Evaluate (3)/(sqrt(0.0136)) - (3.72)2 correct to 4 s.f.

Here are the solutions to the problems. 5. Evaluate (3)/(sqrt(0.0136)) - (3.72)^2 correct to 4 s.f. Note: As I do not have access to physical tables, I will perform the calculations directly and round the final answer to 4 significant figures. Step 1: Evaluate sqrt(0.0136). sqrt(0.0136) ≈ 0.11662076 Step 2: Evaluate (3)/(sqrt(0.0136)). (3)/(0.11662076) ≈ 25.72457 Step 3: Evaluate (3.72)^2. (3.72)^2 = 13.8384 Step 4: Perform the subtraction. 25.72457 - 13.8384 = 11.88617 Step 5: Round the result to 4 significant figures. 11.88617 ≈ 11.89 The value is 11.89. 6. Simplify as far as possible (3)/(x-y) - (1)/(x+y) Step 1: Find a common denominator, which is (x-y)(x+y). Step 2: Rewrite each fraction with the common denominator. (3)/(x-y) - (1)/(x+y) = (3(x+y))/((x-y)(x+y)) - (1(x-y))/((x+y)(x-y)) Step 3: Combine the numerators over the common denominator. (3(x+y) - 1(x-y))/((x-y)(x+y)) Step 4: Expand the numerator and the denominator. Numerator: 3x + 3y - x + y = 2x + 4y Denominator: (x-y)(x+y) = x^2 - y^2 Step 5: Write the simplified expression. (2x+4y)/(x^2-y^2) The simplified expression is (2x+4y)/(x^2-y^2). 7. Fifteen men working for eight hours a day can complete a certain job in exactly 24 days. For how many hours a day must sixteen men work in order to complete the same job in exactly 20 days. This is an inverse proportion problem. The total work done is constant. Let M be the number of men, H be the hours per day, and D be the number of days. The total work is proportional to M × H × D. Step 1: Set up the equation based on the given information. M_1 × H_1 × D_1 = M_2 × H_2 × D_2 Given: M_1 = 15 men H_1 = 8 hours/day D_1 = 24 days M_2 = 16 men H_2 = ? hours/day D_2 = 20 days Step 2: Substitute the known values into the equation. 15 × 8 × 24 = 16 × H_2 × 20 Step 3: Calculate the left side of the equation. 15 × 8 × 24 = 120 × 24 = 2880 Step 4: Simplify the equation and solve for H_2. 2880 = 320 × H_2 H_2 = (2880)/(320) H_2 = 9 Sixteen men must work 9 hours a day. The number of hours per day is 9 hours. That's 2 down. 3 left today — send the next one.