Answer:
y=6.7
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
y+4=10.7
Step 2: Subtract 4 from both sides.
y+4−4=10.7−4
y=6.7
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)]
Answer:
the solution is (2, -6)
Step-by-step explanation:
Substitute the second equation into the first, replacing y in the first:
2x - (-4x+2) = 10
Simplifying, we get:
2x + 4x - 2 = 10, or:
6x = 12, which yields x = 2.
Substituting 2 for x in the second equation yields y = -4(2) + 2 = 0, or y = -6
Then the solution is (2, -6).
