d. Convert 3km" to m² e. Convert 10°m to km. 12 f. Convert 10"mm-to mn".

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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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D, E, F
### Unit Conversion Problems

#### Given Problems:

c. Convert 9 cm² to mm²  
d. Convert 3 km² to m²  
e. Convert 10⁶ m² to km²  
f. Convert 10¹² mm² to m²

#### Partially Solved Example:

a. Convert 10 m² to cm²  

Given Solution:  
\[ 10 \text{ m}^2 = 100000 \text{ cm}^2 \]

**Note:** Simplify your answer as needed. Type and verify each step to ensure accuracy in your conversions.

#### Explanations:

1. **Conversion from square centimeters to square millimeters (Problem c):**
   - \( 1 \text{ cm}^2 = 100 \text{ mm}^2 \)
   - Therefore, \( 9 \text{ cm}^2 = 9 \times 100 \text{ mm}^2 = 900 \text{ mm}^2 \)

2. **Conversion from square kilometers to square meters (Problem d):**
   - \( 1 \text{ km}^2 = 1,000,000 \text{ m}^2 \)
   - Therefore, \( 3 \text{ km}^2 = 3 \times 1,000,000 \text{ m}^2 = 3,000,000 \text{ m}^2 \)

3. **Conversion from square meters to square kilometers (Problem e):**
   - \( 10^6 \text{ m}^2 = 1 \text{ km}^2 \)
   - Therefore, \( 10^6 \text{ m}^2 = 1 \text{ km}^2 \)

4. **Conversion from square millimeters to square meters (Problem f):**
   - \( 1 \text{ mm}^2 = 1 \times 10^{-6} \text{ m}^2 \)
   - Therefore, \( 10^{12} \text{ mm}^2 = 10^{12} \times 10^{-6} \text{ m}^2 = 10^6 \text{ m}^2 \)
Transcribed Image Text:### Unit Conversion Problems #### Given Problems: c. Convert 9 cm² to mm² d. Convert 3 km² to m² e. Convert 10⁶ m² to km² f. Convert 10¹² mm² to m² #### Partially Solved Example: a. Convert 10 m² to cm² Given Solution: \[ 10 \text{ m}^2 = 100000 \text{ cm}^2 \] **Note:** Simplify your answer as needed. Type and verify each step to ensure accuracy in your conversions. #### Explanations: 1. **Conversion from square centimeters to square millimeters (Problem c):** - \( 1 \text{ cm}^2 = 100 \text{ mm}^2 \) - Therefore, \( 9 \text{ cm}^2 = 9 \times 100 \text{ mm}^2 = 900 \text{ mm}^2 \) 2. **Conversion from square kilometers to square meters (Problem d):** - \( 1 \text{ km}^2 = 1,000,000 \text{ m}^2 \) - Therefore, \( 3 \text{ km}^2 = 3 \times 1,000,000 \text{ m}^2 = 3,000,000 \text{ m}^2 \) 3. **Conversion from square meters to square kilometers (Problem e):** - \( 10^6 \text{ m}^2 = 1 \text{ km}^2 \) - Therefore, \( 10^6 \text{ m}^2 = 1 \text{ km}^2 \) 4. **Conversion from square millimeters to square meters (Problem f):** - \( 1 \text{ mm}^2 = 1 \times 10^{-6} \text{ m}^2 \) - Therefore, \( 10^{12} \text{ mm}^2 = 10^{12} \times 10^{-6} \text{ m}^2 = 10^6 \text{ m}^2 \)
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