You need to make an open-top box from a rectangle of cardboard 9 by 13 inches by cutting a square from each corner and folding up the sides. You want the box to have the maximum possible volume. Complete the following problems showing all your work:
If each square you cut out is x by x inches, write an expression for the volume of the box, V(x), in terms of x. A sketch may help. Show all your work.
Sketch (or use technology to plot) the function to find the maximum. Clearly label or state the (x,y) coordinates of the value of x that optimizes the function and the maximum Volume (y).
How many dollars worth of quarters (25 cent pieces) would it take to fill the box? Show all your work!
I'm not sure how accurate this is but I've attempted.
13* 9 inch, to create a cuboid with an open top, would need 4 squares cut out, each located in the corners. Length of one square will be x.
So (13-2x)(9-2x)(x) = vol
For the function graphs things, I'm not too good at but I put it into something to plot and got (1.745, 91.438) so I'm now assuming that the y coordinate is the volume.
I'm not sure what dimensions you're using for the quarters (and I'm not A
merican, sorry) but according to wikipidea, the diameter is 0.955 and the thickness is 0.069
So pi*(0.955/2)^2 * 0.69 gives you the volume of the quarter. What I then did was 91.438/( pi*(0.955/2)^2 * 0.69)= 1850.03...
Then, as you want it in dollars, I believe you do 1850*0.25 = $462.50 (If that's correct. I believe that's how the US currancy works)
I can't get an image of the graph here but I did it on https://www.desmos.com/calculator