The following exercises are geometric in nature and lead to polyn...

Question

The following exercises are geometric in nature and lead to polynomial models. Solve each problem. A standard piece of notebook paper measuring 8.5 in. by 11 in. is to be made into a box with an open top by cutting equal-size squares from each cor-ner and folding up the sides. Let x represent the length of a side of each such square in inches. Use the table feature of a graphing calculator to do the following. Round to the nearest hundredth.

Find the maximum volume of the box.

Accepted Answer

A cardboard has a dimension of 100 centimeters by 70 centimeters. This will be turned into a storage box by cutting squares from each of its corners and folding up its sides determine the value X that will maximize the volume of the storage box by using the table feature of a graphic utility. There are possible answers being 13.48 13. 14.28 14.32. We notice here our diagram has the corners cut out. If I were to put them back in, we know our entire width is 100 tire length is 70. Now, we can find each sides of our new box. You would have 100 minus X. We have two XS we're taking out. So it's 100 minus two X for both corners. That is our length. In this case, same thing for the width, 70 D minus two X width. And finally, our height is just the side length of our cut up. That is just X. Now to find the maximum, we want to plug in our volume equation into a graphing calculator and find the maximum point we noticed here on our first table, we looked at our values. Our maximum will be somewhere between 12, 14 or 16, most likely close to 14. So let's check numbers close to the 14th. If you go to our next table, we notice again, their maximum will be somewhere between 30.4 and 13.6. Those are our highest values. So let's check our final table and see which one is the next one be, look even farther. We notice 13.52 has our highest value. We just say our maximum happens at 13. which corresponds to answer B OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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