1. Problem 3.2: If 5 litres of water weigh 3.5kg, how much does 2 litres of water weigh? Step 1: Understand the problem. We know the weight of 5 litres and want to find the weight of 2 litres. Step 2: Use the formula for direct proportion: $$\frac{weight_1}{volume_1} = \frac{weight_2}{volume_2}$$ Step 3: Substitute known values: $$\frac{3.5}{5} = \frac{weight_2}{2}$$ Step 4: Solve for $weight_2$: $$weight_2 = \frac{3.5}{5} \times 2 = 0.7 \times 2 = 1.4$$ Step 5: So, 2 litres of water weigh 1.4 kg. 2. Problem 3.3.1: Arrange these numbers in ascending order: $5^2$, $10^4$, $4^1$, $1^{200}$, $4^2$, $5^3$ Step 1: Calculate each value: - $5^2 = 25$ - $10^4 = 10000$ - $4^1 = 4$ - $1^{200} = 1$ - $4^2 = 16$ - $5^3 = 125$ Step 2: Arrange in ascending order: $1$, $4$, $16$, $25$, $125$, $10000$ 3. Problem 3.3.2: Simplify $\sqrt{25} + \sqrt{27} + \sqrt{121}$ Step 1: Simplify each square root: - $\sqrt{25} = 5$ - $\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}$ - $\sqrt{121} = 11$ Step 2: Add the simplified terms: $$5 + 3\sqrt{3} + 11 = 16 + 3\sqrt{3}$$ 4. Problem 3.4: A microwave oven increases the temperature of a piece of meat from -12°C to 67°C. What is the change in temperature? Step 1: Use the formula for change in temperature: $$\Delta T = T_{final} - T_{initial}$$ Step 2: Substitute values: $$\Delta T = 67 - (-12) = 67 + 12 = 79$$ Step 3: The temperature change is 79°C.