Evaluate the following expressions: Problem 45: (0.1)2 - (0.01)2 / 0.0001 + 1. Problem 46: 3.25 3.20 - 3.20 3.05 / 0.064. Problem 47: (0.6)4 - (0.5)4 / (0.6)2 + (0.5)2.

Welcome back rahul970871 — been a while! Let's pick up where you left off. Here are the solutions to the problems: Problem 45: We need to evaluate the expression ((0.1)^2 - (0.01)^2)/(0.0001) + 1. Step 1: Calculate the squares in the numerator. (0.1)^2 = 0.01 (0.01)^2 = 0.0001 Step 2: Substitute these values into the expression. (0.01 - 0.0001)/(0.0001) + 1 Step 3: Perform the subtraction in the numerator. 0.01 - 0.0001 = 0.0099 Step 4: Perform the division. (0.0099)/(0.0001) = 99 Step 5: Add 1 to the result. 99 + 1 = 100 The correct option is (d). The final answer is 100. Problem 46: We need to evaluate the expression (3.25 × 3.20 - 3.20 × 3.05)/(0.064). Step 1: Factor out the common term 3.20 from the numerator. 3.20 × (3.25 - 3.05) Step 2: Perform the subtraction inside the parenthesis. 3.25 - 3.05 = 0.20 Step 3: Substitute this back into the numerator and calculate the product. 3.20 × 0.20 = 0.64 Step 4: Perform the division. (0.64)/(0.064) = 10 The correct option is (d). The final answer is 10. Problem 47: We need to evaluate the expression ((0.6)^4 - (0.5)^4)/((0.6)^2 + (0.5)^2). Step 1: Apply the difference of squares formula, a^2 - b^2 = (a-b)(a+b), to the numerator. Here, a = (0.6)^2 and b = (0.5)^2. (0.6)^4 - (0.5)^4 = ((0.6)^2)^2 - ((0.5)^2)^2 = ((0.6)^2 - (0.5)^2)((0.6)^2 + (0.5)^2) Step 2: Substitute this back into the expression. (((0.6)^2 - (0.5)^2)((0.6)^2 + (0.5)^2))/((0.6)^2 + (0.5)^2) Step 3: Cancel out the common term ((0.6)^2 + (0.5)^2) from the numerator and denominator. (0.6)^2 - (0.5)^2 Step 4: Calculate the squares. (0.6)^2 = 0.36 (0.5)^2 = 0.25 Step 5: Perform the subtraction. 0.36 - 0.25 = 0.11 The correct option is (c). The final answer is 0.11. Send me the next one 📸