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:
You can use Gaussian Elimination.
Double both sides of the first equation and add the second equation.
6x + 4y = 8
5x - 4y = 3
---------------
11x = 11
x = 1
5 - 4y = 3
-4y = -2
y = 1/2
Step-by-step explanation:
Answer:
250 cookies
Step-by-step explanation:
The employee burns 55 chocolate chip cookies
if this represented 22% of the days production
Let x = the total production of cookies for the day
how many cookies did you plan on producing that day?
22% of x = 55
22 / 100 * x = 55
0.22x = 55
Divide both sides by 0.22
x = 55 / 0.22
= 250
x = 250 cookies
Therefore, the total production of cookies for the day is 250

and

This means that Kayle found 10 eggs while Kevin found 5 eggs.
so 20-(10+5)= 5 eggs left.
To find the fraction, divide the number of eggs left over the number of total eggs.

Hope this helps!