This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey master — ready when you are. Here are the solutions for Item one: a) Calculate the total area of the land allocated for cabbage. Step 1: Calculate the total area of the land. The land measures 120 meters by 80 meters. Total Area = 120\, m × 80\, m = 9600\, m^2 Step 2: Calculate the area used for maize and beans. Area for maize = (1)/(3) of total area Area_maize = (1)/(3) × 9600\, m^2 = 3200\, m^2 Area for beans = 25% of total area Area_beans = 0.25 × 9600\, m^2 = 2400\, m^2 Step 3: Calculate the remaining land. Remaining Area = Total Area - (Area_maize + Area_beans) Remaining Area = 9600\, m^2 - (3200\, m^2 + 2400\, m^2) Remaining Area = 9600\, m^2 - 5600\, m^2 = 4000\, m^2 Step 4: Allocate the remaining land to cabbage. The remaining land is shared by tomatoes and cabbage in the ratio 2:3. The total ratio parts are 2+3=5. The fraction of land for cabbage is (3)/(5). Area_cabbage = (3)/(5) × Remaining Area Area_cabbage = (3)/(5) × 4000\, m^2 = 2400\, m^2 The total area of the land allocated for cabbage is 2400 m^2. b) Determine the actual yield of maize in kg after the percentage changes. Step 1: Calculate the estimated maize yield. From part a), the area for maize is 3200\, m^2. Each square meter of maize land produces 5 kg of maize. Estimated Maize Yield = 3200\, m^2 × 5\, kg/m^2 = 16000\, kg Step 2: Apply the percentage decrease to find the actual yield. The maize yield decreased by 15%. Actual Maize Yield = Estimated Maize Yield × (1 - 0.15) Actual Maize Yield = 16000\, kg × 0.85 Actual Maize Yield = 13600\, kg The actual yield of maize is 13600 kg. c) Determine the final altitude of the farm land relative to sea level after the flood. Step 1: Identify the initial altitude of the farm land. The farm is located 30 meters above sea level. Initial Altitude = 30\, m Step 2: Account for the rise in water levels. The water levels rose by 12 meters. This means the new effective sea level is 12 meters higher than the original sea level. To find the farm land's altitude relative to the new sea level, subtract the water level rise from the initial altitude. Final Altitude = Initial Altitude - Water Level Rise Final Altitude = 30\, m - 12\, m = 18\, m The final altitude of the farm land relative to sea level after the flood is 18 m. Send me the next one 📸