Answer:
a. cosθ = ¹/₂[e^jθ + e^(-jθ)] b. sinθ = ¹/₂[e^jθ - e^(-jθ)]
Step-by-step explanation:
a.We know that
e^jθ = cosθ + jsinθ and
e^(-jθ) = cosθ - jsinθ
Adding both equations, we have
e^jθ = cosθ + jsinθ
+
e^(-jθ) = cosθ - jsinθ
e^jθ + e^(-jθ) = cosθ + cosθ + jsinθ - jsinθ
Simplifying, we have
e^jθ + e^(-jθ) = 2cosθ
dividing through by 2 we have
cosθ = ¹/₂[e^jθ + e^(-jθ)]
b. We know that
e^jθ = cosθ + jsinθ and
e^(-jθ) = cosθ - jsinθ
Subtracting both equations, we have
e^jθ = cosθ + jsinθ
-
e^(-jθ) = cosθ - jsinθ
e^jθ + e^(-jθ) = cosθ - cosθ + jsinθ - (-jsinθ)
Simplifying, we have
e^jθ - e^(-jθ) = 2jsinθ
dividing through by 2 we have
sinθ = ¹/₂[e^jθ - e^(-jθ)]
4/5n – 1/5 = 2/5n
Add 1/5 to both sides
4/5n = 2/5n + 1/5
Subtract 2/5n from both sides
2/5n = 1/5
Divide both sides by 2/5
n = 1/2
Answer:
expected profit is - $0.50
Step-by-step explanation:
1 $(7.00) 0.166666667 $(1.17)
2 $(7.00) 0.166666667 $(1.17)
3 $1.00 0.166666667 $0.17
4 $1.00 0.166666667 $0.17
5 $1.00 0.166666667 $0.17
6 $8.00 0.166666667 $1.33
$(0.50)
The domain of the function f(x) is where the area under the square root (aka the radicand) is positive or zero. We have to write that the radicand is greater than or equal to zero, so
.
C
