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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Here are the solutions to the problems you've provided. Question 1: Make r the subject of the relation y = (r-1)/(r+1) and find the value of r when y = 1. Step 1: Multiply both sides of the equation by (r+1) to remove the denominator. y(r+1) = r-1 yr + y = r-1 Step 2: Gather all terms containing r on one side of the equation and all other terms on the opposite side. yr - r = -1 - y Step 3: Factor out r from the terms on the left side. r(y-1) = -(1+y) Step 4: Divide both sides by (y-1) to make r the subject. r = (-(1+y))/(y-1) r = (1+y)/(1-y) The expression for r is r = (1+y)/(1-y). Step 5: Find the value of r when y=1. Substitute y=1 into the expression for r. r = (1+1)/(1-1) = (2)/(0) Division by zero is undefined. Therefore, there is no value of r for which y=1. The value of r when y=1 is undefined. Question 2: A woman bought 240 tubers of yam for GH¢1200.00. She later sold all of them at 5 for GH¢20.00. Find her percentage profit. Step 1: Calculate the selling price of one tuber of yam. Selling Price per tuber = GH¢20.005 tubers = GH¢4.00/tuber Step 2: Calculate the total selling price for all 240 tubers. Total Selling Price = 240 tubers × GH¢4.00/tuber = GH¢960.00 Step 3: Calculate the profit or loss. Profit/Loss = Total Selling Price - Cost Price Profit/Loss = GH¢960.00 - GH¢1200.00 = -GH¢240.00 Since the result is negative, the woman incurred a loss of GH¢240.00. Step 4: Calculate the percentage profit (which will be a negative value, indicating a loss). Percentage Profit = Profit/LossCost Price × 100\% Percentage Profit = -GH¢240.00GH¢1200.00 × 100\% = -0.2 × 100\% = -20\% The woman made a 20% loss. Question 3: Transformations of triangle PQR with P(2, 3), Q(6, 5), R(2, 5). iii) Draw the image P₁Q₁R₁ of triangle PQR under enlargement with scale factor 2 from the origin. For an enlargement from the origin with scale factor k, a point (x, y) maps to (kx, ky). • P₁: (2 × 2, 3 × 2) = (4, 6) • Q₁: (6 × 2, 5 × 2) = (12, 10) • R₁: $(2 × 2, 5 \ ✂️ _That answer was long and got cut off. Reply continue and I'll finish it._