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user100 [1]
3 years ago
12

Liem is 6 feet 2 inches, Eli is 5 feet 9 inches, Faith is 6 feet, and Simon is 5 feet 4 inches. In yards, what is the total of t

heir heights?
Mathematics
1 answer:
Oksi-84 [34.3K]3 years ago
7 0
<span>First step is find total height of all the figures expressed in feet: Liem: 6 ft 2 inch = 6,167 ft Eli: 5 ft 9 inch = 5,75 ft Faith 6 ft Simon: 5 ft 4 inch = 5,34 ft To calculate the total height we need to know that 12 inches are 1 foot 6’2”+5’9”+6+5’4”= 22 ft 15 inch = 23 ft 3 inch Another way is by adding decimal figurel: 6,167 + 5,75 + 6 + 5,34 = 23,25 feet Then we know that 3 feet are 1 yard, so then total height is: 23,25 / 3 = 7,75 yards</span>
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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:

i^0 = 1\\\\i^1 = i\\\\i^2 = -1\\\\i^3 = -i\\\\i^4 = 1\\\\

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

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Similarly,

315/4 = 78 remainder 3

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

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102/4 = 25 remainder 2

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

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

76/4 = 19 remainder 0

i^{76} = i^0 = 1

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