(√3 - <em>i </em>) / (√3 + <em>i</em> ) × (√3 - <em>i</em> ) / (√3 - <em>i</em> ) = (√3 - <em>i</em> )² / ((√3)² - <em>i</em> ²)
… = ((√3)² - 2√3 <em>i</em> + <em>i</em> ²) / (3 - <em>i</em> ²)
… = (3 - 2√3 <em>i</em> - 1) / (3 - (-1))
… = (2 - 2√3 <em>i</em> ) / 4
… = 1/2 - √3/2 <em>i</em>
… = √((1/2)² + (-√3/2)²) exp(<em>i</em> arctan((-√3/2)/(1/2))
… = exp(<em>i</em> arctan(-√3))
… = exp(-<em>i</em> arctan(√3))
… = exp(-<em>iπ</em>/3)
By DeMoivre's theorem,
[(√3 - <em>i </em>) / (√3 + <em>i</em> )]⁶ = exp(-6<em>iπ</em>/3) = exp(-2<em>iπ</em>) = 1
A geologist in South America discovers a bird skeleton that contains 80% of its original amount of C-14
We use formula 
N0= initial amont of C-14 (at time t=0)
N= amount of C-14 at time t
t= time, in years
k= 0.0001
N is 80% of N0 that is 


Divide both sides by N_o

Take ln on both sides

ln(0.8) = -0.0001t ln(e)
ln(0.8) = -0.0001t
Divide both sides by -0.001
t = 2231.435513
The age of the bird skeleton is 2231 years old
Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answer:
x is in (0, 17)
Step-by-step explanation:
The compound inequality is ...
0 < x < 17
The "equal to" case is not included on either end, so round brackets are used:
(0, 17)