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ElenaW [278]
3 years ago
5

For P​ = ​{3, 5, 10, 15​}, Q​ = ​{1,6, 13​}, and R​ = ​{4, 6, 10, 13​}, find P U ​(Q∩​R).

Mathematics
1 answer:
nikitadnepr [17]3 years ago
4 0

Answer:

 P U ​(Q∩​R)={3, 5, 6, 10, 13, 15}

Step-by-step explanation:

The first step that we have to do is find  (Q∩​R) then, we ned to find the elements in common between Q and R, as we can see we have the element 6 and the element 13, then:

(Q∩​R)={6, 13}

Now we just need to do the union between  P and  ​(Q∩​R), that is just put all the elements of P and  ​(Q∩​R) in one set, then:

P U ​(Q∩​R)={3, 5, 6, 10, 13, 15}

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x+i*y≠0 ==> x≠0 and y≠0

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\dfrac{1}{x+i*y} +\dfrac{2}{x-i*y} =1+i\\\\\dfrac{1*(x-i*y)}{(x+i*y)(x-i*y)} +\dfrac{2*(x+i*y)}{(x-i*y)(x+i*y)} =1+i\\\\\\\dfrac{x-i*y+2x+2i*y}{x^2+y^2} =1+i\\\\3x+i*y=(1+i)(x^2+y^2)\\\\3x+i*y=(x^2+y^2)+i(x^2+y^2+i*(x^2+y^2)\\\\\left\{\begin{array}{ccc}3x&=&x^2+y^2\\y&=&x^2+y^2\\\end {array}\right.\\\\\\\left\{\begin{array}{ccc}y&=&3x\\3x&=&x^2+9x^2\\\end {array}\right.\\\\\\\left\{\begin{array}{ccc}y&=&3x\\x(10x-3)&=&0\\\end {array}\right.\\\\

\left\{\begin{array}{ccc}x&=&0\\y&=&0\\\end {array}\right.\ (to\ exclude) \ or \ \left\{\begin{array}{ccc}x&=&\dfrac{3}{10}\\\\y&=&\dfrac{9}{10}\\\end {array}\right.\\\\Sol=\{(\dfrac{3}{10},\dfrac{9}{10})\}\\

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3 years ago
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Zanzabum

Answer:

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2) The talented boy - <em>El chico talentoso/El joven talentoso</em>

3) An outgoing girl - <em>Una chica extrovertida/Una joven extrovertida</em>

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Step-by-step explanation:

Now, we present a possible set of solution, as there are solutions as many synonyms exist in Spanish. Then:

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2) The talented boy - <em>El chico talentoso/El joven talentoso</em>

3) An outgoing girl - <em>Una chica extrovertida/Una joven extrovertida</em>

4) The tasty ice cream - <em>El helado delicioso/El helado sabroso</em>

5) A funny book - <em>Un libro divertido/Un libro entretenido</em>

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