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frutty [35]
3 years ago
14

Suppose you bought a pizza for $8.00. You also bought a salad, but you cannot remember how

Mathematics
2 answers:
Fittoniya [83]3 years ago
6 0
8+s=10 which could also be switched like this: 10-s=8 OR 10-8=s
katen-ka-za [31]3 years ago
3 0
8+s=10 is the answer. you need to add the total of your pizza and the salad to get the complete total.
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If x+y = 1, and x^2 + y^2 = -1, what is x^7 + y^13?<br> 1) 0<br> 2) 1<br> 3) -2<br> 4) 2<br> 5) -1
damaskus [11]

Solve for <em>x</em> and <em>y</em> :

<em>x</em> + <em>y</em> = 1   →   <em>y</em> = 1 - <em>x</em>

<em>x</em> ² + <em>y</em> ² = -1

<em>x</em> ² + (1 - <em>x</em>)² = -1

<em>x</em> ² + (1 - 2<em>x</em> + <em>x</em> ²) = -1

2<em>x</em> ² - 2<em>x</em> + 1 = -1

2<em>x</em> ² - 2<em>x</em> + 2 = 0

<em>x</em> ² - <em>x</em> + 1 = 0

<em>x</em> ² - <em>x</em> + 1/4 = -3/4

(<em>x</em> - 1/2)² = -3/4

<em>x</em> - 1/2 = ±√(-3/4)

<em>x</em> - 1/2 = ±√3/2 <em>i</em>

<em>x</em> = 1/2 ± √3/2 <em>i</em>   →   <em>x</em> = exp(± <em>iπ</em>/3)

<em>y</em> = 1 - (1/2 ± √3/2 <em>i</em> )   →   <em>y</em> = -1/2 ± √3/2 <em>i</em>   →   <em>y</em> = exp(± 2<em>iπ</em>/3)

Then

<em>x </em>⁷ + <em>y </em>¹³ = exp(± 7<em>iπ</em>/3) + exp(± 26<em>iπ</em>/3)

… = exp(± <em>iπ</em>/3) + exp(± 2<em>iπ</em>/3)

since 7<em>π</em>/3 is equivalent to <em>π</em>/3, and 26<em>π</em>/3 is equivalent to 2<em>π</em>/3 (both modulo 2<em>π</em>).

In either case, we get

<em>x </em>⁷ + <em>y </em>¹³ = <em>x</em> + <em>y</em> = 1

so the answer is (2) 1.

8 0
3 years ago
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