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anonymous
 one year ago
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
anonymous
 one year ago
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

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triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440636145968:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440636232302:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0volume changes with area and area changes with height

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, from there can I just solve for the h and then plug it into the volume function which is V=s^2*h

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440636504171:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1solve 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
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large V = s^2*h\] \[\Large V = s^2*\frac{1200  s^2}{4s}\] \[\Large V = s*\frac{1200  s^2}{4}\] \[\Large V = \frac{1200s  s^3}{4}\] so it looks good so far

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the volume formula would be

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440637090561:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0yes read above by jim he found the expression for h then substitute in the formula for the volume

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yes correct, the volume is s^2*h

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you want to find the max volume, so you'll need to graph \[\Large y = \frac{1200xx^3}{4}\] and locate the local max

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What intervals should I use, My graph doesn't show it clearly.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1https://www.desmos.com/calculator/bbcpea5fld my window I used was xmin = 10 xmax = 40 ymin = 3000 ymax = 5000

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1on the desmos graph, you should be able to click the local max (maybe click twice) to have the coordinates of that point show up

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yeah 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
 one year ago
Best ResponseYou've already chosen the best response.0OMG, thank you so much! ... DO you think you can help me with another one?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0provide one the two positive integers whose sum is 200 and whose product is a product

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0what do you mean the product is a product?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0like if the two integers are multiplied, that equals to the maximun value

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0the constant is not prime?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't know to be honest

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1do you mean `provide one the two positive integers whose sum is 200 and whose product is a MAXIMUM` ??

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1`integers whose sum is 200` x+y = 200 solve for y to get y = 200x

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the product is the result of multiplying x*y = x*(200x) = 200x  x^2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the goal is to max out 200x  x^2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you can graph 200x  x^2 or complete the square to find the vertex

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 so the answer is 10000

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so the two numbers are 100 and 100 100+100 = 200 100*100 = 10,000 the max product is indeed 10,000

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I think they are asking for one of the two numbers and not the max product

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 thanks

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you're welcome
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