Answer:
1) w₁=4 - i w₂= -4 + i
2) w₁= 3 - i w₂= -3 + i
3) w₁= 1 + 2i w₂= - 1 - 2i
4) w₁= 2- 3i w₂= -2 + 3i
5) w₁= 5 - 2i w₂= -5 + 2i
6) w₁= 5 - 3i w₂= -5 + 3i
Step-by-step explanation:
The root of a complex number is given by:
![\sqrt[n]{z}=\sqrt[n]{r}(Cos(\frac{\theta+2k\pi}{n}) + i Sin(\frac{\theta+2k\pi}{n}))](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bz%7D%3D%5Csqrt%5Bn%5D%7Br%7D%28Cos%28%5Cfrac%7B%5Ctheta%2B2k%5Cpi%7D%7Bn%7D%29%20%2B%20i%20Sin%28%5Cfrac%7B%5Ctheta%2B2k%5Cpi%7D%7Bn%7D%29%29)
where:
r: is the module of the complex number
θ: is the angle of the complex number to the positive axis x
n: index of the root
1) z = 15 − 8i ⇒ r=17 θ= -0.4899 rad
w₁=
=4-i
w₂=
=-1+i
2) z = 8 − 6i ⇒ r=10 θ= -0.6435 rad
w₁=
= 3 - i
w₂=
= -3 + i
3) z = −3 + 4i ⇒ r=5 θ= -0.9316 rad
w₁=
= 1 + 2i
w₂=
= -1 - 2i
4) z = −5 − 12i ⇒ r=13 θ= 0.4426 rad
w₁=
= 2- 3i
w₂=
= -2 + 3i
5) z = 21 − 20i ⇒ r=29 θ= -0.8098 rad
w₁=
= 5 - 2i
w₂=
= -5 + 2i
6) z = 16 − 30i ⇒ r=34 θ= -1.0808 rad
w₁=
= 5 - 3i
w₂=
= -5 + 3i
Answer: she would catch up with Tom in 1 hour.
Step-by-step explanation:
Let t represent the time it will take for Mary to catch up with Tom.
Tom leaves his boat from a dock and travels at a rate of 25 miles per hour.
Distance = speed × time
Distance travelled by Tom in t hours is
25 × t = 25t
Ten minutes later, Mary leaves the same dock in her speedboat and heads after Tom. Converting 10 minutes to hours, it becomes 10/60 hour
Time spent by Mary is (t - 10/60) hours. If she travels at a rate of 30 miles per hour, it means that the distance that she would travel in
(t - 10/60) hours is
30(t - 10/60)
= 30t - 5
By the time she catches up with Tom, they would have covered the same distance. It means that
25t = 30t - 5
30t - 25t = 5
5t = 5
t = 5/5 = 1 hour
M(x)=−(x−5) 2 +25m, left parenthesis, x, right parenthesis, equals, minus, left parenthesis, x, minus, 5, right parenthesis, squ
Aleksandr [31]
Answer:
25
Step-by-step explanation:
Given the function that represents the amount of mosquitoes as;
M(x) = -(x-5)² + 25
To get the maximum mosquitoes possible, we need to first find x;
At the maximum dM/dx = 0
dM//dx = -2(x-5)
0 = -2(x-5)
-2(x-5) = 0
-2x + 10 = 0
-2x = -10
x = 10/2
x = 5
Substitute x = 5 into the function;
M(5) = −(5−5)² +25
M(5) = 0+25
M(5) = 25
Hence the maximum number of mosquitoes is 25
12, 20, 16, 10, 17, 9, 23, 13
1. add them all up
=120
divide by the number of numbers
120/8
=15
15 is the MAD
