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
You're on a roll — here are the solutions to the remaining problems: 3a) Step 1: Identify the path from Dream School to Excellence. The path is Dream School Tassan Excellence. Step 2: Find the distances for each segment from the legend. Dream School to Tassan = 8 km Tassan to Excellence = 10 km Step 3: Add the distances. Total distance = 8 km + 10 km = 18 km It is 18 km from Dream School to Excellence. 3b) Step 1: Identify the path from Tassah to Olympic Glory. The path is Tassah Gayap Olympic Glory. Step 2: Find the distances for each segment from the legend. Tassah to Gayap = 16 km Gayap to Olympic Glory = 4 km Step 3: Add the distances. Total distance = 16 km + 4 km = 20 km It is 20 km from Tassah to Olympic Glory. 3c) Step 1: Identify the path from Excellence to Gayap. The path is Excellence Tassan Gayap. Step 2: Find the distances for each segment from the legend. Excellence to Tassan = 10 km Tassan to Gayap = 16 km Step 3: Add the distances. Total distance = 10 km + 16 km = 26 km It is 26 km from Excellence to Gayap. 3d) Step 1: Calculate the distance from Dream School to Gayap. Path: Dream School Tassan Gayap Distance = 8 km + 16 km = 24 km Step 2: Calculate the total distance for the round trip. Total distance = 2 × 24 km = 48 km Step 3: Calculate the time taken for the journey. Speed = 12 km/h Time = DistanceSpeed = 48 km12 km/h = 4 hours Step 4: Determine the return time. Starting time = 11:50 am Add 4 hours to the starting time: 11:50 am + 4 hours = 15:50 In 12-hour format, 15:50 is 3:50 pm. Mr. Anselm returns to Dream School at 3:50 pm. 4a) Step 1: Identify the relationship between the pool's radius and the yard's length CD. The length CD is the diameter of the semi-circular swimming pool. Step 2: Use the given radius to find the diameter. Radius (r) = 3.5 m Diameter (d) = 2 × r = 2 × 3.5 m = 7 m The length of the yard CD is 7 m. 4b) Step 1: Identify the dimensions of the rectangular yard ABCD. Length (CD) = 7 m (from 4a) Width (AD) = 5 m (given in the diagram) Step 2: Calculate the area of the rectangle ABCD. Area of rectangle = Length × Width = 7 m × 5 m = 35 m^2 The area of the yard ABCD is 35 m^2. 4c) Step 1: Calculate the area of the semi-circular swimming pool. Radius (r) = 3.5 m Area of a full circle = r^2 Area of semi-circle = (1)/(2) r^2 Using ≈ (22)/(7): Area of semi-circle = (1)/(2) × (22)/(7) × (3.5)^2 = (1)/(2) × (22)/(7) × 12.25 = 11 × (12.25)/(7) = 11 × 1.75 = 19.25 m^2 Step 2: Calculate the area to be concreted (shaded area). Area to concrete = Area of rectangle ABCD - Area of semi-circular pool = 35 m^2 - 19.25 m^2 = 15.75 m^2 Step 3: Calculate the cost of concreting. Cost per square metre = 2000 frs Total cost = Area to concrete × Cost per square metre = 15.75 m^2 × 2000 frs/m^2 = 31500 frs The cost of concreting the yard is 31500 frs. Got more? Send 'em!