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Solutions For Five Problems of Mixed Type

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Trigonometry/Algebra
1) An open-top box with a square base is to be constructed from 150 square centimeters of material.
What dimensions will produce a box with largest possible volume?

A)
B)
C)
D)
E)

2) Assume h 0. Compute and simplify the difference quotient for f(x) = 1 / x.

3) Solve the inequality.

A)
B)
C)
D)
E)

4) Solve the equation without using logarithms.

x=_________ Large x-Value
x=__________ Smaller x-Value

5) Solve the equation.

x=________

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Solution Summary

This solution contains an attached file that solves the following problems:
1.What are the dimensions of a box constructed of 150 square centimeters that will produce the largest volume possible?
2.compute the difference quotient for f(x)=1/x
3.Solve (3x^2-8x -3 ) /(x^2-4x+4) >=0
4.)Sole 7^(2x^2+3x)=49^(6-x) without using logarithms.
5.)Solve log(3x+1)=log(x+1) +log(2).

Solution Preview

1.) D this volume is 927cm^3
1.D A was 797
1.DI B was 797
1.DII C was 714
1.DIII E was 737
Simply solved by computing volumes of the choices presented and choosing the largest volume.

2 (1/(x-h)-1/x)/h= 1/(xh-h^2)-1/xh = -h^2/( (xh)^2-xh^3) = -1/(x^2-xh)
3 Since h ->0, the final answer is 1/x^2

1.D is the correct ...

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