The formula A\approx 5\cdot v^{\frac{2}{3}} relates the approximate surface area of a sphere, A, with its volume, V. What is the approximate volume, in cubic centimenters, of a sphere with the surface area A=320 \textrm{ cm}^{2}?
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Question 3
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For what value(s) of x is the following equation true?
e^{\frac{6}{7}} \cdot e^{\frac{5x}{3}} =e^{-2}?
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Question 4
4.
What is the solutoin for 11^{\frac{3z}{5}}=121^{8z-4} ?
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Question 5
5.
The diagram below shows a regular dodecagon. A "dodecagon" is a twelve-sided polygon. The word "regular" here has a specific geometric meaning; it means that all the side lengths are equal and all the angles are congruent. For a regular polygon with any number of sides, the area A of the shape is given by A=\frac{p\cdot a}{2} where p is the length of the polygon's perimeter (the sum of all the side lengths) and a is the length of the "apothem" - a line from the center of the polygon to the midpoint of a side.
In this dodecagon, each side has a length s=\sqrt[2]{6}^{x+3}.
The apothem has the length a=2\sqrt[4]{6}^{12x}.
The total area of the decagon is A=72\sqrt[3]{6}^{\frac{5}{2}}.