Mathematics, 24.10.2019 18:43 webbjalia04

For each given pair of functions, multiply or divide as instructed. be sure to show all the steps
required to write your answer in simplest form. review the rubric to see how your work will be
graded.
1) f(x)=2x
g(x)=3x^3

f(x)/g(x)=?

Answers

Answer from: FailingstudentXD

$\frac{f(x)}{g(x)} =?$

Since you know f(x) = 2x and g(x) = 3x^3, you can substitute that into the function

$\frac{f(x)}{g(x)} =?$

$\frac{2x}{3x^3} =?$

When a variable(x or y) with an exponent is divided by another variable with an exponent, you subtract the exponents, only if the variables are the same.

For example:

$\frac{x}{y}$ Since the variables on the top and bottom are not the same, you can't simplify it (or its already simplified)

$\frac{x^3}{x^2} =x^{3-2} =x^1$

$\frac{y^5}{y^7}=y^{5-7}=y^{-2} = \frac{1}{y^2}$ (when an exponent is negative, you move it to the other side of the fraction to make the exponent positive)

$\frac{2x}{3x^3} =?$

$\frac{2x}{3x^3}= (\frac{2}{3})x^{1-3}= (\frac{2}{3})x^{-2} = (\frac{2}{3})\frac{1}{x^2}$ Since you can't simplify 2/3, you get:

(not sure if this is how it should look ---> (2/3)x^(1-3) but i'm assuming it is)

$\frac{2}{3x^2}$

Answer from: Quest

$\cos( \frac{4\pi}{5} ) + i \: sin( \frac{4\pi}{5}) \\ \\ = e {}^{i \frac{4\pi}{5} } \\ \\ \ \\ so \\ \\ \sqrt[3]{8 \: ( \cos( \frac{4\pi}{5} ) + isin \frac{4\pi}{5 } ) } \\ \\ \\ \\ 2 \: \: \sqrt[3]{e {}^{ \frac{i4\pi}{5} } } \\ \\ 2 \: e {}^{ \frac{i4\pi}{15} }$

Use de moivre’s theorem to compute the following: i attempted to do it but i got the wrong answer a

Answer from: Quest

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 = $6^{2}$

x = 3, y = 216 = $6^{3}$

x = 4, y = 1296 = $6^{4}$

x = 5, y = 7776 = $6^{5}$

so, the geometric series obtained is $6, 6^{2}, 6^{3}, 6^{4}, 6^{5}$ .

thus, the common ratio is given by $\frac{6^{2}}{6}$ = $\frac{36}{6}$ = 6.

hence, the common ratio is 6.

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For each given pair of functions, multiply or divide as instructed. be sure to show all the steps