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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Fresh day Oliverkoome@gmail254.Com., let's solve. 10. The figure shows a circle with tangents CP and CQ at points P and Q respectively. The circle is to be inscribed in a triangle ABC, where point B lies on CQ produced and CBA = 90^. a) Locate point O, the centre of the circle. Step 1: The center of an inscribed circle is equidistant from the sides of the triangle. Since CP and CQ are tangents from C, the center O must lie on the angle bisector of PCQ. Step 2: Since the circle is tangent to CQ at Q, the radius OQ is perpendicular to CQ. Therefore, draw a line perpendicular to CQ at point Q. This line passes through O. Step 3: The intersection of the angle bisector of PCQ and the perpendicular line from Q is the center O. b) Complete triangle ABC. Step 1: Measure the radius of the circle, which is the length OQ. Step 2: Since CBA = 90^ and the circle is tangent to BC at Q, the distance BQ must be equal to the radius OQ. Mark point B on the line CQ such that BQ = OQ and B is to the left of Q (as B lies on CQ produced). Step 3: From point B, draw a line perpendicular to CQ. This line represents the side AB of the triangle. Step 4: Extend the line CP. The intersection of line AB and line CP is point A. Step 5: Connect points A, B, and C to complete triangle ABC. 11. The deviations of the masses of 10 students from an assumed mean are: -10, -5, -2, 1, 4, 5, 7, 8, 9, 13. The mass of the heaviest student was 58 kg. Calculate the mean mass of the students. Step 1: Calculate the sum of the deviations ( d). d = -10 + (-5) + (-2) + 1 + 4 + 5 + 7 + 8 + 9 + 13 d = -17 + 47 d = 30 Step 2: Determine the assumed mean (A). The heaviest student has the largest positive deviation, which is 13. Let x_heaviest be the mass of the heaviest student. The deviation d_heaviest = x_heaviest - A. Given x_heaviest = 58 kg and d_heaviest = 13. 13 = 58 - A A = 58 - 13 A = 45 kg Step 3: Calculate the mean mass (x) using the formula x = A + ( d)/(n). Here, n = 10 (number of students). x = 45 + (30)/(10) x = 45 + 3 x = 48 kg The mean mass of the students is: 48 kg Got more? Send 'em!