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: Find the length of AC using the Pythagorean theorem in ABC. Since ABC = 90^, we have: AC^2 = AB^2 + BC^2 AC^2 = (3 cm)^2 + (4 cm)^2 AC^2 = 9 cm^2 + 16 cm^2 AC^2 = 25 cm^2 AC = sqrt(25 cm)^2 AC = 5 cm Step 2: Find the length of CD using the Pythagorean theorem in ACD. Since ACD = 90^, we have: AD^2 = AC^2 + CD^2 (13 cm)^2 = (5 cm)^2 + CD^2 169 cm^2 = 25 cm^2 + CD^2 CD^2 = 169 cm^2 - 25 cm^2 CD^2 = 144 cm^2 CD = sqrt(144 cm)^2 CD = 12 cm i. The length of CD is 12 cm. Step 3: Find (angle ADC). In ACD, ACD = 90^. The side opposite to ADC is AC. The side adjacent to ADC is CD. ( ADC) = oppositeadjacent = (AC)/(CD) ( ADC) = 5 cm12 cm ( ADC) = (5)/(12) ii. The value of (angle ADC) is (5)/(12). b) Step 1: Calculate the depreciation amount. Depreciation = 15% of GH¢ 6,500.00 Depreciation = 0.15 × GH¢ 6,500.00 Depreciation = GH¢ 975.00 Step 2: Calculate the value of the car after one year. Value after one year = Original value - Depreciation Value after one year = GH¢ 6,500.00 - GH¢ 975.00 Value after one year = GH¢ 5,525.00 The value of the car after one year is GH¢ 5,525.00. c) Step 1: Substitute the given values of a and b into the expression 2a - 3b. Given a = (1)/(3) and b = -(1)/(2). 2a - 3b = 2((1)/(3)) - 3(-(1)/(2)) Step 2: Simplify the expression. 2a - 3b = (2)/(3) - (-(3)/(2)) 2a - 3b = (2)/(3) + (3)/(2) Step 3: Add the fractions by finding a common denominator. The least common multiple of 3 and 2 is 6. 2a - 3b = (2 × 2)/(3 × 2) + (3 × 3)/(2 × 3) 2a - 3b = (4)/(6) + (9)/(6) 2a - 3b = (4+9)/(6) 2a - 3b = (13)/(6) The value of the expression is (13)/(6).