Posted by Andy G on Tuesday, January 14, 2014 at 6:29pm.
An open box with a volume of 1500cm^3 is to be constructed by taking a piece of cardboard of 20 cm by 40 cm, cutting squares of sides length x cm from each corner and folding up the sides. Show that this can be done in two different ways, and find exact dimensions of the box in each case.
I have already found the solution using the quadratic equation, can someone help me find the solution using synthetic division?
- Pre-Calc - Damon, Tuesday, January 14, 2014 at 6:59pm
L = 40 - 2x
w = 20 -2x
V = 1500 = L w x
1500= (40-2x)(20-2x)x = (800 -120 x + 4 x^2)x
4x^3 - 120 x^2 + 800 x -1500 = 0
make a reasonable guess
x = 5 for example
then the box would be 30*10 * 5 = 1500
good, height of five is a solution
so divide by (x-5)
x^3 - 120 x^2 + 800 x -1500
= 4 x^2-100 x +300
4 (x^2- 25 x + 75) = 0
I get about 21 which is too big to take off the width and 2.89
check x = 2.89
20 - 5.78 = 14.22
40 - 5.78 = 34.22
v = 14.22*34.22*2.89 = 1406
well, better do it a bit more accurately
Answer This Question
More Related Questions
- pre-calc please help!! - an open box with a volume of 1500cm cubed is to be ...
- pre-calc - A box with an open top is to be constructed by cutting equal-sized ...
- Calculus 1 - A box with an open top is to be constructed from a rectangular ...
- Math - A box with an open top is to be constructed from a rectangular piece of ...
- Pre Calculus - A piece of cardboard measuring 13 inches by 11 inches is formed ...
- Pre-Calculus - An open box is to be made from a piece of cardboard 11 in by 17 ...
- math - a piece of cardboard is twice as it is wide. It is to be made into a box ...
- Math - An open-topped box is constructed from a piece of cardboard with a length...
- calculus - Help!!! A rectangle piece of cardboard twice as long as wide is to be...
- PRE-CALCULUS - AN OPEN BOX IS FORMED BY CUTTING SQUARES OUT OF A PIECE OF ...