100%-26%=74%
x=the original price
=
=
627=x
The original price was $627.
Option( d ) is the correct one.
Answer:
See below for all the cube roots
Step-by-step explanation:
<u>DeMoivre's Theorem</u>
Let 
be a complex number in polar form, where 
is an integer and 
. If 
, then 
.
<u>Nth Root of a Complex Number</u>
If is any positive integer, the nth roots of 
are given by ![\sqrt[n]{rcis\theta}=(rcis\theta)^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Brcis%5Ctheta%7D%3D%28rcis%5Ctheta%29%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
where the nth roots are found with the formulas:
![\sqrt[n]{r}\biggr[cis(\frac{\theta+360^\circ k}{n})\biggr]](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Br%7D%5Cbiggr%5Bcis%28%5Cfrac%7B%5Ctheta%2B360%5E%5Ccirc%20k%7D%7Bn%7D%29%5Cbiggr%5D)
for degrees (the one applicable to this problem)![\sqrt[n]{r}\biggr[cis(\frac{\theta+2\pi k}{n})\biggr]](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Br%7D%5Cbiggr%5Bcis%28%5Cfrac%7B%5Ctheta%2B2%5Cpi%20k%7D%7Bn%7D%29%5Cbiggr%5D)
for radians
for 
<u>Calculation</u>
<u />![z=27(cos330^\circ+isin330^\circ)\\\\\sqrt[3]{z} =\sqrt[3]{27(cos330^\circ+isin330^\circ)}\\\\z^{\frac{1}{3}} =(27(cos330^\circ+isin330^\circ))^{\frac{1}{3}}\\\\z^{\frac{1}{3}} =27^{\frac{1}{3}}(cos(\frac{1}{3}\cdot330^\circ)+isin(\frac{1}{3}\cdot330^\circ))\\\\z^{\frac{1}{3}} =3(cos110^\circ+isin110^\circ)](https://tex.z-dn.net/?f=z%3D27%28cos330%5E%5Ccirc%2Bisin330%5E%5Ccirc%29%5C%5C%5C%5C%5Csqrt%5B3%5D%7Bz%7D%20%3D%5Csqrt%5B3%5D%7B27%28cos330%5E%5Ccirc%2Bisin330%5E%5Ccirc%29%7D%5C%5C%5C%5Cz%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%20%3D%2827%28cos330%5E%5Ccirc%2Bisin330%5E%5Ccirc%29%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5C%5C%5C%5Cz%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%20%3D27%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%28cos%28%5Cfrac%7B1%7D%7B3%7D%5Ccdot330%5E%5Ccirc%29%2Bisin%28%5Cfrac%7B1%7D%7B3%7D%5Ccdot330%5E%5Ccirc%29%29%5C%5C%5C%5Cz%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%20%3D3%28cos110%5E%5Ccirc%2Bisin110%5E%5Ccirc%29)
<u>First cube root where k=2</u>
<u />![\sqrt[3]{27}\biggr[cis(\frac{330^\circ+360^\circ(2)}{3})\biggr]\\3\biggr[cis(\frac{330^\circ+720^\circ}{3})\biggr]\\3\biggr[cis(\frac{1050^\circ}{3})\biggr]\\3\biggr[cis(350^\circ)\biggr]\\3\biggr[cos(350^\circ)+isin(350^\circ)\biggr]](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27%7D%5Cbiggr%5Bcis%28%5Cfrac%7B330%5E%5Ccirc%2B360%5E%5Ccirc%282%29%7D%7B3%7D%29%5Cbiggr%5D%5C%5C3%5Cbiggr%5Bcis%28%5Cfrac%7B330%5E%5Ccirc%2B720%5E%5Ccirc%7D%7B3%7D%29%5Cbiggr%5D%5C%5C3%5Cbiggr%5Bcis%28%5Cfrac%7B1050%5E%5Ccirc%7D%7B3%7D%29%5Cbiggr%5D%5C%5C3%5Cbiggr%5Bcis%28350%5E%5Ccirc%29%5Cbiggr%5D%5C%5C3%5Cbiggr%5Bcos%28350%5E%5Ccirc%29%2Bisin%28350%5E%5Ccirc%29%5Cbiggr%5D)
<u>Second cube root where k=1</u>
![\sqrt[3]{27}\biggr[cis(\frac{330^\circ+360^\circ(1)}{3})\biggr]\\3\biggr[cis(\frac{330^\circ+360^\circ}{3})\biggr]\\3\biggr[cis(\frac{690^\circ}{3})\biggr]\\3\biggr[cis(230^\circ)\biggr]\\3\biggr[cos(230^\circ)+isin(230^\circ)\biggr]](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27%7D%5Cbiggr%5Bcis%28%5Cfrac%7B330%5E%5Ccirc%2B360%5E%5Ccirc%281%29%7D%7B3%7D%29%5Cbiggr%5D%5C%5C3%5Cbiggr%5Bcis%28%5Cfrac%7B330%5E%5Ccirc%2B360%5E%5Ccirc%7D%7B3%7D%29%5Cbiggr%5D%5C%5C3%5Cbiggr%5Bcis%28%5Cfrac%7B690%5E%5Ccirc%7D%7B3%7D%29%5Cbiggr%5D%5C%5C3%5Cbiggr%5Bcis%28230%5E%5Ccirc%29%5Cbiggr%5D%5C%5C3%5Cbiggr%5Bcos%28230%5E%5Ccirc%29%2Bisin%28230%5E%5Ccirc%29%5Cbiggr%5D)
<u>Third cube root where k=0</u>
<u />![\sqrt[3]{27}\biggr[cis(\frac{330^\circ+360^\circ(0)}{3})\biggr]\\3\biggr[cis(\frac{330^\circ}{3})\biggr]\\3\biggr[cis(110^\circ)\biggr]\\3\biggr[cos(110^\circ)+isin(110^\circ)\biggr]](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27%7D%5Cbiggr%5Bcis%28%5Cfrac%7B330%5E%5Ccirc%2B360%5E%5Ccirc%280%29%7D%7B3%7D%29%5Cbiggr%5D%5C%5C3%5Cbiggr%5Bcis%28%5Cfrac%7B330%5E%5Ccirc%7D%7B3%7D%29%5Cbiggr%5D%5C%5C3%5Cbiggr%5Bcis%28110%5E%5Ccirc%29%5Cbiggr%5D%5C%5C3%5Cbiggr%5Bcos%28110%5E%5Ccirc%29%2Bisin%28110%5E%5Ccirc%29%5Cbiggr%5D)
I'll be honest, this is a pretty interesting question. I've never seen anything like it before!
We can start off by making equations with the given. If there are 100 heads, that means that the total number of chickens and pigs combined is 100. Thus, we can form our first equation:
p + c = 100
('p' represents number of pigs, and 'c' represents number of chickens)
We also know that there are 270 legs total. Since chickens have 2 and pigs have 4, we can make the following equation:
2c + 4p = 270
I suppose the quickest way to solve for this equation is to use the subtraction method. Put the equations on top of each other:
2c + 4p = 270
c + p = 100
___________
Multiply the bottom equation by -2;
2c + 4p = 270
-2c -2p = 100
____________
"Add" these two equations together:
2c + 4p = 270
-2c -2p = -200
___________
2p = 70
Divide both sides by 2:
p = 35
Ah, finally. Now that we know that there are 35 pigs, input this variable into the first equation to find the number of chickens:
c + 35 = 100
Subtract:
c = 65
There are 35 pigs and 65 chickens
-T.B.
18 wrist bands and 12 belts.
You can solve this using the following system of equations.
x + y = 30
5.5x + 8.75y = 204
