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:
The velocities after 739 s of firing of each engine would be 6642.81 m/s in the x direction and 5306.02 in the y direction
Step-by-step explanation:
- For a constant acceleration:
, where
is the final velocity in a direction after the acceleration is applied,
is the initial velocity in that direction before the acceleration is applied, a is the acceleration applied in such direction, and t is the amount of time during where that acceleration was applied. - <em>Then for the x direction</em> it is known that the initial velocity is
5320 m/s, the acceleration (the applied by the engine) in x direction is
1.79 m/s2 and, the time during the acceleration was applied (the time during the engines were fired) of the is 739 s. Then: 
- In the same fashion, <em>for the y direction</em>, the initial velocity is
0 m/s, the acceleration in y direction is
7.18 m/s2, and the time is the same that in the x direction, 739 s, then for the final velocity in the y direction: 
Answer:x= -54.7
Step-by-step explanation:
-66.5-66.5= -133+ 78.3= -54.7
The total cost if x passengers booked reclining seats and one fifths y passengers booked twin-sharing rooms is (197x + 98y) dollars
<em><u>Solution:</u></em>
Given that,
Cost for reclining seat = $ 197
Cost for twin sharing room = $ 490
We have to find the cost if x passengers booked reclining seats and one fifths y passengers booked twin-sharing rooms
<em><u>Cost for reclining room when "x" passengers booked is:</u></em>
Cost for reclining room = $ 197x
<em><u>Cost when One fifths y passengers booked twin-sharing rooms</u></em>
Cost for twin sharing room = 
Cost for twin sharing room = 98y
<em><u>Total cost is given as:</u></em>
Total cost = Cost for reclining room "x" passengers + Cost for twin sharing room for one fifths y passengers

Thus total cost is (197x + 98y) dollars