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Anika [276]
3 years ago
5

Diane left a 15% tip for a meal that cost $44.

Mathematics
1 answer:
BlackZzzverrR [31]3 years ago
6 0

Answer:

the tip is $2.93

Step-by-step explanation:

44 divided by 15

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Match each complex number with its equivalent expression i^157 i^315 i^102 i^76
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Answers:

i^{157} = i\\\\i^{315} = -i\\\\i^{102} = -1\\\\i^{76} = 1\\\\

=====================================================

Explanation:

By definition, i = \sqrt{-1}

Squaring both sides gets us i^2 = -1

Then multiply both sides by i to get i^3 = -i

Repeat the last step and you should get i^4 = -i^2 = -(-1) = 1

---------------

Notice we have this pattern going on:

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Once we reach i^4, we start the process over again.

It repeats every 4 terms.

This means we'll divide the exponent over 4 and look at the remainder. We ignore the quotient completely.

157/4 = 39 remainder 1

That remainder 1 is the exponent of the simplified term

i^{157} = i^1 = i

---------------

Similarly,

315/4 = 78 remainder 3

So i^{315} = i^3 = -i

---------------

102/4 = 25 remainder 2

i^{102} = i^2 = -1

----------------

76/4 = 19 remainder 0

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Step-by-step explanation:

36÷4=9

4 0
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