Plz help to do it of math

Mathematics

1 answer:

koban [17]3 years ago

5 0

A leap year consists of 366 days.

52 weeks + 2 days.

These 2 days can be: (mon,tue),(tue,wed),(wed,thu),(thu,fri),(fri,sat)(sat,sun)(sun,mon)

Thus, the total number of cases = 7.

The number of cases in which we get Friday = 2(Thu, Fri)(Fri, Sat).

Therefore the required probability = 2/7.

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What is the completely simplified equivalent of 2/(5+i)?

Bezzdna [24]

namely, let's rationalize the denominator in the fraction, for which case we'll be using the conjugate of that denominator, so we'll multiply top and bottom by its conjugate.

so the denominator is 5 + i, simply enough, its conjugate is just 5 - i, recall that same/same = 1, thus (5-i)/(5-i) = 1, and any expression multiplied by 1 is just itself, so we're not really changing the fraction per se.

$\bf \cfrac{2}{5+i}\cdot \cfrac{5-i}{5-i}\implies \cfrac{2(5-i)}{\stackrel{\textit{difference of squares}}{(5+i)(5-i)}}\implies \cfrac{2(5-i)}{\stackrel{\textit{recall }i^2=-1}{5^2-i^2}}\implies \cfrac{2(5-i)}{25-(-1)} \\\\\\ \cfrac{2(5-i)}{25+1}\implies \cfrac{2(5-i)}{26}\implies \cfrac{5-i}{13}$