What does 8.3 × 10^ -5 in standard notation
1 answer:
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If 
, then
and
.
Then
.
Since![\theta \in (-\pi,\pi]](https://tex.z-dn.net/?f=%5Ctheta%20%5Cin%20%28-%5Cpi%2C%5Cpi%5D)
, you can conclude that 
.
The triginometric form of z is
.
Use formula![\sqrt[3]{z} =\{ \sqrt[3]{|z|} (cos \frac{\theta+2\pi k}{n}+isin \frac{\theta+2\pi k}{n} ), k=0,1,2\}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7Bz%7D%20%3D%5C%7B%20%5Csqrt%5B3%5D%7B%7Cz%7C%7D%20%28cos%20%5Cfrac%7B%5Ctheta%2B2%5Cpi%20%0Ak%7D%7Bn%7D%2Bisin%20%5Cfrac%7B%5Ctheta%2B2%5Cpi%20k%7D%7Bn%7D%20%29%2C%20k%3D0%2C1%2C2%5C%7D)
to find cube
root.
For k=0,![z_1= \sqrt[3]{2} (cos \frac{ \frac{2\pi}{3} }{3} +isin\frac{ \frac{2\pi}{3} }{3})= \sqrt[3]{2} (cos 40^0+isin 40^0)](https://tex.z-dn.net/?f=z_1%3D%20%5Csqrt%5B3%5D%7B2%7D%20%28cos%20%5Cfrac%7B%20%0A%5Cfrac%7B2%5Cpi%7D%7B3%7D%20%7D%7B3%7D%20%2Bisin%5Cfrac%7B%20%5Cfrac%7B2%5Cpi%7D%7B3%7D%20%7D%7B3%7D%29%3D%20%5Csqrt%5B3%5D%7B2%7D%20%28cos%20%0A40%5E0%2Bisin%2040%5E0%29)
,
For k=1,![z_1= \sqrt[3]{2} (cos \frac{ \frac{2\pi}{3}+2\pi }{3} +isin\frac{ \frac{2\pi}{3}+2\pi }{3})= \sqrt[3]{2} (cos 160^0+isin 160^0)](https://tex.z-dn.net/?f=z_1%3D%20%5Csqrt%5B3%5D%7B2%7D%20%28cos%0A%20%5Cfrac%7B%20%5Cfrac%7B2%5Cpi%7D%7B3%7D%2B2%5Cpi%20%7D%7B3%7D%20%2Bisin%5Cfrac%7B%20%5Cfrac%7B2%5Cpi%7D%7B3%7D%2B2%5Cpi%20%7D%7B3%7D%29%3D%20%0A%5Csqrt%5B3%5D%7B2%7D%20%28cos%20160%5E0%2Bisin%20160%5E0%29)
,
For k=2,![z_1= \sqrt[3]{2} (cos \frac{ \frac{2\pi}{3}+4\pi }{3} +isin\frac{ \frac{2\pi}{3}+4\pi }{3})= \sqrt[3]{2} (cos 280^0+isin 280^0)](https://tex.z-dn.net/?f=z_1%3D%20%5Csqrt%5B3%5D%7B2%7D%20%28cos%20%5Cfrac%7B%20%5Cfrac%7B2%5Cpi%7D%7B3%7D%2B4%5Cpi%20%7D%7B3%7D%20%2Bisin%5Cfrac%7B%20%0A%5Cfrac%7B2%5Cpi%7D%7B3%7D%2B4%5Cpi%20%7D%7B3%7D%29%3D%20%5Csqrt%5B3%5D%7B2%7D%20%28cos%20280%5E0%2Bisin%20280%5E0%29)
.
Answer: The correct choice is C.
Then
Since
The triginometric form of z is
Use formula
For k=0,
For k=1,
For k=2,
Answer: The correct choice is C.
Expression A decays at a rate of 5% every three months, while Expression B grows at a rate of 12% every four months and Expression A has an initial value of 624, while expression B has an initial value of 725 , Option B and E are the correct statements.
<h3>What is an Expression ?</h3>It is a mathematical statement tat consists of variables , constants and mathematical operators.
It is given that
The company's records show the sales of short boards decrease every three months as represented by expression A, where t is the number of years that the boards have been for sale.
The company's records show that the sales of long boards increase every four months as represented by expression B, where t is the number of years that the boards have been for sale.
From observing both the expression the initial value is when t = 0
when t = 0,
A = 624
B = 725
and so Expression A decays at a rate of 5% every three months, while expression B grows at a rate of 12% every four months and Expression A has an initial value of 624, while expression B has an initial value of 725 , Option B and E are the correct statements.
To know more about Expression
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