<span>use De Moivre's Theorem:
⁵√[243(cos 260° + i sin 260°)] = [243(cos 260° + i sin 260°)]^(1/5)
= 243^(1/5) (cos (260 / 5)° + i sin (260 / 5)°)
= 3 (cos 52° + i sin 52°)
z1 = 3 (cos 52° + i sin 52°) ←← so that's the first root
there are 5 roots so the angle between each root is 360/5 = 72°
then the other four roots are:
z2 = 3 (cos (52 + 72)° + i sin (52+ 72)°) = 3 (cos 124° + i sin 124°)
z3 = 3 (cos (124 + 72)° + i sin (124 + 72)°) = 3 (cos 196° + i sin 196°)
z4 = 3 (cos (196 + 72)² + i sin (196 + 72)°) = 3 (cos 268° + i sin 268°)
z5 = 3 (cos (268 + 72)° + i sin (268 + 72)°) = 3 (cos 340° + i sin 340°) </span>
Answer:
4
Step-by-step explanation:
When using the slope equation (y2-y1/x2-x1) you get 12/3 which when divided out equals 4.
The binomial expansion:
a = 2y, b = 4 x^3, n = 4
( x )^3k = x^ 9
k = 3
Answer: the coefficient is
512.
Answer:
s = 3
Step-by-step explanation:
we know the rectangles are similar
2 × __ = 16
s × __ = 24
so,
16÷2 = 8
2 × 8 =16
s × 8 =24
then,
24 ÷ 8 = s
3 = s
2 × 8 = 16
3 × 8 =24
hoped i helped :)
Answer:
4th option
Step-by-step explanation:
The relationship is linear,
putting the value of x in the right side of the equation of option 4, you'll get the value of the left side
putting, x=1
y+4=-1/2(x-1)
y=-1/2(1-1)-4
y=-4
putting, x=7
y+4=-1/2(7-1)
y=-1/2(6)-4
y=-6/2-4
y=-3-4
y=-7
