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Answer :
Certainly! Let's go through the solution step-by-step:
### Part 1: Circumference of a Circle
#### Given Data:
1. Diameter [tex]\( d_1 = 62.8 \)[/tex] cm
2. Diameter [tex]\( d_2 = 31.4 \)[/tex] cm
#### Formula for Circumference:
The circumference [tex]\( C \)[/tex] of a circle can be calculated using the formula:
[tex]\[ C = \pi \times d \][/tex]
where [tex]\( \pi \)[/tex] (pi) is approximately 3.14159.
#### Calculations:
1. For diameter [tex]\( d_1 = 62.8 \)[/tex] cm:
[tex]\[ C_1 = \pi \times 62.8 \][/tex]
[tex]\[ C_1 \approx 3.14159 \times 62.8 \][/tex]
[tex]\[ C_1 \approx 197.29 \text{ cm} \][/tex]
2. For diameter [tex]\( d_2 = 31.4 \)[/tex] cm:
[tex]\[ C_2 = \pi \times 31.4 \][/tex]
[tex]\[ C_2 \approx 3.14159 \times 31.4 \][/tex]
[tex]\[ C_2 \approx 98.65 \text{ cm} \][/tex]
### Part 2: Reciprocal Calculation
#### Given Data:
The fraction is [tex]\( \frac{-1}{9} \)[/tex].
#### Definition of Reciprocal:
The reciprocal of a fraction [tex]\( \frac{a}{b} \)[/tex] is [tex]\( \frac{b}{a} \)[/tex].
#### Calculation:
The reciprocal of [tex]\( \frac{-1}{9} \)[/tex] is:
[tex]\[ \text{Reciprocal} = \frac{9}{-1} \][/tex]
[tex]\[ \text{Reciprocal} = -9 \][/tex]
### Summary of Results:
1. Circumference of a circle with diameter 62.8 cm:
[tex]\[ 197.29 \text{ cm} \][/tex]
2. Circumference of a circle with diameter 31.4 cm:
[tex]\[ 98.65 \text{ cm} \][/tex]
3. The reciprocal of [tex]\( \frac{-1}{9} \)[/tex] is:
[tex]\[ -9 \][/tex]
### Part 1: Circumference of a Circle
#### Given Data:
1. Diameter [tex]\( d_1 = 62.8 \)[/tex] cm
2. Diameter [tex]\( d_2 = 31.4 \)[/tex] cm
#### Formula for Circumference:
The circumference [tex]\( C \)[/tex] of a circle can be calculated using the formula:
[tex]\[ C = \pi \times d \][/tex]
where [tex]\( \pi \)[/tex] (pi) is approximately 3.14159.
#### Calculations:
1. For diameter [tex]\( d_1 = 62.8 \)[/tex] cm:
[tex]\[ C_1 = \pi \times 62.8 \][/tex]
[tex]\[ C_1 \approx 3.14159 \times 62.8 \][/tex]
[tex]\[ C_1 \approx 197.29 \text{ cm} \][/tex]
2. For diameter [tex]\( d_2 = 31.4 \)[/tex] cm:
[tex]\[ C_2 = \pi \times 31.4 \][/tex]
[tex]\[ C_2 \approx 3.14159 \times 31.4 \][/tex]
[tex]\[ C_2 \approx 98.65 \text{ cm} \][/tex]
### Part 2: Reciprocal Calculation
#### Given Data:
The fraction is [tex]\( \frac{-1}{9} \)[/tex].
#### Definition of Reciprocal:
The reciprocal of a fraction [tex]\( \frac{a}{b} \)[/tex] is [tex]\( \frac{b}{a} \)[/tex].
#### Calculation:
The reciprocal of [tex]\( \frac{-1}{9} \)[/tex] is:
[tex]\[ \text{Reciprocal} = \frac{9}{-1} \][/tex]
[tex]\[ \text{Reciprocal} = -9 \][/tex]
### Summary of Results:
1. Circumference of a circle with diameter 62.8 cm:
[tex]\[ 197.29 \text{ cm} \][/tex]
2. Circumference of a circle with diameter 31.4 cm:
[tex]\[ 98.65 \text{ cm} \][/tex]
3. The reciprocal of [tex]\( \frac{-1}{9} \)[/tex] is:
[tex]\[ -9 \][/tex]
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