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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..
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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 = &#960;r2h 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 "&#61552;" in the function's equation.
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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.
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c) Graph this function.
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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.
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