Find x if 4, 6, x, 18 are in proportion 3. The first, third and fourth terms of a proportion are 12.8 and 14 respectively. Find the second term.

Answer

Let's solve the given questions step by step.

### Question 1: Find x if 4, 6, x, 18 are in proportion.

1. **Understanding Proportion**: When four numbers are in proportion, the ratio of the first two numbers is equal to the ratio of the last two numbers. This can be expressed as:
\[ \frac{4}{6} = \frac{x}{18} \]

2. **Cross Multiplication**: To solve for x, we cross multiply:
\[ 4 \cdot 18 = 6 \cdot x \]

3. **Calculate the Left Side**: Calculate \(4 \cdot 18\):
\[ 4 \cdot 18 = 72 \]

4. **Set Up the Equation**: Now we have:
\[ 72 = 6x \]

5. **Solve for x**: Divide both sides by 6 to isolate x:
\[ x = \frac{72}{6} \]

6. **Final Calculation**: Calculate \( \frac{72}{6} \):
\[ x = 12 \]

### Conclusion for Question 1:
The value of x is **12**.

---

### Question 2: The first, third and fourth terms of a proportion are 12, 18, and 14 respectively. Find the second term.

1. **Understanding Proportion**: The first term is 12, the second term is unknown (let's call it y), the third term is 18, and the fourth term is 14. Since they are in proportion, we can write:
\[ \frac{12}{y} = \frac{18}{14} \]

2. **Cross Multiplication**: Cross multiply to solve for y:
\[ 12 \cdot 14 = 18 \cdot y \]

3. **Calculate the Left Side**: Calculate \(12 \cdot 14\):
\[ 12 \cdot 14 = 168 \]

4. **Set Up the Equation**: Now we have:
\[ 168 = 18y \]

5. **Solve for y**: Divide both sides by 18 to isolate y:
\[ y = \frac{168}{18} \]

6. **Final Calculation**: Calculate \( \frac{168}{18} \):
\[ y = 9.33 \text{ (approximately)} \]

### Conclusion for Question 2:
The second term is approximately **9.33**.

---