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
Welcome back Diashu — missed you this week. Part i: a) Draw a sketch of the plot. Step 1: Draw a right-angled triangle ABC with the right angle at A. Mark side AB as 10 meters and side AC as 26 meters. Locate point D on side AB such that BD = 3 meters. This means AD = AB - BD = 10 - 3 = 7 meters. Draw a line segment from C to D, and label the angle ACD as . [scale=0.6] (A) at (0,0); (B) at (10,0); (C) at (0,26); (D) at (7,0); % D is on AB, AD = 7, DB = 3 (A) -- (B) node[midway, below] 10 m -- (C) -- cycle; (A) -- (C) node[midway, left] 26 m; (C) -- (D); at (A) [below left] A; at (B) [below right] B; at (C) [above left] C; at (D) [below] D; (0.5,0) -- (0.5,0.5) -- (0,0.5); % Right angle at A at (D) [below] D; at (B) [below] B; at (A) [below] A; (D) -- (A) node[midway, below] 7 m; (B) -- (D) node[midway, below] 3 m; pic["", draw, angle radius=1cm] angle = D--C--A; b) Help him to get the length of the side BC. Step 1: Use the Pythagorean theorem for the right-angled triangle ABC. BC^2 = AB^2 + AC^2 Step 2: Substitute the given values for AB and AC. BC^2 = (10\, m)^2 + (26\, m)^2 BC^2 = 100\, m^2 + 676\, m^2 BC^2 = 776\, m^2 Step 3: Calculate the square root to find BC. BC = sqrt(776)\, m BC ≈ 27.8567\, m BC ≈ 27.86\, m c) Calculate the value of to two decimal places. Step 1: Identify the relevant right-angled triangle, which is ADC. In ADC, the right angle is at A. AD = 7 m (since D is 3 m from B along AB, and AB = 10 m, so AD = 10 - 3 = 7 m). AC = 26 m. Step 2: Use the tangent function to find . () = OppositeAdjacent = (AD)/(AC) Step 3: Substitute the values and calculate . () = (7)/(26) = ((7)/(26)) ≈ 15.0699^ ≈ 15.07^ Part ii: a) Using the bar chart, copy and complete the following table. Step 1: Read the number of bottles for each color from the bar chart. • Red: 25 bottles • Blue: 15 bottles • Green: 28 bottles • Yellow: 20 bottles • Black: 8 bottles • White: 11 bottles | Color | Red | Blue | Green | Yellow | Black | White | |---|---|---|---|---|---|---| | Number of bottles | 25 | 15 | 28 | 20 | 8 | 11 | b) Find the total number of bottles of coloring materials in the workshop. Step 1: Sum the number of bottles for all colors. Total bottles = 25 + 15 + 28 + 20 + 8 + 11 Step 2: Perform the addition. Total bottles = 107 The total number of bottles is 107. c) What is the modal color? Step 1: Identify the color with the highest number of bottles from the table in part a). The highest number of bottles is 28, which corresponds to Green. The modal color is Green. Send me the next one 📸