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
Hey Cecilia — ready when you are. a) (ii) Step 1: Substitute the given values of m and n into the expression. Given m = 2 and n = (2)/(3). The expression is m^2(n-1). 2^2 ((2)/(3) - 1) Step 2: Calculate the term inside the parenthesis. (2)/(3) - 1 = (2)/(3) - (3)/(3) = -(1)/(3) Step 3: Calculate m^2. 2^2 = 4 Step 4: Multiply the results. 4 × (-(1)/(3)) = -(4)/(3) The value of m^2(n-1) is -(4)/(3). b) (i) Step 1: Identify the radii of the inner tube and the outer insulating material. Inner diameter = 7 cm, so inner radius r_1 = (7)/(2) cm = 3.5 cm. Outer diameter (total diameter including insulation) = 14 cm, so outer radius r_2 = (14)/(2) cm = 7 cm. Step 2: Calculate the area occupied by the outer material. This is the area of the larger circle minus the area of the smaller circle. The formula for the area of a circle is A = r^2. Area of outer material = r_2^2 - r_1^2 = (r_2^2 - r_1^2). Step 3: Substitute the values and calculate, using = 3.14. Area = 3.14 × (7^2 - 3.5^2) Area = 3.14 × (49 - 12.25) Area = 3.14 × 36.75 Area = 115.495 cm^2 The total area occupied by the outer material is 115.495 cm^2. b) (ii) Step 1: Use the area calculated in part (b)(i). Area of outer material = 115.495 cm^2. Step 2: Calculate the total cost by multiplying the area by the cost per cm^2. Cost per cm^2 = GHe 2.00. Total cost = 115.495 cm^2 × GHe 2.00/cm^2 Total cost = GHe 230.99 The total cost to install the outer material is GHe 230.99. What's next?