Answer:
6 5/10
Step-by-step explanation:
De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.
For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes
[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))]
it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.
For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)
[2^6(cos(40*6))+isin(40*6)],
[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)
And the answer is -32 -32 √3 i
Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i
The unknown number . . . . . (z)
The sum of the unknown number and 22 . . . . . (z + 22)
The sum of the unknown number and 22
divided by the same unknown number . . . . . . . (z + 22) / z
You said that quotient is 12. (z + 22) / z = 12
Multiply each side by 'z' : (z + 22) = 12 z
Subtract 'z' from each side: 22 = 11 z
Divide each side by 11 : 2 = z .
Here they are:
36,16,81,64
Answer:
73.3%
Step-by-step explanation:
We can express 44 out of 60 as 44/60. Since the fraction viniculum means division, this reaches 44 divided by 60.
In doing so, we achieve the answer 73.33333.... terminating.
Rounding to the nearest place gives 73.3 as our answer.
