An open box is to be made from cutting squares of side s from each corner of a piece of cardboard 25" by 30".
a.Write an expression for the volume, V, of the box in terms of s.
b. Graph V(s) using your graphing calculator. Identify the domain and range of this graph.
I believe I've asked this question before, but I would like to check it. I think the expression is
s(30-2s)(25-2s)
expanded, I believe it's 4s^3-110s^2+750s
However, I try to graph it, but I don't see anything. Could someone help me out with the window of the graph? I have no idea how to change it so I can see the graph.
Thanks!
well, s will run from zero to 12.5
I didn't check your expansion, I graphed it on the web as the algrebraic function of ()() ().
V will run from zero to guessing, 1760 try that.
You are correct, the expression for the volume V of the box in terms of s is:
V(s) = s(30 - 2s)(25 - 2s)
To graph this function on a graphing calculator, you need to adjust the window settings to properly view the graph.
Here's how you can set the window on your graphing calculator:
1. Press the "Y=" button on your calculator.
2. Enter the expression for V(s) in terms of s on the Y1 line: Y1 = s(30 - 2s)(25 - 2s)
3. Press the "WINDOW" or "ZOOM" button to access the window settings.
To set up a suitable window, consider the range of values for s that makes sense in this context. Since you are cutting squares of side s from each corner, the value of s should be positive and less than half the minimum side length of the original cardboard, which is 12.5 in this case.
Here's a recommended window setup:
Xmin: 0
Xmax: 13 (or any value slightly greater than half of the minimum side length)
Ymin: 0 (since volume cannot be negative)
Ymax: 1500 (or any reasonable value)
Adjust these settings based on the scale you want for your graph. Once the window is set up, you should be able to see the graph of V(s).
The domain of the graph is the range of valid values for s, which is between 0 and approximately 12.5. The range of the graph will depend on the specific numbers, but it will represent the volume of the box, which should be non-negative.
Hope this helps!