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
Step 1: Simplify question 7 part i). The expression is 28x^11 ÷ 7x^9. To simplify, divide the coefficients and use the exponent rule a^m ÷ a^n = a^m-n for the variables. 28x^117x^9 = ((28)/(7)) × (x^11x^9) = 4 × x^(11-9) = 4x^2 The simplified expression is 4x^2. Step 2: Simplify question 7 part ii). The expression is 25m^12 ÷ 5m^7. To simplify, divide the coefficients and use the exponent rule a^m ÷ a^n = a^m-n for the variables. 25m^125m^7 = ((25)/(5)) × (m^12m^7) = 5 × m^(12-7) = 5m^5 The simplified expression is 5m^5. Step 3: Evaluate question 8 using logarithms. Let P = sqrt((269.1 × 89.33)/(41.72)). This can be written as P = ((269.1 × 89.33)/(41.72))^(1)/(2). Take the logarithm (base 10) of both sides: P = [((269.1 × 89.33)/(41.72))^(1)/(2)] Using the logarithm property (a^b) = b a: P = (1)/(2) ((269.1 × 89.33)/(41.72)) Using the logarithm properties ((a)/(b)) = a - b and (ab) = a + b: P = (1)/(2) [(269.1) + (89.33) - (41.72)] Now, find the logarithms of each number: (269.1) ≈ 2.4300 (89.33) ≈ 1.9519 (41.72) ≈ 1.6203 Substitute these values into the equation for P: P = (1)/(2) [2.4300 + 1.9519 - 1.6203] P = (1)/(2) [4.3819 - 1.6203] P = (1)/(2) [2.7616] P = 1.3808 Finally, find the antilog of 1.3808 to get P: P = 10^1.3808 P ≈ 24.03 The value of the expression is 24.03. 3 done, 2 left today. You're making progress.