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.)
Answer:
765 miles
Step-by-step explanation:
Find the rate (mph) and then multiply the result by 9 hours:
340 mi
------------- * 9 hrs = 765 miles
4 hrs
X = 12400
20/100 = 1/5
2480 x 5 = 12400
Answer:
$22.68
Step-by-step explanation:
Meal Price =$18
Sales tax =6%
Tip = 20%
Total Price of the Meal =$18 + (6% of 18)+ (20% of 18)
=$18 + (0.06 X 18)+ (0.2 X 18)
=18+1.08+3.6
=$22.68
The total price of Alyssa's meal is $22.68.
