anonymous
  • anonymous
Guys please help me, I give medals If 1,200 cm2 of material is available to make a box with a square base and an open top, find the maximum volume of the box in cubic centimeters
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@Loser66
triciaal
  • triciaal
|dw:1440636145968:dw|
triciaal
  • triciaal
|dw:1440636232302:dw|

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triciaal
  • triciaal
volume changes with area and area changes with height
anonymous
  • anonymous
okay, from there can I just solve for the h and then plug it into the volume function which is V=s^2*h
anonymous
  • anonymous
|dw:1440636504171:dw|
triciaal
  • triciaal
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
solve for h to get \[\Large 1200 = s^2 + 4sh\] \[\Large 1200 - s^2 = 4sh\] \[\Large 4sh = 1200 - s^2\] \[\Large h = \frac{1200 - s^2}{4s}\]
jim_thompson5910
  • jim_thompson5910
\[\Large V = s^2*h\] \[\Large V = s^2*\frac{1200 - s^2}{4s}\] \[\Large V = s*\frac{1200 - s^2}{4}\] \[\Large V = \frac{1200s - s^3}{4}\] so it looks good so far
anonymous
  • anonymous
the volume formula would be
anonymous
  • anonymous
|dw:1440637090561:dw|
anonymous
  • anonymous
right?
triciaal
  • triciaal
yes read above by jim he found the expression for h then substitute in the formula for the volume
jim_thompson5910
  • jim_thompson5910
yes correct, the volume is s^2*h
jim_thompson5910
  • jim_thompson5910
you want to find the max volume, so you'll need to graph \[\Large y = \frac{1200x-x^3}{4}\] and locate the local max
anonymous
  • anonymous
What intervals should I use, My graph doesn't show it clearly.
jim_thompson5910
  • jim_thompson5910
https://www.desmos.com/calculator/bbcpea5fld my window I used was xmin = -10 xmax = 40 ymin = -3000 ymax = 5000
jim_thompson5910
  • jim_thompson5910
on the desmos graph, you should be able to click the local max (maybe click twice) to have the coordinates of that point show up
anonymous
  • anonymous
is it 4000
jim_thompson5910
  • jim_thompson5910
yeah that local max is (20,4000) meaning that x = 20 and y = 4000 so if the side length is s = 20 cm then the max volume is 4000 cubic cm
anonymous
  • anonymous
OMG, thank you so much! ... DO you think you can help me with another one?
jim_thompson5910
  • jim_thompson5910
sure
anonymous
  • anonymous
provide one the two positive integers whose sum is 200 and whose product is a product
triciaal
  • triciaal
what do you mean the product is a product?
anonymous
  • anonymous
like if the two integers are multiplied, that equals to the maximun value
triciaal
  • triciaal
the constant is not prime?
anonymous
  • anonymous
I don't know to be honest
jim_thompson5910
  • jim_thompson5910
do you mean `provide one the two positive integers whose sum is 200 and whose product is a MAXIMUM` ??
anonymous
  • anonymous
yes
jim_thompson5910
  • jim_thompson5910
`integers whose sum is 200` x+y = 200 solve for y to get y = 200-x
jim_thompson5910
  • jim_thompson5910
the product is the result of multiplying x*y = x*(200-x) = 200x - x^2
jim_thompson5910
  • jim_thompson5910
the goal is to max out 200x - x^2
jim_thompson5910
  • jim_thompson5910
you can graph 200x - x^2 or complete the square to find the vertex
anonymous
  • anonymous
I got (100, 10000)
anonymous
  • anonymous
@jim_thompson5910 so the answer is 10000
jim_thompson5910
  • jim_thompson5910
so the two numbers are 100 and 100 100+100 = 200 100*100 = 10,000 the max product is indeed 10,000
jim_thompson5910
  • jim_thompson5910
I think they are asking for one of the two numbers and not the max product
anonymous
  • anonymous
okay, thank you
jim_thompson5910
  • jim_thompson5910
sure thing
triciaal
  • triciaal
@jim_thompson5910 thanks
jim_thompson5910
  • jim_thompson5910
you're welcome

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