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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Alright PRECIOUS — let's do this. This problem involves distances and directions, which can be represented using vectors or a right-angled triangle. 11. Mr Niba lives 400 m due east of a school while Mr Ako lives due south of the same school. The direct distance between two residences is 500 m. a) Draw a vector diagram to represent this information. Step 1: Establish a reference point. Let the school be at the origin (0,0). Step 2: Represent Mr. Niba's position. Mr. Niba lives 400 m due east of the school. We can represent this as a vector pointing 400 m along the positive x-axis. Let Niba's house be point N. N = (400, 0) Step 3: Represent Mr. Ako's position. Mr. Ako lives due south of the school. This means he is along the negative y-axis. Let Ako's house be point A. A = (0, -y) for some distance y. Step 4: Represent the direct distance between them. The direct distance between Niba's house and Ako's house is 500 m. This forms the hypotenuse of a right-angled triangle with the school at the right angle. School (S) at (0,0) \\ Niba's house (N) at (400,0) \\ Ako's house (A) at (0,-y) The vector diagram would show: • A point for the school at the origin. • A line segment from the school to Niba's house, 400 m long, pointing right (East). • A line segment from the school to Ako's house, y m long, pointing down (South). • A line segment connecting Niba's house and Ako's house, 500 m long, forming the hypotenuse. b) Find the distance covered by Ako's child to reach the school. Step 1: Identify the sides of the right-angled triangle. The school, Mr. Niba's house, and Mr. Ako's house form a right-angled triangle. • One leg is the distance from the school to Niba's house: 400 m. • The other leg is the distance from the school to Ako's house: Let this be x m. • The hypotenuse is the direct distance between Niba's and Ako's houses: 500 m. Step 2: Apply the Pythagorean theorem. The Pythagorean theorem states that for a right-angled triangle, a^2 + b^2 = c^2, where a and b are the lengths of the legs and c is the length of the hypotenuse. (400)^2 + x^2 = (500)^2 Step 3: Solve for x. 160000 + x^2 = 250000 x^2 = 250000 - 160000 x^2 = 90000 x = sqrt(90000) x = 300 The distance covered by Ako's child to reach the school is 300 m. The distance covered by Ako's child to reach the school is 300 m. Send me the next one 📸