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    Algebra - Volume

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    1) An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of each side of the square to be cut out.

    a) Find the function V that represents the volume of the box in terms of x.

    b) Graph this function and show the graph over the valid range of the variable x..
    Show Graph here.

    c) Using the graph, what is the value of x that will produce the maximum volume?

    2) The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters.

    a) Write h as a function of r. Keep "" in the function's equation.
    Show work in this space.

    b) What is the measurement of the height if the radius of the cylinder is 3 centimeters? Round your answer to the hundredth's place.
    Show work in this space.

    c) Graph this function.
    Show graph here.

    3) Logarithms:
    a) Using a calculator, find log 1000 where log means log to the base of 10.

    b) Most calculators have 2 different logs on them: log, which is base 10, and ln, which is base e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to the computer, 0 and 1. When a computer scientist needs a logarithm, he needs a log to base 2 which is not on any calculator. To find the log of a number to any base, we can use a conversion formula as shown here:

    Using this formula, find . Round your answer to the hundredth's place.
    Show work in this space.

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    Solution Summary

    Solution to the posted problems given with step by step explanation.