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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20. Step 1: Convert the volume from litres to cubic centimetres. We know that 1 litre = 1000 cm^3. So, the volume of the cuboid is V = 1000 cm^3. Step 2: Use the formula for the volume of a cuboid. The volume of a cuboid is given by V = length × breadth × height. Given length L = 25 cm and breadth B = 8 cm. Let the height be H. 1000 cm^3 = 25 cm × 8 cm × H Step 3: Calculate the product of length and breadth. 1000 cm^3 = 200 cm^2 × H Step 4: Solve for the height H. H = 1000 cm^3200 cm^2 H = 5 cm The height of the cuboid is 5 cm. The correct option is A. A. 5 cm 21. Step 1: Identify the given roots. Let the roots be = -(2)/(3) and = -(1)/(4). Step 2: Calculate the sum of the roots. + = -(2)/(3) + (-(1)/(4)) + = -(2)/(3) - (1)/(4) To add these fractions, find a common denominator, which is 12. + = -(2 × 4)/(3 × 4) - (1 × 3)/(4 × 3) + = -(8)/(12) - (3)/(12) + = -(11)/(12) Step 3: Calculate the product of the roots. = (-(2)/(3)) × (-(1)/(4)) = (2 × 1)/(3 × 4) = (2)/(12) = (1)/(6) Step 4: Form the quadratic equation using the general form x^2 - ( + )x + = 0. Substitute the sum and product of the roots: x^2 - (-(11)/(12))x + (1)/(6) = 0 x^2 + (11)/(12)x + (1)/(6) = 0 Step 5: Clear the denominators by multiplying the entire equation by the least common multiple (LCM) of 12 and 6, which is 12. 12 (x^2 + (11)/(12)x + (1)/(6)) = 12 × 0 12x^2 + 12 ((11)/(12))x + 12 ((1)/(6)) = 0 12x^2 + 11x + 2 = 0 The quadratic equation is 12x² + 11x + 2 = 0. The correct option is A. A. 12x^2 + 11x + 2 = 0 Send me the next one 📸