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3 years ago

Aubrey's dinner cost $85. She tips the waitstaff 30 percent for excellent service. How much does aubrey tip the waitstaff

Mathematics

2 answers:

vovangra [49]3 years ago

6 0

$25.50 thats how much she tip the waitstaff.

Papessa [141]3 years ago

4 0

Total cost for Aubrey's dinner = $85

The percent she tips the waitstaff = 30%

we have to determine the amount which Aubrey tip the waitstaff.

The amount she tips the waitstaff = $30\%$ of Dinner cost

= 30% of $85

= $\frac{30}{100} \times 85$

= $\frac{2550}{100}$

= $25.5

Therefore, Aubrey tips $25.5 to the waitstaff.

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What is the correct justification for the indicated steps?

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

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<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;

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