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Andrew [12]
3 years ago
14

Which of the following is not a rigid motion

Mathematics
1 answer:
77julia77 [94]3 years ago
7 0
Dilation is not a rigid motion.
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Using Euler's relation, derive the following relationships:a. Cosθ=½(e^jθ+e^−jθ)b. Sinθ=½(e^jθ−e(^−jθ)
Montano1993 [528]

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)]

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If y = kx, where k is a constant,<br> and y = 30 when x = 6, what is<br> the value of y when x = 3?
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Answer:

Step-by-step explanation:

Actually it's 11 because 11 is technically the same when added to constant of x =6 = 11

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Shannon has 1 nickel, 2 dimes, and 5 unknown coins totaling $0.81. What kind of coins does Shannon have and how many are there o
AlekseyPX

Answer:

The 5 unknown are 1 quarter, 3 dimes, and 1 penny.

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30 Points!!! Please help!! Will give Brainliest!! Please...
AlekseyPX

Answer:

11

Step-by-step explanation:

Opposite sides are congruent at parallelograms. So x+16 must be equal to 2x+5. Solve the equation;

2x+5 = x+16

x = 11 .

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