No because the laws of energy state that an equal force is being applied oppositely and also think about the friction of air and the inertia can only get so great as the speed is
Number 3 is .4 i think just minus 1.2 - .8
General formula for n-th term of arithmetical progression is
a(n)=a(1)+d(n-1).
For 3d term we have
a(3)=a(1) +d(3-1), where a(3)=7
7=a(1)+2d
For 7th term we have
a(7)=a(1) +d(7-1)
a(7)=a(1) + 6d
Also, we have that the <span>seventh term is 2 more than 3 times the third term,
a(7)=3*a(3)+2= 3*7+2=21+2=23
So we have, </span>a(7)=a(1) + 6d and a(7)=23. We can write
23=a(1) + 6d.
Now we can write a system of equations
23=a(1) + 6d
<span> - (7=a(1)+2d)
</span>16 = 4d
d=4,
7=a(1)+2d
7=a(1)+2*4
a(1)=7-8=-1
a(1)= - 1
First term a(1)=-1, common difference d=4.
Sum of the 20 first terms is
S=20 * (a(1)+a(20))/2
a(1)=-1
a(n)=a(1)+d(n-1)
a(20) = -1+4(20-1)=-1+4*19=75
S=20 * (-1+75)/2=74*10=740
Sum of 20 first terms is 740.
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)
