9514 1404 393
Answer:
2√30 ∠-120°
Step-by-step explanation:
The modulus is ...
√((-√30)² +(-3√10)²) = √(30 +90) = √120 = 2√30
The argument is ...
arctan(-3√10/-√30) = arctan(√3) = -120° . . . . a 3rd-quadrant angle
The polar form of the number can be written as ...
(2√30)∠-120°
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<em>Additional comments</em>
Any of a number of other formats can be used, including ...
(2√30)cis(-120°)
(2√30; -120°)
(2√30; -2π/3)
2√30·e^(i4π/3)
Of course, the angle -120° (-2π/3 radians) is the same as 240° (4π/3 radians).
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At least one app I use differentiates between (x, y) and (r; θ) by the use of a semicolon to separate the modulus and argument of polar form coordinates. I find that useful, as a pair of numbers (10.95, 4.19) by itself does not convey the fact that it represents polar coordinates. As you may have guessed, my personal preference is for the notation 10.95∠4.19. (The lack of a ° symbol indicates the angle is in radians.)
You did not include the problem therefore i cannot help you with this but if you could message me the problem i’d be happy too
Answer:
X = 30°, y = 15° and z = 150°.
Reason: Look below.
Step-by-step explanation:
Hey there!
When we look into the figure, we find that;
For x:
x+ 2x + 90° = 180° {Being linear pair}
or, 3x = 180°-90°
or, 3x = 90°
or, x= 90°/3
<u>Therefore, X = 30°.</u>
For y :
2y = x = 30° {Alternate angles are equal}
or, 2y = 30°
y = 30°/2
<u>Therefore, y = </u><u>1</u><u>5</u><u>°</u>
For z:
2y + z = 180° { Being linear pair}
or, 30°+z = 180°
or, z = 180°-30°
or, z = 150°
<u>Therefore, z = 150°.</u>
<em><u>Hope</u></em><em><u> </u></em><em><u>it</u></em><em><u> helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>
