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.
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Haya hapa masuluhisho ya maswali uliyotoa: 1. Using mathematical tables, find the reciprocal of 0.5641, hence evaluate sqrt(0.0441)0.5641. Step 1: Find the reciprocal of 0.5641. The reciprocal of 0.5641 is (1)/(0.5641). Using a calculator (or mathematical tables for reciprocals): (1)/(0.5641) ≈ 1.772735 Step 2: Find the square root of 0.0441. Using a calculator (or mathematical tables for square roots): sqrt(0.0441) = 0.21 Step 3: Evaluate the expression. Substitute the values found in Step 1 and Step 2 into the expression: sqrt(0.0441)0.5641 = (0.21)/(0.5641) This can also be written as 0.21 × (1)/(0.5641). 0.21 × 1.772735 ≈ 0.372274 Rounding to four decimal places: (0.21)/(0.5641) ≈ 0.3723 The final answer is 0.3723 2. In the diagram below, XY is a transverse tangent to the circles whose centres are A and B with radii 20cm and 12cm respectively. The distance between centres A and B is 40cm. Calculate the length of tangent XY. Step 1: Identify the given values. Radius of circle A, R_1 = 20 cm. Radius of circle B, R_2 = 12 cm. Distance between centres A and B, D = 40 cm. We need to find the length of the transverse common tangent, L = XY. Step 2: Use the formula for the length of a transverse common tangent. The formula for the length of a transverse common tangent is: L = sqrt(D^2 - (R_1 + R_2)^2) Step 3: Substitute the values and calculate. L = sqrt(40^2 - (20 + 12)^2) L = sqrt(40^2 - 32^2) L = sqrt(1600 - 1024) L = sqrt(576) L = 24 cm The final answer is 24 cm 3. The figure below shows a right pyramid on a square base of side 10cm. The slant length of the pyramid is 13cm. X is the mid-point of RS and OY is the perpendicular height of the pyramid. Calculate the height of the pyramid. Step 1: Identify the given information from the figure and text. The base PQRS is a square with side length = 10 cm. The slant edge YS = 13 cm (as indicated in the diagram). OY is the perpendicular height of the pyramid. O is the center of the square base. Step 2: Calculate the length of OS. O is the center of the square base. OS is half the length