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Dafna1 [17]
3 years ago
12

WILL MARK BRAINLIEST!!! Find the fifth roots of 243(cos 240° + i sin 240°).

Mathematics
1 answer:
Snowcat [4.5K]3 years ago
6 0

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)

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17. surface area ≈ 441.84

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19. volume of the smaller solid = 339 yards³

Step-by-step explanation:

17 .

To find the surface area of the sphere we have to find the radius of the sphere first.

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18

If two figure or solid are similar with scale factor or ratio of x/y then the ratio of their volume is (x/y)³. If the ratio of of two similar prism is 2 : 3 the volume will be (2/3)³ = 8/27 .

19

If two solids are similar then the ratio of their surface area is the squared of the scale factor.

121/361 = (x/y)²

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x/y = 11/19

If two solids are similar then the ratio of their volume is the cube of the scale factor.

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1331/6859  = a/1747

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6859a = 2325257

divide both sides by 6859

a = 2325257/6859

a = 339.008164455

a ≈ 339 yards³

volume of the smaller solid ≈ 339 yards³

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