Algebra 2. Help! Which grows faster as x increases, x3 or 3x? Explain.

Mathematics

1 answer:

lesya692 [45]3 years ago

6 0

X^3 grows much faster. Definition of exponential growth vs linear growth

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Find the complex fourth roots of 81(cos(3π/8)+isin(3π/8)). a) Find the fourth root of 81. b) Divide the angle in the problem by

WARRIOR [948]

Answer:

The answer is below

Step-by-step explanation:

Let a complex z = r(cos θ + isinθ), the nth root of the complex number is given as:

$z_1=r^{\frac{1}{n} }(cos(\frac{\theta +2k\pi}{n} )+isin(\frac{\theta +2k\pi}{n} )),\\k=0,1,2,.\ .\ .,n-1$

Given the complex number z = 81(cos(3π/8)+isin(3π/8)), the fourth root (i.e n = 4) is given as follows:

$z_{k=0}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(0)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(0)\pi}{4} ))=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})] \\z_{k=0}=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})]\\\\z_{k=1}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(1)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(1)\pi}{4} ))=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})] \\z_{k=1}=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})]\\\\$

$z_{k=2}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(2)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(2)\pi}{4} ))=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})] \\z_{k=2}=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})]\\\\z_{k=3}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(3)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(3)\pi}{4} ))=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})] \\z_{k=3}=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})]$

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A car travels 88 miles in 2 hours (with a constant speed). How much time will it take traveling 360 miles?

n200080 [17]

Answer:

5hat is so easy

Step-by-step explanation:

that is so esy

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Please hurry

Leya [2.2K]

The second answer i think is the best one

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The annual expenditure of the US federal government is approximately 444 trillion dollars.

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Answer:

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In triangle FGH, angle G is 30 degrees and angle H is 100 degrees. What is the measure of angle F? * 1 point 50 degrees 70 degre

serg [7]

Mark brainlist please!

Answer is 50 degrees

Since,

measure of angle F + measure of angle G + measure of angle H = 180

30 + 100 + measure of angle F = 180

Measure of angle F = 180 - 130

Measure of angle F = 50 degrees

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2 years ago