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Answer :
To solve this problem, we have to determine how many geraniums are needed, if we plant one approximately every foot around the circumference of a circular garden. Here's how to do it step by step:
1. Convert the Diameter to Feet:
The diameter of the circular garden is given as [tex]\(6'\)[/tex] [tex]\(4^n\)[/tex]. To find how many feet this is in total, we combine the feet and the inches:
- There are 12 inches in a foot. Therefore, [tex]\(4^n\)[/tex] inches can be converted to feet by dividing by 12.
- [tex]\(4^n = 4\)[/tex] inches, so we convert it: [tex]\(4 \div 12 = \frac{1}{3}\)[/tex] feet.
- The total diameter in feet is [tex]\(6 + \frac{1}{3} = 6.333...\)[/tex] feet.
2. Calculate the Radius:
The radius is half of the diameter:
[tex]\[
\text{Radius} = \frac{6.333...}{2} = 3.166...\text{ feet}
\][/tex]
3. Calculate the Circumference:
The formula for the circumference of a circle is [tex]\(C = 2\pi r\)[/tex], where [tex]\(r\)[/tex] is the radius.
- Plugging in our radius, we get:
[tex]\[
C = 2 \times \pi \times 3.166...
\][/tex]
- This calculation gives a circumference of approximately [tex]\(19.896753472735355\)[/tex] feet.
4. Determine the Number of Geraniums:
To find out how many geraniums are needed, since we want to plant one every foot around the circumference, we round the circumference to the nearest whole number.
- Round [tex]\(19.896753472735355\)[/tex] to the nearest whole number, which is [tex]\(20\)[/tex].
Therefore, approximately 20 geraniums are needed to be planted every foot along the circumference of this circular garden.
1. Convert the Diameter to Feet:
The diameter of the circular garden is given as [tex]\(6'\)[/tex] [tex]\(4^n\)[/tex]. To find how many feet this is in total, we combine the feet and the inches:
- There are 12 inches in a foot. Therefore, [tex]\(4^n\)[/tex] inches can be converted to feet by dividing by 12.
- [tex]\(4^n = 4\)[/tex] inches, so we convert it: [tex]\(4 \div 12 = \frac{1}{3}\)[/tex] feet.
- The total diameter in feet is [tex]\(6 + \frac{1}{3} = 6.333...\)[/tex] feet.
2. Calculate the Radius:
The radius is half of the diameter:
[tex]\[
\text{Radius} = \frac{6.333...}{2} = 3.166...\text{ feet}
\][/tex]
3. Calculate the Circumference:
The formula for the circumference of a circle is [tex]\(C = 2\pi r\)[/tex], where [tex]\(r\)[/tex] is the radius.
- Plugging in our radius, we get:
[tex]\[
C = 2 \times \pi \times 3.166...
\][/tex]
- This calculation gives a circumference of approximately [tex]\(19.896753472735355\)[/tex] feet.
4. Determine the Number of Geraniums:
To find out how many geraniums are needed, since we want to plant one every foot around the circumference, we round the circumference to the nearest whole number.
- Round [tex]\(19.896753472735355\)[/tex] to the nearest whole number, which is [tex]\(20\)[/tex].
Therefore, approximately 20 geraniums are needed to be planted every foot along the circumference of this circular garden.
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