Sign up for FREE

Algebra L6-1 Quiz v2

Last updated about 2 years ago

5 questions

1

1

Question 2

2.

The current population of an island is 12 thousand. The population is expected to grow according to the mathematical model p(t)=3t^{\frac{5}{3}}+12, where p(t) gives the population in thousands of people t years in the future. How many years until the population of the island reaches 108,000 people?

HINT: Please note that the function p(t) takes a number of years, t, and outputs the number of thousands of people in the population. So you will want to set up an equation like p(t)=108, not p(t)=108,000.

1

1

1

Question 1

1.

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

z^{\frac{7}{3}}

\frac{z^{7}}{n^{3}}

z^21

z^{\frac{3}{7}}

Question 3

3.

For what value(s) of z is the following equation true?
\Big( (abc)^{\frac{z}{3}} \Big) \Big( (abc)^{9} \Big)=(abc)^{7}?

z=6

z=\frac{7}{3}

z=\frac{3}{7}

z=-6

Question 4

4.

What is the solution for 25^{\frac{y}{4}}=5^{3y-4} ?

\frac{4}{5}

\frac{8}{5}

\frac{5}{4}

6

Question 5

5.

The diagram below shows a "regular" heptagon. The word "regular" here has a specific geometric meaning; it means that all the side lengths are equal and all the angles are congruent.

The diagram indicates that the side length (remember - all sides are the same) is \frac{3}{14}(\sqrt[3]{5})^\frac{2r}{3} \textrm{ cm}.

The diagram also shows us the length of a line called the "apothem" (the dotted line), which goes from the center of the polygon to the midpoint of a side. The length of the apothem is (\sqrt[3]{5})^{\frac{r}{3}} \textrm{ cm}.

The hexagon's total area is \frac{15}{4}\sqrt[3]{5} \textrm{ cm}^{2}. And it is known that the area of a regular polygon is equal to \frac{1}{2} the product of the perimiter length and the apothem length. That is, if A is the total area, a the length of the apothem, and p the total perimeter length (all the sides together), then:

\large{A=\frac{p\cdot a}{2}=\frac{\big[\textrm{(number of sides)}\cdot \textrm{(length of each side)} \big]\cdot \textrm{(length of the apothem)}}{2}}

Use this information to determine the value of r.