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: c. Solve the following equations, correct to one decimal place: (ii) 5 - 1 = 0, where 0 90^ Step 1: Isolate . 5 - 1 = 0 5 = 1 = (1)/(5) Step 2: Find the value of . = ^-1((1)/(5)) ≈ 78.463^ Step 3: Round to one decimal place. ≈ 78.5^ The value 78.5^ is within the range 0^ 90^. The final answer is 78.5^. 11a. Calculate, correct to 3 s.f. the area of the minor segment cut-off by XY. Step 1: Identify the given values. Radius r = 5 cm. Angle subtended at the centre = 96^. = (22)/(7). Step 2: Calculate the area of the sector OXY. The formula for the area of a sector is ()/(360^) r^2. Area of sector = (96)/(360) × (22)/(7) × (5)^2 Area of sector = (96)/(360) × (22)/(7) × 25 Area of sector = (440)/(21) ≈ 20.95238 cm^2 Step 3: Calculate the area of the triangle OXY. The formula for the area of a triangle with two sides and the included angle is (1)/(2) r^2 . Area of triangle = (1)/(2) × (5)^2 × (96^) Area of triangle = (1)/(2) × 25 × (96^) Area of triangle ≈ 12.5 × 0.994521 ≈ 12.43151 cm^2 Step 4: Calculate the area of the minor segment. Area of minor segment = Area of sector - Area of triangle. Area of segment ≈ 20.95238 - 12.43151 Area of segment ≈ 8.52087 cm^2 Step 5: Round the answer to 3 significant figures. Area of segment ≈ 8.52 cm