3 years ago

The ratio equivelent ot 1/3 is

Mathematics

1 answer:

Ann [662]3 years ago

7 0

1:3 is equivalent to 1/3

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Find the coefficient of x^5y^8 in (x+y)^13

Dafna1 [17]

recall that the exponent for the first term will be starting at 13, and descending by one on every expanded term, in the binomial theorem.

so, 13, 12, 11, 10, 9, 8, 7, 6, 5 <---- x⁵ will then be in the 9th term

now, using the "combination" formula to get the coefficient of the 9th term.

k = 8 <--- the 9th term

n = 13 <--- highest exponent

$\bf \textit{the coefficient and values of an expanded term} \\\\ (x+y)^{13} \qquad \qquad \begin{array}{llll} expansion\\ for\\ 9^{th}~term \end{array} \quad \begin{cases} \stackrel{term}{k}=0..n\\ \stackrel{exponent}{n}\\ -----\\ k=\stackrel{9~term}{8}\\ n=13 \end{cases}$

$\bf \stackrel{coefficient}{\left(\frac{n!}{k!(n-k)!}\right)} \qquad \stackrel{\stackrel{first~term}{factor}}{\left( a^{n-k} \right)} \qquad \stackrel{\stackrel{second~term}{factor}}{\left( b^k \right)} \\\\\\ \cfrac{13!}{8!(13-8)!}~~x^{13-8}~~(+y)^8\implies 1287~x^5y^8$