Find the derivative of the curve y = x2 - 2x + 6.

You're on a roll — here are the answers to your questions: 12. To find the coordinates of the point on the curve where the gradient is 4: Step 1: Find the derivative of the curve y = x^2 - 2x + 6. The gradient function, (dy)/(dx), is found by differentiating the equation with respect to x. (dy)/(dx) = (d)/(dx)(x^2 - 2x + 6) (dy)/(dx) = 2x - 2 Step 2: Set the gradient equal to 4 and solve for x. 2x - 2 = 4 2x = 4 + 2 2x = 6 x = (6)/(2) x = 3 Step 3: Substitute the value of x back into the original curve equation to find the corresponding y coordinate. y = x^2 - 2x + 6 y = (3)^2 - 2(3) + 6 y = 9 - 6 + 6 y = 9 Step 4: State the coordinates of the point. The coordinates of the point are (x, y) = (3, 9). The coordinates are (3, 9). 13. To find the number of Sh 50 notes and Sh 20 coins: Step 1: Define variables. Let n be the number of Sh 50 notes. Let c be the number of Sh 20 coins. Step 2: Formulate equations based on the given conditions. Condition 1: She has 3 times as many Sh 20 coins as Sh 50 notes. c = 3n (1) Condition 2: Altogether she has Sh 3400. The total value is the sum of the value of notes and coins. 50n + 20c = 3400 (2) Step 3: Solve the system of equations. Substitute equation (1) into equation (2): 50n + 20(3n) = 3400 50n + 60n = 3400 110n = 3400 n = (3400)/(110) n = (340)/(11) n = 30.909... There seems to be an issue with the numbers provided in the question, as the number of notes/coins must be an integer. Let's re-check the calculation. If n must be an integer, then 3400 must be divisible by 110. 3400/110 = 340/11, which is not an integer. Assuming there might be a typo in the total amount or the ratio, and proceeding with the given numbers to show the method. If the total amount was, for example, Sh 3300, then n = 3300/110 = 30. Let's assume the total amount was intended to be Sh 3300 for integer results. If 110n = 3300, then n = 30. Then c = 3n = 3(30) = 90. Number of Sh 50 notes = 30, Number of Sh 20 coins = 90. Total value = 50(30) + 20(90) = 1500 + 1800 = 3300. Given the exact numbers in the problem, an integer solution for the number of notes/coins is not possible. This indicates a potential error in the problem statement itself. However, if we must provide an answer based on the given numbers: n = (3400)/(110) ≈ 30.91 c = 3n = 3 × (3400)/(110) = (10200)/(110) ≈ 92.73 Since the number of notes and coins must be whole numbers, this problem as stated does not yield an integer solution. If we assume the total amount was Sh 3300: Number of Sh 50 notes: 30 Number of Sh 20 coins: 90 (Note: This assumes a slight adjustment to the total amount to allow for integer counts of notes/coins.) 14. To find how many days the remaining workers would take to complete the work: Step 1: Calculate the total amount of work in "worker-days". Initial workers = 45 Initial days to complete = 10 Total Work = 45 workers × 10 days = 450 worker-days Step 2: Calculate the amount of work done in the first 4 days. Workers for the first 4 days = 45 Days worked = 4 Work Done = 45 workers × 4 days = 180 worker-days Step 3: Calculate the remaining work. Remaining Work = Total Work - Work Done Remaining Work = 450 worker-days - 180 worker-days = 270 worker-days Step 4: Determine the number of remaining workers. Initial workers = 45 Workers laid off = 15 Remaining Workers = 45 - 15 = 30 workers Step 5: Calculate the number of days the remaining workers will take to complete the remaining work. Days Needed = Remaining WorkRemaining Workers Days Needed = 270 worker-days30 workers = 9 days The remaining workers would take 9 days to complete the work. Send me the next one 📸