anonymous
  • anonymous
A box with no top is made by taking a rectangular sheet of metal and cutting away four equal-sized squares (one from each corner of the sheet) and then folding up the resulting aps. The box should be made 4 cm deep and the length of the base should be 15 cm more than the width. If the volume is to be 1000 then what should be the width of the sheet of metal?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
width is 10 length is 25
anonymous
  • anonymous
you use a system of equations to solve this
anonymous
  • anonymous
depth = 4 length = width + 15 length * width * depth = 1000 substitute width +15 for length in the third equation and substitute depth for 4 in it also and you get (width +15)*width*4=1000 you then get \[4w ^{2} + 60w=1000\] then you bring the 1000 over to the left side and factor this gives you \[4(w ^{2}+15w -250)=0\] then you factor and end up with \[4((w ^{2}+25)(w-10))=0 \] and you solve for w which will give you -25 and 10 and since you cant have a negative width you know that the width is 10 and then you plug this into the second equation which was length = width +15 so 10+15 = 25 and that is your length

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anonymous
  • anonymous
thats not one of the answers in my multiple choices ...

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