<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:
Step-by-step explanation:
1. Add 19 to both sides.
2. Divide both sides by 2.
Answer:
yes
Step-by-step explanation:
It is because 9 divides into 54 and 63
Answer:
$98.33 was deposited in the account
Step-by-step explanation:
simple interest formula = (PRT)/100 ...where p is money, r is rate, t is time
using formula $17.70 = (P * 3% * 6)/100
P = 1770/18
P = $98.33
To find the area of the arena, you will need to find the areas of the rectangular spaces and the 2 semicircles. Because the formulas are given, I will just substitute in the values and show the work for finding the areas.
To find the perimeter, you will look at the distances of lines that take you around the space. Because two of these spaces are half circles, you will need to find the circumference of the full circle.
Also, the answers need to be given in meters, so all units given in centimeters will be divided by 100 to convert them to meters.
Perimeter:
C= 3.14 x 20 m
C = 62.8 meters
62.8 + 8 + 25 + 8 + 5 + 8 + 10 + 8 + 40= 174.8 meters for the Perimeter
Area:
A = 25 x 8
A = 200 square meters
A = 10 x 8
A = 80 square meters
A = 20 x 40
A = 800 square meters
A = 3.14 x 10^2
A = 314 square meters
Total Area: 314 + 800 + 80 + 200= 1394 square meters
