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RSB [31]
3 years ago
7

The long jump distance of four students are listed in the table below. How much farther did the student with the longest distanc

e jump than the student with the shortest distance.
Joe 6.25
Shakira 4.37
Jackson 5.85
Chelsey 4.20
Mathematics
1 answer:
Tamiku [17]3 years ago
3 0

Answer:

5.85

Step-by-step explanation:

how long she is gonna be jumping

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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

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e^(-jθ) = cosθ - jsinθ

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Simplifying, we have

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dividing through by 2 we have

sinθ = ¹/₂[e^jθ - e^(-jθ)]

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