Mathematics: Susan makes a rectangular rug that has an area of 300 square inches and a width of 15 inches. what is the length of the rug?

teamsStep-by-step explanation:Let s do it by parts. Let s consider a fact: there has to be only one winner. After six games:So, Since it s a decreasing Geometric Sequence (we have to lead to one winner), and each match two teams play, the beaten one leaves the championship.a) Explicit Rule (Formula):That s to say the tournament started with 32 teamsb) Recursive RuleIf we have the first term of the Geometric Sequence we can recursively find the subsequent terms. The Recursive Rule is useful when...

Susan makes a rectangular rug that has an area - id32603048, KaitlynLucas5132

Ответ:

samuelerlikhman

28.11.2021

Mathematics

teams

Step-by-step explanation:

Let's do it by parts.

Let's consider a fact: there has to be only one winner. After six games:

So, $a_{6}=1$

Since it's a decreasing Geometric Sequence (we have to lead to one winner), and each match two teams play, the beaten one leaves the championship.

$r=(\frac{1}{2})$

$a_{1}=?$

a) Explicit Rule (Formula):

$a_{6}=1,a_{1}=?r=\frac{1}{2}\\1=a_{1}\left ( \frac{1}{2} \right )^{6-1}\\1=a_{1}\left ( \frac{1}{2} \right )^{5}\\1=\frac{a_{1}}{32}\\a_{1}=32$

That's to say the tournament started with 32 teams

$\{32,16,8,4,2,1\}$

b) Recursive Rule

If we have the first term of the Geometric Sequence we can recursively find the subsequent terms. The Recursive Rule is useful when we have the prior term and we need the following one. Also, to derive the explicit rule.

$a_{1}=32\\a_{n}=\left ( \frac{1}{2} \right )a_{n+1}\\a_{2}=\left ( \frac{1}{2} \right )32=16\\a_{3}=\left ( \frac{1}{2} \right )16=8\\a_{4}=\left ( \frac{1}{2} \right )8=4\\a_{5}=\left ( \frac{1}{2} \right )4=2\\a_{6}=\left ( \frac{1}{2} \right )2=1\\$

$\{32,16,8,4,2,1\}$

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Susan makes a rectangular rug that has an area of 300 square inches and a width of 15 inches. what is the length of the rug?

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