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.)
a = 30
a = 16
-a² + 46a -480 = 0
(-a + 30) (a -16) = 0
(-a)(a) + (-a)(-16) + 30(a) + 30(-16) = 0
-a² + 16a + 30a -480 = 0
-a² + 46a - 480 = 0
(-a + 30) = 0 ; (a - 16) = 0
-a = -30 ; a = 16
a = 30
To check:
a = 30
-(30)² + 46(30) - 480 = 0
-900 + 1380 - 480 = 0
480 - 480 = 0
0 = 0
a = 16
-(16)² + 46(16) - 480 = 0
-256 + 736 - 480 = 0
480 - 480 = 0
0 = 0
-3(y + 5) + 3(2y + 6)
-3y - 15 + 6y + 18
3y + 3
Answer:
3y + 3
Hope this helps.
Answer:
She would be able to buy
4 Chicken Salads &
2 Egg Salads
Step-by-step explanation:
4x5=20
leaving 8 dollars
2x4=8
Answer:
<h2>10 weeks </h2>
Step-by-step explanation:
Step one:
given data
Ryan
number of baseball cards=150
number collected per week= 10
let the number of weeks be x
and the total be y
y=10x+150-----------------1
Sarah
number of baseball cards=200
number collected per week= 5
let the number of weeks be x
and the total be y
y=5x+200------------2
Step two:
Required
the number of weeks where both total will be the same
10x+150=5x+200
10x-5x=200-150
5x=50
divide both sides by 5
x=50/5
x=10 weeks
