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
a) Step 1: Use the algebraic identity (a+b)^2 = a^2 + b^2 + 2ab. Substitute the given values a+b=9 and a^2+b^2=71 into the identity. (9)^2 = 71 + 2ab Step 2: Solve for ab. 81 = 71 + 2ab 81 - 71 = 2ab 10 = 2ab ab = (10)/(2) ab = 5 Step 3: Calculate (ab)^3. (ab)^3 = (5)^3 (ab)^3 = 5 × 5 × 5 (ab)^3 = 125 The value of (ab)^3 is 125. b) Step 1: To factorise x^2 - x - 20, find two numbers that multiply to -20 and add to -1. The numbers are -5 and 4. Step 2: Write the expression in factored form. x^2 - x - 20 = (x-5)(x+4) The factorised expression is (x-5)(x+4). c) Step 1: Substitute l = 22.8 and g = 9.8 into the formula T = 2((l)/(g)). T = 2((22.8)/(9.8)) Step 2: Calculate the value inside the square root. T = 2(2.3265306...) Step 3: Calculate the square root and then multiply by 2. T = 2 × 1.5252969... T = 2 × 3.14159265... × 1.5252969... T = 9.5839... Rounding to three significant figures: T ≈ 9.58 The value of T is 9.58. d) Step 1: Find a common denominator for the fractions (a+2)/(4) and (a+3)/(5). The least common multiple of 4 and 5 is 20. Step 2: Rewrite each fraction with the common denominator. (a+2)/(4) = (5(a+2))/(5 × 4) = (5a+10)/(20) (a+3)/(5) = (4(a+3))/(4 × 5) = (4a+12)/(20) Step 3: Add the two fractions. (5a+10)/(20) + (4a+12)/(20) = ((5a+10) + (4a+12))/(20) Step 4: Combine like terms in the numerator. (5a+4a+10+12)/(20) = (9a+22)/(20) The expression as a single fraction is (9a+22)/(20). Send me the next one 📸