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![\rightarrow z^4=-625\\\\\rightarrow z=(-625+0i)^{\frac{1}{4}}\\\\\rightarrow x+iy=(-625+0i)^{\frac{1}{4}}\\\\ x=r \cos A\\\\y=r \sin A\\\\r \cos A=-625\\\\ r \sin A=0\\\\x^2+y^2=625^{2}\\\\r^2=625^{2}\\\\|r|=625\\\\ \tan A=\frac{0}{-625}\\\\ \tan A=0\\\\ A=\pi\\\\\rightarrow z= [625(\cos (2k \pi+pi) +i \sin (2k\pi+ \pi)]^{\frac{1}{4}}\\\\k=0,1,2,3,4,....\\\\\rightarrow z=(625)^{\frac{1}{4}}[\cos \frac{(2k \pi+pi)}{4} +i \sin \frac{(2k\pi+ \pi)}{4}]](https://tex.z-dn.net/?f=%5Crightarrow%20z%5E4%3D-625%5C%5C%5C%5C%5Crightarrow%20z%3D%28-625%2B0i%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5C%5C%5C%5C%5Crightarrow%20x%2Biy%3D%28-625%2B0i%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5C%5C%5C%5C%20x%3Dr%20%5Ccos%20A%5C%5C%5C%5Cy%3Dr%20%5Csin%20A%5C%5C%5C%5Cr%20%5Ccos%20A%3D-625%5C%5C%5C%5C%20r%20%5Csin%20A%3D0%5C%5C%5C%5Cx%5E2%2By%5E2%3D625%5E%7B2%7D%5C%5C%5C%5Cr%5E2%3D625%5E%7B2%7D%5C%5C%5C%5C%7Cr%7C%3D625%5C%5C%5C%5C%20%5Ctan%20A%3D%5Cfrac%7B0%7D%7B-625%7D%5C%5C%5C%5C%20%5Ctan%20A%3D0%5C%5C%5C%5C%20A%3D%5Cpi%5C%5C%5C%5C%5Crightarrow%20z%3D%20%5B625%28%5Ccos%20%282k%20%5Cpi%2Bpi%29%20%2Bi%20%5Csin%20%282k%5Cpi%2B%20%5Cpi%29%5D%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5C%5C%5C%5Ck%3D0%2C1%2C2%2C3%2C4%2C....%5C%5C%5C%5C%5Crightarrow%20z%3D%28625%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5B%5Ccos%20%5Cfrac%7B%282k%20%5Cpi%2Bpi%29%7D%7B4%7D%20%2Bi%20%5Csin%20%5Cfrac%7B%282k%5Cpi%2B%20%5Cpi%29%7D%7B4%7D%5D%20)
![\rightarrow z_{0}=(625)^{\frac{1}{4}}[\cos \frac{pi}{4} +i \sin \frac{\pi)}{4}]\\\\\rightarrow z_{1}=(625)^{\frac{1}{4}}[\cos \frac{3\pi}{4} +i \sin \frac{3\pi}{4}]\\\\ \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]\\\\ \rightarrow z_{3}=(625)^{\frac{1}{4}}[\cos \frac{7\pi}{4} +i \sin \frac{7\pi}{4}]](https://tex.z-dn.net/?f=%5Crightarrow%20z_%7B0%7D%3D%28625%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5B%5Ccos%20%5Cfrac%7Bpi%7D%7B4%7D%20%2Bi%20%5Csin%20%5Cfrac%7B%5Cpi%29%7D%7B4%7D%5D%5C%5C%5C%5C%5Crightarrow%20z_%7B1%7D%3D%28625%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5B%5Ccos%20%5Cfrac%7B3%5Cpi%7D%7B4%7D%20%2Bi%20%5Csin%20%5Cfrac%7B3%5Cpi%7D%7B4%7D%5D%5C%5C%5C%5C%20%5Crightarrow%20z_%7B2%7D%3D%28625%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5B%5Ccos%20%5Cfrac%7B5%5Cpi%7D%7B4%7D%20%2Bi%20%5Csin%20%5Cfrac%7B5%5Cpi%7D%7B4%7D%5D%5C%5C%5C%5C%20%5Crightarrow%20z_%7B3%7D%3D%28625%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5B%5Ccos%20%5Cfrac%7B7%5Cpi%7D%7B4%7D%20%2Bi%20%5Csin%20%5Cfrac%7B7%5Cpi%7D%7B4%7D%5D)
Argument of Complex number
Z=x+iy , is given by
If, x>0, y>0, Angle lies in first Quadrant.
If, x<0, y>0, Angle lies in Second Quadrant.
If, x<0, y<0, Angle lies in third Quadrant.
If, x>0, y<0, Angle lies in fourth Quadrant.
We have to find those roots among four roots whose argument is between 270° and 360°.So, that root is
![\rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]](https://tex.z-dn.net/?f=%20%5Crightarrow%20z_%7B2%7D%3D%28625%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5B%5Ccos%20%5Cfrac%7B5%5Cpi%7D%7B4%7D%20%2Bi%20%5Csin%20%5Cfrac%7B5%5Cpi%7D%7B4%7D%5D)
H = -5t^2 +5t + 10
a) t = 0, h = 10 at time 0
b) h = (-5t + 10) ( t + 1)
c) put 0 in for the height and set each factor = to 0 and solve each
0 = (-5t + 10) and 0 = (t + 1)
solve each t = 2 and t = -1, so t = 2 sec is your solution
d) because a parabola is symmetric, the max will be half way between -1 and 2, at t = 1/2
h = -5(1/2)^2 +5(1/2) + 10
h = -5(1/4) + 5/2 +10
h = -5/4 + 5/2 + 10
h = -5/4 + 10/4 + 40/4
h = 45/4
Substituting for values of j:-
S5 = 2(1) + 2(2) + 2(3) + 2(4) + 2(5) = 2+4+6+8+10 = 30 answer
Answer:
x = -0.4
Step-by-step explanation:
Distribute the -2.5 throughout the equation.
-2.5(4x + 4) = -6
-2.5(4x) + -2.5(4) = -6
-10x - 10 = -6 -Add 10 to both sides
-10x = 4 -Divide both sides by -10
x = -0.4
Hope this helps you!
