Mathematics: Please please help Question 1: What is the diameter of the semi-circular cutout in the rectangle? * 2: What is the area of the figure? * 3: The figure represents a rug with a cutout to fit around a fireplace hearth. If the carpet costs $1.50 per square foot, how much will the rug cost? *

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...

Please please help Question 1: What is the diameter

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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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Please please help Question 1: What is the diameter of the semi-circular cutout in the rectangle? *
2: What is the area of the figure? *
3: The figure represents a rug with a cutout to fit around a fireplace hearth. If the carpet costs $1.50 per square foot, how much will the rug cost? *

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