I need the value of x
2 answers:
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Answer:
- modulus: 3√2
- argument: -3π/4 (or 5π/4)
Step-by-step explanation:
The modulus is the magnitude of the complex number; the argument is its angle (usually in radians).
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<h3>rectangular form</h3>The complex number can be cleared from the denominator by multiplying numerator and denominator by its conjugate:
The magnitude of this number is the root of the sum of the squares of the real and imaginary parts:
modulus = √((-3)² +(-3)²) = 3√2
The argument is the arctangent of the ratio of the imaginary part to the real part, taking quadrant into consideration.
arg = arctan(-3/-3) = -3π/4 or 5π/4 . . . . radians
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modulus∠argument = (3√2)∠(-3π/4)
Answer:
x = {40, 80}
Step-by-step explanation:
The profit equation is ...
P = R - C = 100x -0.5x^2 -(40x +800)
P = -0.5x^2 +60x -800
We want to find values of x such that P = 800
800 = -0.5x^2 +60x -800
1600 = -0.5x^2 +60x . . . . add 800
-3200 = x^2 -120x . . . . . . . multiply by -2
400 = x^2 -120x +3600 . . . . add 3600 to complete the square
400 = (x -60)^2 . . . . . . write as a square
±20 = x -60 . . . . . . . . . take the square root
x = 60 ± 20 = {40, 80}
The values of production level (x) that will create profit of $800 are 40 and 80 units.
