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
here are the solutions to the problems: 2. (a) Simplify: (3(1)/(2) + 2(1)/(4)) - (5(1)/(2) - 1(1)/(2)) Step 1: Convert all mixed numbers to improper fractions or work with whole numbers and fractions separately. It's often easier to work with whole numbers and fractions separately for addition/subtraction. For the first parenthesis: 3(1)/(2) + 2(1)/(4) = (3+2) + ((1)/(2) + (1)/(4)) = 5 + ((2)/(4) + (1)/(4)) = 5 + (3)/(4) = 5(3)/(4) For the second parenthesis: 5(1)/(2) - 1(1)/(2) = (5-1) + ((1)/(2) - (1)/(2)) = 4 + 0 = 4 Step 2: Perform the final subtraction. 5(3)/(4) - 4 = (5-4) + (3)/(4) = 1 + (3)/(4) = 1(3)/(4) The simplified expression is 1(3)/(4). 2. (b) Solve for n in the equation 2n^2 = 4n. Step 1: Rearrange the equation to set it equal to zero. 2n^2 - 4n = 0 Step 2: Factor out the common term, which is 2n. 2n(n - 2) = 0 Step 3: Set each factor equal to zero and solve for n. 2n = 0 or n - 2 = 0 n = (0)/(2) or n = 2 n = 0 or n = 2 The solutions for n are n=0 or n=2. 2. (c) Use logarithm tables to evaluate: (734.6)/(56.4) Step 1: Let X = (734.6)/(56.4). Take the logarithm of both sides. X = ((734.6)/(56.4)) Using the logarithm property ((A)/(B)) = A - B: X = 734.6 - 56.4 Step 2: Find the logarithm of 734.6. The characteristic is 2 (since there are 3 digits before the decimal point, 3-1=2). From logarithm tables, the mantissa for 734.6 is approximately .8661. 734.6 = 2.8661 Step 3: Find the logarithm of 56.4. The characteristic is 1 (since there are 2 digits before the decimal point, 2-1=1). From logarithm tables, the mantissa for 56.4 is approximately .7513. 56.4 = 1.7513 Step 4: Subtract the logarithms. X = 2.8661 - 1.7513 X = 1.1148 Step 5: Find the antilogarithm of 1.1148. The characteristic is 1, which means there will be 1+1=2 digits before the decimal point in the answer. Look up the mantissa .1148 in the antilogarithm tables. The number corresponding to .1148 is approximately 1300. Placing the decimal point according to the characteristic: X = 13.00 The value is 13.00. What's next?