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3 years ago

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If there are 12 people sitting at a round table , how many different pairs of people can have conversations during dinner, assum

ing the can all talk to each other? What geometric figure can you use t model this situation?

2 answers:

julsineya [31]3 years ago

7 0

66 different pairs. Use a dodecagon showing sides and angles

kherson [118]3 years ago

5 0

Answer:

Step-by-step explanation:

Given that there are 12 people sitting around at a table.

We see that any two persons can have conversations. If we count A with B as one conversation this is the same as B with A

i.e. order does not matter

So here we have to use combinations.

2 people out of 12 where order does not matter can be done in 12C2 ways

No of conversations = $12C2\\= \frac{12!}{2!10!} \\=66$

If we use a dodedecon as a geometrical figure with 12 vertices representing 12 persons the conversation between pairs can be associated with all diagonals and sides connecting two vertices.

Sides are 12 and diagonals are 54 totalling 66.

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<h3>What are the trigonometry ratios?</h3>

For a right angle triangle, the trigonometry ratios can be given as,

$\rm \sin \theta=\dfrac{b}{c}\\\rm \cos \theta=\dfrac{a}{c}\\\rm \tan \theta=\dfrac{b}{a}$

Here, <em>a</em> is base side<em>, b</em> is perpendicular side and<em> c</em> is the hypotenuse side of the triangle.

In the given triangle, the length of base side<em> </em>is 8 units, perpendicular side is 6 units and hypotenuse side is 10 units.

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2 years ago

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3 years ago

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3 years ago

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2 years ago

What 2 numbers multiply to be -14 and add to be -3

Svetach [21]

Xy = -14
x + y = -3

$xy = -14$
$\frac{xy}{x} = \frac{-14}{x}$
$y = \frac{-14}{x}$

$x + y = -3$
$x + \frac{-14}{x} = -3$
$\frac{x^{2}}{x} + \frac{-14}{x} = -3$
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$x^{2} + 3x - 14 = 0$
$x = \frac{-(3) \± \sqrt{(3)^{2} - 4(1)(-14)}}{2(1)}$
$x = \frac{-3 \± \sqrt{9 + 56}}{2}$
$x = \frac{-3 \± \sqrt{65}}{2}$
$x = \frac{-3 \± 8.06}{2}$
$x = -1.5 \± 4.03$
$x = -1.5 + 4.03$ $or$ $x = -1.5 - 4.03$
$x = 2.53$ $or$ $x = -5.53$

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2.53 + y = -3
- 2.53 - 2.53
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  (x, y) = (2.53, -5.53)

x + y = -3
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+ 5.53   + 5.53
  y = 2.53
  (x, y) = (-5.53, 2.53)

The two numbers that multiply to -14 and add up to -3 are -5.53 and 2.53.

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3 years ago