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.
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You're on a roll — 28) a) Step 1: Identify the given distance and time. Distance (D) = 30 km Time (T) = 30 minutes Step 2: Convert the time to hours. Since there are 60 minutes in an hour, T = (30)/(60) hours = 0.5 hours Step 3: Calculate the speed in kilometers per hour. Speed (S) is calculated as S = (D)/(T). S = 30 km0.5 hours S = 60 km/h His speed in kilometers per hour is 60 km/h. b) Step 1: Convert the speed from kilometers per hour to meters per second. We know that 1 km = 1000 m and 1 hour = 3600 seconds. S = 60 kmh × 1000 m1 km × 1 h3600 s Step 2: Perform the multiplication and division. S = (60 × 1000)/(3600) ms S = (60000)/(3600) ms S = (600)/(36) ms S = (100)/(6) ms S = 16.666... ms Rounding to two decimal places, the speed is 16.67 m/s. 29) Step 1: Write down the given simultaneous equations. Equation (1): 2a + b = 8 Equation (2): 3a - b = 7 Step 2: Use the elimination method. Add Equation (1) and Equation (2) to eliminate b. (2a + b) + (3a - b) = 8 + 7 2a + 3a + b - b = 15 5a = 15 Step 3: Solve for a. a = (15)/(5) a = 3 Step 4: Substitute the value of a into either Equation (1) or Equation (2) to solve for b. Using Equation (1): 2(3) + b = 8 6 + b = 8 Step 5: Solve for b. b = 8 - 6 b = 2 The solution is a=3, b=2. Got more? Send 'em!