Number 9
Can anyone help me set up the problem for section 2.4 number 9? I got that the surface area = x^2+4(x*[30000/x^2]), where x is the length of the base and width and 30000/x^2 is the height, because the volume has to be 30000. When you graph this there doesn't seem to be a minimum, but the back of the book has a numerical answer. I know that x has to be greater than 0, but is there another constraint for x that determines what part of the graph applies to this problem? Otherwise, I can't see how there could be a minimum value for the surface area.
posted by julia at 8:06 PM
1 Comments:
Since the base of the rectangular box is a square teh width and length could be set as x and the height y. The volume of the figure is 30000 so y*x^2=30000. Since there is no top on this figure the surface area would also extend to teh interior of the figure. So SA=(2*x^2)+(8xy). Since we are looking for a two variable equation, substitute in y=30000/(x^2) into the equation SA=(2*x^2)+(8xy).
Equations:
y=30000-x62
SA=(2x^2)+(8xy)
SA=2x^2 + 8(30000/(x^2))
Graph
Windows
xmin=-20
xmax=100
xscl=10
ymin=-10
ymax=30000
yscl=1000
Finally find the minimum.
Post a Comment
<< Home