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Here is a solution to each question in the image provided.

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### Question 1:
The height of horses is often measured in "hands." The reason this may be a poor standard of length is due to the variability and lack of consistency in hand size across different individuals, leading to unreliable and non-standard measurements.

**Correct Answer**: (c) The width of the hand will vary as finger nails grow and get cut.

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### Question 2:
For each calculation, round the final result to the appropriate level of accuracy based on the given significant figures.

1. **(i)** \( 256 + 28.2 + 0.75 + 9.6 \)
   - **Result**: 294.55, rounded to **295** (3 significant figures).

2. **(ii)** \( 6.280 \times \pi \)
   - **Result**: \(6.280 \times 3.14159 \approx 19.7372\), rounded to **19.7** (3 significant figures).

3. **(iii)** \( 0.0018 \times 712.8 \)
   - **Result**: \(0.0018 \times 712.8 = 1.28256\), rounded to **1.3** (2 significant figures).

4. **(iv)** \( \frac{1.98 \times 10^4}{2.71 \times \sqrt{8.112}} \)
   - First, calculate \( \sqrt{8.112} \approx 2.85 \).
   - Then, \( 2.71 \times 2.85 = 7.7235 \).
   - Finally, \( \frac{1.98 \times 10^4}{7.7235} \approx 2563.2 \), rounded to **2560** (3 significant figures).

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### Question 3:
To find the frequency \( f \) of a sound wave with wavelength \( \lambda = 4.0 \, \text{m} \) and speed of sound \( c = 3.0 \times 10^8 \, \text{m/s} \):
\[
f = \frac{c}{\lambda} = \frac{3.0 \times 10^8}{4.0} = 7.5 \times 10^7 \, \text{Hz}
\]

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### Question 4:
In the expression \( x = C t^2 \), the units of \( C \) can be derived by dimensional analysis. Since \( x \) has units of meters (m) and \( t \) has units of seconds (s):
\[
\text{Units of } C = \frac{\text{m}}{\text{s}^2} = \text{m/s}^2
\]

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### Question 5:
For the expression \( x = E \cos(2\pi f t) \), the argument of the cosine function must be dimensionless. Therefore, \( E \) has the same units as \( x \), which are **meters (m)**.

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### Question 6:
Convert the units as follows:

1. **(i)** \( 343 \, \text{m/s} \) to km/h:
   \[
   343 \, \text{m/s} = 343 \times 3.6 = 1234.8 \, \text{km/h}
   \]

2. **(ii)** \( 998 \, \text{mm} \) to m:
   \[
   998 \, \text{mm} = 0.998 \, \text{m}
   \]

3. **(iii)** \( 998 \, \text{mm}^2 \) to \( \text{m}^2 \):
   \[
   998 \, \text{mm}^2 = 998 \times 10^{-6} = 0.000998 \, \text{m}^2
   \]

4. **(iv)** \( 8940 \, \text{kg/m}^3 \) to \( \text{g/cm}^3 \):
   \[
   8940 \, \text{kg/m}^3 = 8.94 \, \text{g/cm}^3
   \]

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Would you like detailed explanations for each calculation? 

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### Additional Questions for Practice:
1. What would be an example where "hands" as a unit is a practical measurement?
2. How do you determine the correct number of significant figures in a calculation?
3. What is the relationship between frequency, wavelength, and wave speed?
4. How does dimensional analysis help in identifying the units of constants?
5. Why must the argument of a trigonometric function be dimensionless?

### Tip:
When working with unit conversions, always ensure your answer has the same level of precision as the input measurements.

Physics mechanics questions on measurement units, accuracy, frequency of sound waves, dimensional analysis, and unit conversions.

Solve physics mechanics problems involving measurement units, accuracy in calculations, frequency of sound waves, dimensional analysis, and unit conversions. Learn concepts like significant figures and understand units for various physical quantities. Suitable for students in Grades 11-12.

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