Use logarithms to evaluate (58.72 x 406)/(0.845). A farmer fenced a rectangular plot of land. The length of the plot is 3 metres more than its width. Given that the total area of the plot is 180 m2. F

Morning Taydey — let's get this done. Here are the solutions to the questions from the image: 16. Use logarithms to evaluate (58.72 × 406)/(0.845). Step 1: Let N = (58.72 × 406)/(0.845). Step 2: Take the logarithm of both sides. N = (58.72) + (406) - (0.845) Step 3: Find the logarithms of each number using a logarithm table. (58.72) = 1.7690 (406) = 2.6085 (0.845) = 1.9269 Step 4: Perform the addition for the numerator. (58.72 × 406) = 1.7690 + 2.6085 = 4.3775 Step 5: Perform the subtraction. N = 4.3775 - 1.9269 N = 4.3775 - (-1 + 0.9269) N = 4.3775 + 1 - 0.9269 N = 5.3775 - 0.9269 N = 4.4506 Step 6: Find the antilogarithm of 4.4506. Antilog(0.4506) ≈ 2.822 N = 2.822 × 10^4 N = 28220 17. A farmer fenced a rectangular plot of land. The length of the plot is 3 metres more than its width. Given that the total area of the plot is 180 m^2. a) Form quadratic equation to represent this situation. Step 1: Let the width of the plot be w metres. Step 2: The length of the plot is 3 metres more than its width, so the length l = (w + 3) metres. Step 3: The area of a rectangle is given by length × width. Area = l × w Step 4: Substitute the expressions for length and width, and the given area. 180 = (w + 3)w Step 5: Expand the equation. 180 = w^2 + 3w Step 6: Rearrange into the standard quadratic form aw^2 + bw + c = 0. w^2 + 3w - 180 = 0 b) Solve the equation by factorisation method to find the dimensions of the plot. Step 1: Use the quadratic equation from part (a): w^2 + 3w - 180 = 0. Step 2: Find two numbers that multiply to -180 and add up to 3. These numbers are 15 and -12. Step 3: Rewrite the middle term using these numbers. w^2 + 15w - 12w - 180 = 0 Step 4: Factor by grouping. w(w + 15) - 12(w + 15) = 0 (w - 12)(w + 15) = 0 Step 5: Solve for w. w - 12 = 0 or w + 15 = 0 w = 12 or w = -15 Step 6: Since width cannot be negative, we take the positive value for w. w = 12 m Step 7: Calculate the length using l = w + 3. l = 12 + 3 = 15 m The dimensions of the plot are: Width = 12 m Length = 15 m All done! Send me the next one 📸