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Algebra L6-1 Quiz v4

Last updated about 2 years ago

5 questions

1

1

Question 2

2.

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}?

1

1

1

Question 1

1.

How do you write \sqrt[7]{11^{3}}?

11^{\frac{7}{3}}

\frac{11^{3}}{11^{7}}

11^{\frac{3}{7}}

\big(11^{-7}\big)^{3}

Question 3

3.

For what value(s) of x is the following equation true?
e^{\frac{6}{7}} \cdot e^{\frac{5x}{3}} =e^{-2}?

x=-\frac{2}{7}

x=\frac{1}{35} \textrm{ and } x=35

x=\frac{2}{7} \textrm{ and } x=-\frac{2}{7}

x=-\frac{12}{7}

Question 4

4.

What is the solutoin for 11^{\frac{3z}{5}}=121^{8z-4} ?

\frac{11}{7}

\frac{40}{77}

\frac{7}{2}

\frac{11}{40}

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}}.

Use this information to determine the value of x.