The middle row is long on one side and short in the other side which is the shape of a rectangle.
The net is a rectangular prism
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: 12/4 or 3
Step-by-step explanation: Switch the numerator and denominator. This should leave you with the answer above.
<h3>
Answers: x = -17 and x = 64</h3>
====================================================
Explanation
Consider three scenarios:
- A) The value of x is the smallest of the set (aka the min)
- B) The value of x is the largest of the set (aka the max)
- C) The value of x is neither the min, nor the max. So 8 < x < 39.
These scenarios cover all the possible cases of what x could be. It's either the min, the max, or somewhere in between the min and max.
--------------------
We'll start with scenario A.
If x is the min, then that must mean 39 is the max as it's the largest of the set {18, 36, 16, 39, 27, 8, 34}
The range is 56, so,
range = max - min
56 = 39 - x
56+x= 39
x = 39-56
x = -17 which is one possible answer
--------------------
If instead we go with scenario B, then x is the max and 8 is the min
range = max - min
56 = x - 8
56+8 = x
64 = x
x = 64 is the other possible answer
--------------------
Lastly, let's consider scenario C. If x is not the min or the max, then it's somewhere between the min 8 and max 39. in short, 8 < x < 39.
Note that range = max - min = 39-8 = 31 which is not the range of 56 that we want. So there's no way scenario C can be possible here.
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