (330  h)h How about a little interaction :l
 2 years ago

LaddiusMaximusBest ResponseYou've already chosen the best response.0
so is that a standard formula?
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
This is normally what you do yes
 2 years ago

LaddiusMaximusBest ResponseYou've already chosen the best response.0
Sorry my son is crying.
 2 years ago

LaddiusMaximusBest ResponseYou've already chosen the best response.0
is that all there is to it?
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
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
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
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
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
Do you follow so far?
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
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
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
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
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
sub a number smaller than 165 and a number larger than 165 into the function A'(x) = 330  2h
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
Do this on your test for more marks :)
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
then check to see if it is positive or negative and put it in the square of the chart
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
Keep it simple !!! I would go 330  2(0)
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
= 330 this is positive f'(x) > 0 Function is increasing so dw:1334017519222:dw
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
Remember you can use any number smaller (unless it is not defined by the domain) :)
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
Fill in the next part of the chart :)
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
hell I will do it I should be studying General intermediary metabolism :) FML dw:1334017660396:dw
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
yup you can tell that the function will give you a negative number right 330  2(166)
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
thus you can deduce that your graph looks something like thisdw:1334017724724:dw
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
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?
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
do you follow? If you dont understand something ask
 2 years ago

LaddiusMaximusBest ResponseYou've already chosen the best response.0
do i use base times heighy?
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
dw:1334017945453:dw
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
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
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
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
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
solve for b to find the length of the base
 2 years ago

LaddiusMaximusBest ResponseYou've already chosen the best response.0
0h 330165. sorry Im way behind in this class. Its been a rough semester.
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
Do you see how obvious the answer is :) I hear you, I'm probably going to fail some of my classes :(
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
Remember when deal with these questions though always take into consideration each side of the object
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
so what would the actual lengths of h and b, be
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
I even explained how to get the final question earlier on lol. Think about it
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
you have b= 165 inch and h = 165 inch and you have a 4 sided rectangle
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
I went a little more of an indirect route because it kept the arithmatic simpler
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
The actual formula would be 2b + 2h = A you cant make a 4 sided object with only 2 strands of wire
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
165/2 = 82.5 inches dw:1334018556160:dw
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
To get the max area of a rectangle all sides have to be the same length :)
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
sorry for over complicating it but you would get the same answer if you used 2b + 2h = Area
 2 years ago

LaddiusMaximusBest ResponseYou've already chosen the best response.0
82.5 is not right either.
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
To maximize the area of a rectangle all sides must be of equal length
 2 years ago

LaddiusMaximusBest ResponseYou've already chosen the best response.0
dimension of maximum area? 82.5 in^(2)?
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
yes you probably forgot units
 2 years ago

LaddiusMaximusBest ResponseYou've already chosen the best response.0
it doesnt require me to enter units
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
well I recommend email the people overseeing your course, but lets ask someone to check first
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
Someone else on the site
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
The answer I got is h = 82.5 and b = 82.5
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
You sadisfied Laddius?
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
do you understand the process?
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
Trust me it is right, logically it makes sense
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
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
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
The answer would be 85.5*85.5 or the Max Area sorry
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
the real answer would be 7310.25
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
sorry that is the answer I'm not use to using a calculator for these kinds of questions
 2 years ago

cuddleponyBest ResponseYou've already chosen the best response.2
try it I bet it works
 2 years ago
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