Need help please? A box with an open top is to be constructed by cutting a-inch squares from the corners of a rectangular sheet of tin whose length is twice its width. What size sheet will produce a box having a volume of 1248 in3, when a = 3? It wants the width and length.

Question

anonymous · Answer

http://www.webassign.net/swokatg13/2-3-figure-02-alt.gif

anonymous · Answer

I don't know if that will help

anonymous · Answer

You have to do these problems by drawing them out, look at this pic http://i.ytimg.com/vi/8k7yTz0jYVw/maxresdefault.jpg

anonymous · Answer

Okay

anonymous · Answer

that really didn't help...

anonymous · Answer

especially for someone who has no clue how to makeup the formula

alyssa_xo · Answer

your question didnt copy/paste entirely
how big are the cutout squares?

anonymous · Answer

attachment

anonymous · Answer

that's what it looks like.

alyssa_xo · Answer

oh, okay

anonymous · Answer

the area is given by 4 little rectangles plus the square in the middle

anonymous · Answer

the length is x

anonymous · Answer

find the dimensions of the squares and rectangle

anonymous · Answer

volume = l * w * h

anonymous · Answer

okay, if you want me to find the dimensions of the squares and rectangles why are you giving me the formula for volume?

anonymous · Answer

It's easier for me if we go one baby step at a time and then smush it all together at the end, if you don't mind

anonymous · Answer

you have a sheet of metal and you want to make a open top box that holds a certain amount of space

anonymous · Answer

Yes, so lets find the size of each sheet of metal first before me weld them together right?

anonymous · Answer

for the square on the inside, we would take x-2a multiplied by 2x-2a right?

anonymous · Answer

sorry im making you do steps you dont need. they mostly what you need in the bottom picture

anonymous · Answer

x is the length of the sheet of metal, just multiply out all the sides in the bottom pictures and set it equal to the volume they want and then solve for x

anonymous · Answer

1248 = (a)(2x-2a)(x-2a), a = 36

anonymous · Answer

Oh, okay. Gotcha, I'm sorry, I'm just trying to understand and I thought the simplest of steps would help me

anonymous · Answer

ohh
so you just take those and put it into to make the volume?

anonymous · Answer

yup

anonymous · Answer

we should solve for x also correct?
so we can find the width and height?

anonymous · Answer

height = a, length = 2x-2a, width = x-2a though

anonymous · Answer

a is a constant, 36, so you just need to solve that eqn

anonymous · Answer

okay.

anonymous · Answer

it says if a is three though? should I plug in 3 or 36?

anonymous · Answer

oh yea do 3

anonymous · Answer

okay! one second!

anonymous · Answer

so far I have 3(2x-6)(x-6) should I distribute three into both parts
?

anonymous · Answer

or just the first one and then multiply the two?

anonymous · Answer

I'm sorry for all the stupid questions :/

anonymous · Answer

you just multiply 1 term out at a time

alyssa_xo · Answer

just the first one and multiply. if you had something like: $3[(2x-6)+(x-6) ]$, then you'd distribute into both

anonymous · Answer

ok

anonymous · Answer

like 4*3*2 what would you do?

anonymous · Answer

12*2

anonymous · Answer

same thing with that equation then

anonymous · Answer

okay, now I have the 6x^2-54x+108

anonymous · Answer

so I continue to solve for x?

anonymous · Answer

1248 = (a)(2x-2a)(x-2a), a = 36
416=(2x-3)(x-3)
416=2x^2 -3x - 3x +9
2x^2 - 6x + 9 - 416 = 0
2x^2 - 6x - 407 =0

can you solve from there?

anonymous · Answer

sorry messed up

anonymous · Answer

1248 = (a)(2x-2a)(x-2a), a = 36
416=(2x-6)(x-6)

anonymous · Answer

2x^2 -6x -6x + 36 = 416
2x^2 -6x -6x + 36 - 416 = 0

anonymous · Answer

2x^2 - 12x -380 = 0

anonymous · Answer

Now I factor it? I'm really sorry, this is just beyond my knowledge. I think I'm losing my brain because it's late here.

anonymous · Answer

1248 = (a)(2x-2a)(x-2a), a = 36 should be a = 3 of course

anonymous · Answer

yeah you can factor or do quadratic formula

anonymous · Answer

do you understand the steps?

anonymous · Answer

isn't the quadratic formula easier?

anonymous · Answer

its what i would do

anonymous · Answer

Yeah I get the steps, I just don't know why my head isn't freaking functioning lol. I'm really sorry, I'm not this stupid on a daily basis

anonymous · Answer

dont worry about it

anonymous · Answer

Ok

anonymous · Answer

ugh i keep multiplying wrong, hopefully this is right ill see if i can look it up

1248 = (a)(2x-2a)(x-2a), a = 3
1248 = 3(2x - 6)(x - 6)
2x^2 - 12x - 6x + 36 = 416
2x^2 - 18x - 381 = 0

anonymous · Answer

okay

anonymous · Answer

-380, not -381

anonymous · Answer

x = 19, -10

anonymous · Answer

okay now what?

anonymous · Answer

but x is the length of the sheet, length cant be negative so dont consider the negative answer

anonymous · Answer

so 19 should be the answer

anonymous · Answer

so solve with quadratic formula now?

anonymous · Answer

19 is one side, then 2*19 is the other

anonymous · Answer

yeah at 2x^2 - 18x - 381 = 0 you solve with quadratic and should get -10, 19 = x

anonymous · Answer

-380

anonymous · Answer

i got to go, do you understand how to finish?

anonymous · Answer

my laptop is being super slow, sorry

anonymous · Answer

you cancheck you quadratic formula work with a website

anonymous · Answer

http://www.mathwarehouse.com/quadratic/quadratic-formula-calculator.php

anonymous · Answer

a is number infront of x^2, b infront of x, c is -380

anonymous · Answer

then just look at what the problem asks and what the picture showers you just plug into like 2 equations for each side

anonymous · Answer

the answer was 19 and 38. it wanted the length and width and that was it. thank you sooo soo much

anonymous · Answer

You have a great day. I'm sorry for the slowness

anonymous · Answer

no problem