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:
Perimetro = 4 cm + 7 cm + 12 cm
= 23 cm
Step-by-step explanation:
Answer:
Equation 0.5 + 1.75(x) = 4
x = 2movies
Step-by-step explanation:
Given that,
movie night will last for 4 hours
each movie take 1.75 hours
time for eating popcorn 0.5 hours
To find,
number of movies which can be watched
<h2>Equation</h2><h2>0.5 + 1.75(x) = 4</h2><h2>Solve for x</h2><h3>1.75(x) = 4 - 0.5</h3><h3>1.75(x) = 3.5</h3><h3>x = 3.5/1.75</h3><h3>x = 2 </h3>
So, total number of movies which could be watched in 4hr = 2
<h3 /><h3 /><h3 /><h3 /><h3 /><h3 /><h3 />
In circle O, RT and SU are diameters. mArc R V = mArc V U = 64°. Thus, option C is correct.
Given that:
mArc R V = mArc V U,
Angle S O R = 13 x degrees
Angle T O U = 15 x - 8 degrees
<h3>How to calculate the angle TOU ?</h3>
∠SOR = ∠TOU (Vertically opposite angles are equal).
Therefore:
13 x = 15x - 8
Subtracting 13x from both sides
13x - 13x = 15x - 8 - 13x
0 = 15x - 13x - 8
2x - 8 = 0
Adding 8 to both sides:
2x - 8 + 8 = 0 + 8
2x = 8
2x/2 = 8/2
x = 4
∠SOR = 13x
= 13(4)
= 52°
∠TOU = 15x - 8
= 15(4) - 8
= 60 - 8
= 52°
Let a = mArc R V = mArc V U
Therefore:
mArc R V + mArc V U + ∠TOU = 180 (sum of angles on a straight line)
Substituting:
a + a + 52 = 180
2a = 180-52
2a = 128
a = 128/2
a= 64°
mArc R V = mArc V U = 64°
In circle O, RT and SU are diameters. mArc R V = mArc V U = 64°. Thus, option C is correct.
Learn more about angles here:
brainly.com/question/2882938
#SPJ1
Answer:
The maximum value of a function is the place where a function reaches its highest point, or vertex, on a graph.
I hope it helps.
