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
Here are the solutions to the problems you've provided: 1.i) Equation of the line CD Step 1: Identify the coordinates of points C and D. From the given information, C is (6, 0) and D is (8, 0). Step 2: Calculate the slope of the line CD. The slope m is given by the formula m = (y_2 - y_1)/(x_2 - x_1). m = (0 - 0)/(8 - 6) = (0)/(2) = 0 Step 3: Write the equation of the line. Since the slope is 0, the line is horizontal. The equation of a horizontal line is y = k, where k is the y-coordinate of any point on the line. Both C and D have a y-coordinate of 0. The equation of the line CD is y = 0. 1.ii) Distance AB Step 1: Identify the coordinates of points A and B. From the given information, A is (0, 7) and B is (0, 2). Step 2: Calculate the distance between A and B. The distance d between two points (x_1, y_1) and (x_2, y_2) is given by the formula d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2). d_AB = sqrt((0 - 0)^2 + (2 - 7)^2) d_AB = sqrt(0^2 + (-5)^2) d_AB = sqrt(0 + 25) d_AB = sqrt(25) The distance AB is 5 units. 2. Calculate the value of k Step 1: Identify the given points and gradient. The points are (6, k) and (k, 10). The gradient m is 2. Step 2: Use the gradient formula to set up an equation for k. The gradient formula is m = (y_2 - y_1)/(x_2 - x_1). 2 = (10 - k)/(k - 6) Step 3: Solve the equation for k. Multiply both sides by (k - 6): 2(k - 6) = 10 - k 2k - 12 = 10 - k Add k to both sides: 3k - 12 = 10 Add 12 to both sides: 3k = 22 Divide by 3: k = (22)/(3) The value of k is (22)/(3). 3. The image provides a sketch of the curve y = x(x-2) but does not state a specific question to be solved for this part. Therefore, I cannot provide a solution for question 3. Send me the next one 📸