Step-by-step explanation:
z
3
=8(cos216
∘
+isin216
∘
)
z^3=2^3(\cos(6^3)^\circ+i\sin(6^3)^\circ)z
3
=2
3
(cos(6
3
)
∘
+isin(6
3
)
∘
)
\implies z=8^{1/3}\left(\cos\left(\dfrac{216+360k}3\right)^\circ+i\sin\left(\dfrac{216+360k}3\right)^\circ\right)⟹z=8
1/3
(cos(
3
216+360k
)
∘
+isin(
3
216+360k
)
∘
)
where k=0,1,2k=0,1,2 . So the third roots are
\begin{gathered}z=\begin{cases}2(\cos72^\circ+i\sin72^\circ)\\2(\cos192^\circ+i\sin192^\circ)\\2(\cos312^\circ+i\sin312^\circ)\end{cases}\end{gathered}
z=
⎩
⎪
⎪
⎨
⎪
⎪
⎧
2(cos72
∘
+isin72
∘
)
2(cos192
∘
+isin192
∘
)
2(cos312
∘
+isin312
∘
)
Answer:
The common difference of the progression is 3.
Step-by-step explanation:
Given:
First term of the AP = (a) = -8
Ratio of 7th and 9th term = 5:8
So,
General term of an AP, Tn= a+(n-1)d
Where 'd' is the common difference.
equation...(i)
equation...(ii)
According to the question.
⇒ ...cross-multiplying the terms.
⇒
⇒
⇒ ...subtracting 40d and adding 64 both sides.
⇒
⇒ ...dividing both sides with 3.
So the common difference of the progression is 'd' = 3.
Answer:
-1.540
Step-by-step explanation:
H0 : μ = 18
H0 : μ ≠ 18
The sample size, n = 48
Sample mean, xbar = 17
Sample standard deviation, s = 4.5
α = 0.05
The test statistic :
(xbar - μ) ÷ (s/√(n))
(17 - 18) ÷ (4.5 / √48))
-1 ÷ 0.6495190
= -1.5396
= -1.540 (3 decimal places ).