PreCalculus Homework

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PreCalculus Homework

  1. An open box is to be made by cutting congruent squares from each corner of a 20cm by 30cm rectangular piece of cardboard.  

    1. What are the conditions on the HEIGHT of the box?

    2. Draw and appropriately label a NET for the box if its height is arbitrary (h cm)

    3. Write an equation for the VOLUME of this box if its height is h

    4. Determine the volume when h = 4cm,  & when h =  9cm,  & h = 12cm

    5. What dimensions will maximize the volume of a box made from this material?

    6. What will the maximum volume be?

    7. Use an online resource or app to create a valid, properly scaled and labeled graphic model for this investigation.  Label applicable points.

    8. Practice creating & investigating the same version of the graph on your calculator.

2.  The COST FUNCTION (what the owner pays for upkeep, supplies, etc) for a certain business is given by C(x) = 200+10x+0.2×2, where x = # items produced.

The REVENUE FUNCTION (amount from the sale of items) is given by

R(x) = 40x-0.1×2, where x = # items sold

When is the REVENUE greater than the cost?  And what does this indicate about the status of the business with respect to this item?

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