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ANTONII [103]
3 years ago
5

The dimensions of an Olympic-sized swimming pool are 50 m long, 25 m wide, and the water is 2 m deep. What is the volume of wate

r?
Mathematics
2 answers:
il63 [147K]3 years ago
6 0
50 x 25 x 2=2500 cubic meters

aliina [53]3 years ago
5 0

Answer:

2500 m

Step-by-step explanation:

Mulitply 50, 25, and 2!

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Help me please I dont get it
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x>10

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Suppose $P$ is the point $(5,3)$ and $Q$ is the point $(-3,6)$. Find point $T$ such that $Q$ is the midpoint of segment $\overli
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(1,4.5)

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3 years ago
Find the constant of variation k for the direct variation 4x = -y
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3 years ago
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What is the correct justification for the indicated steps?
yanalaym [24]

The given proof of De Moivre's theorem is related to the operations of

complex numbers.

<h3>The Correct Responses;</h3>
  • Step A: Laws of indices
  • Step C: Expanding and collecting like terms
  • Step D: Trigonometric formula for the cosine and sine of the sum of two numbers

<h3>Reasons that make the above selection correct;</h3>

The given proof is presented as follows;

\mathbf{\left[cos(\theta) + i \cdot sin(\theta) \right]^{k + 1}}

  • Step A: By laws of indices, we have;

\left[cos(\theta) + i \cdot sin(\theta) \right]^{k + 1} = \mathbf{\left[cos(\theta) + i \cdot sin(\theta) \right]^{k} \cdot \left[cos(\theta) + i \cdot sin(\theta) \right]}

\left[cos(\theta) + i \cdot sin(\theta) \right]^{k} \cdot \left[cos(\theta) + i \cdot sin(\theta) \right] =  \mathbf{\left[cos(k \cdot \theta) + i \cdot sin(k \cdot \theta) \right] \cdot \left[cos(\theta) + i \cdot sin(\theta) \right]}

  • Step B: By expanding, we have;

\left[cos(k \cdot \theta) + i \cdot sin(k \cdot \theta) \right] \cdot \left[cos(\theta) + i \cdot sin(\theta) \right] = cos(k \cdot \theta) \cdot cos(\theta) - sin(k \cdot \theta) \cdot sin(\theta) + i  \cdot \left [sin(k \cdot \theta) \cdot cos(\theta) + cos(k \cdot \theta) \cdot sin(\theta) \right]

  • Step D: From trigonometric addition formula, we have;

cos(A + B) = cos(A)·cos(B) - sin(A)·sin(B)

sin(A + B) = sin(A)·cos(B) + sin(B)·cos(A)

Therefore;

cos(k \cdot \theta) \cdot cos(\theta) - sin(k \cdot \theta) \cdot sin(\theta) + i  \cdot \left [sin(k \cdot \theta) \cdot cos(\theta) + cos(k \cdot \theta) \cdot sin(\theta) \right] = \mathbf{ cos(k \cdot \theta + \theta) + i \cdot sin(k \cdot \theta  + \theta)}

Learn more about  complex numbers here:

brainly.com/question/11000934

4 0
2 years ago
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