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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Question 1 a) (i) To express 7560 in standard form, move the decimal point to the left until there is only one non-zero digit before it. Step 1: Identify the number of places the decimal point moves. 7560 = 7.560 × 10^3 The decimal point moved 3 places to the left. The standard form is 7.56 × 10^3. a) (ii) To express 0.0000006892 in standard form, move the decimal point to the right until there is only one non-zero digit before it. Step 1: Identify the number of places the decimal point moves. 0.0000006892 = 6.892 × 10^-7 The decimal point moved 7 places to the right. The standard form is 6.892 × 10^-7. b) To solve the equation (3x-1)/(5) - (x-4)/(3) = 1: Step 1: Find a common denominator, which is 15, and multiply all terms by it. 15 ( (3x-1)/(5) ) - 15 ( (x-4)/(3) ) = 15(1) 3(3x-1) - 5(x-4) = 15 Step 2: Distribute and simplify. 9x - 3 - 5x + 20 = 15 Step 3: Combine like terms. 4x + 17 = 15 Step 4: Subtract 17 from both sides. 4x = 15 - 17 4x = -2 Step 5: Divide by 4. x = (-2)/(4) x = -(1)/(2) The solution is x = -0.5. c) The lengths of rods A and B are in the ratio 4:3, and their total length is 35 cm. Step 1: Let the lengths of the rods be 4k and 3k. 4k + 3k = 35 Step 2: Combine terms and solve for k. 7k = 35 k = (35)/(7) k = 5 Step 3: Calculate the length of each rod. Length of rod A: 4k = 4(5) = 20 cm Length of rod B: 3k = 3(5) = 15 cm The lengths of the rods are Rod A: 20 cm, Rod B: 15 cm. d) The base of a tank is a trapezium with an area of 21 m², and the volume is 1050 litres. Find its height in metres. Step 1: Convert the volume from litres to cubic metres. 1 m^3 = 1000 litres 1050 litres = (1050)/(1000) m^3 = 1.05 m^3 Step 2: Use the formula for the volume of a prism: Volume = Base Area × Height. Volume = Area_base × Height 1.05 m^3 = 21 m^2 × Height Step 3: Solve for Height. Height = 1.05 m^321 m^2 Height = 0.05 m The height of the tank is 0.05 m. e) To convert the fraction 0.125 to a percentage: Step 1: Multiply the decimal by 100. 0.125 × 100\% = 12.5\% The percentage is 12.5\%. f) It takes 0.74 minutes to make one soldered joint. Calculate the total time for 379 joints. Step 1: Multiply the time per joint by the number of joints. Total time = 0.74 minutes/joint × 379 joints Total time = 279.46 minutes The total time is 279.46 minutes. Send me the next one 📸