Answer:
<h2>3(cos 336 + i sin 336)</h2>
Step-by-step explanation:
Fifth root of 243 = 3,
Suppose r( cos Ф + i sinФ) is the fifth root of 243(cos 240 + i sin 240),
then r^5( cos Ф + i sin Ф )^5 = 243(cos 240 + i sin 240).
Equating equal parts and using de Moivre's theorem:
r^5 =243 and cos 5Ф + i sin 5Ф = cos 240 + i sin 240
r = 3 and 5Ф = 240 +360p so Ф = 48 + 72p
So Ф = 48, 120, 192, 264, 336 for 48 ≤ Ф < 360
So there are 5 distinct solutions given by:
3(cos 48 + i sin 48),
3(cos 120 + i sin 120),
3(cos 192 + i sin 192),
3(cos 264 + i sin 264),
3(cos 336 + i sin 336)
Answer:
a(n) = 1 + 7(n-1)
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
f(x) = 2ˣ + 1
-f(x) = -(2ˣ) − 1
First, let's find the y-intercept.
-f(0) = -(2⁰) − 1 = -2
Only C can be correct.
2.5x - 3 + 2x = 1.75x - 1.25x + 13
4.5x - 3 = 0.50x + 13
4.0x = 16
x = 4
Answer: 4
2. We'll assume those xs are in the numerator
(3/7)x - 1/4 + (3/7)x = (9/7)x - (3/7)x + 3/4 - 1
(6/7)x - 1/4 = (6/7)x - 1/4
0 = 0
That's always true.
Answer: Any x is a solution.
Check the picture below.
notice the composite is just,
a 5x2 rectangle.
a triangle(yellow) with a base of 2 and a height of 2.
a triangle(red) with a base of 6 and a height of 4.
get the area of each, sum them up, and that's the area of the composite.