Question 1 What is the square root of 16? Answer 1 The square root of a number means what number squared equals the number. Therefore, we know that 4 × 4 = 16 4×4=16, so the square root of 16 is 4. Question 2 Divide 1 4 ÷ 3 4 1 ÷3. Answer 1 Dividing by a number is the same as multiplying by its reciprocal. Since the reciprocal of 3 is 1 3 3 1 , then: 1 4 ÷ 3 = 1 4 × 1 3 = 1 × 1 4 × 3 = 1 12 4 1 ÷3= 4 1 × 3 1 = 4×3 1×1 = 12 1 Therefore, 1 4 ÷ 3 = 1 12 4 1 ÷3= 12 1 . Question 3 A scuba diver dove from the surface of the ocean to an elevation of − 79 9 10 −79 10 9 feet at a rate of − 18.8 −18.8 feet per minute. After spending 12.75 12.75 minutes at that elevation, the diver ascended to an elevation of − 28 9 10 −28 10 9 feet. The total time for the dive so far was 19 1 8 19 8 1 minutes. What was the rate of change in the diver's elevation during the ascent? Answer 1 Calculate the change in elevation during the ascent: Change in elevation = final elevation − initial elevation Change in elevation=final elevation−initial elevation Final elevation = − 28 9 10 −28 10 9 , Initial elevation = − 79 9 10 −79 10 9 . = − 28.9 − ( − 79.9 ) = − 28.9 + 79.9 = 51 feet =−28.9−(−79.9)=−28.9+79.9=51 feet Calculate the time spent ascending: Total time of the dive = 19 1 8 19 8 1 minutes, Time spent at elevation = 12.75 12.75 minutes, so: Time to ascend = 19.125 − 12.75 = 6.375 minutes Time to ascend=19.125−12.75=6.375 minutes Calculate the rate of change in elevation during ascent: Rate = change in elevation time = 51 6.375 ≈ 8 feet per minute Rate= time change in elevation = 6.375 51 ≈8 feet per minute Result: The rate of change in the diver's elevation during the ascent was approximately 8 feet per minute. Question 4 Consider each set of numbers and determine if the set has an additive identity, additive inverse, multiplicative identity, or a multiplicative inverse. Explain your reasoning for each. a. The set of natural numbers. Answer 1 Additive Identity: The set of natural numbers does not have an additive identity because natural numbers start from 1, and the additive identity is 0 (since 𝑎 + 0 = 𝑎 a+0=a) which is not included in natural numbers. Additive Inverse: The set of natural numbers does not have an additive inverse because adding a negative number to make the sum zero would require integers, not just natural numbers. For example, the additive inverse of 1 is -1, which is not a natural number. Multiplicative Identity: The multiplicative identity is 1 (since 𝑎 × 1 = 𝑎 a×1=a), which is included in the set of natural numbers. Therefore, natural numbers do have a multiplicative identity. Multiplicative Inverse: The set of natural numbers does not have a multiplicative inverse. For example, the inverse of 2 would be 1 2 2 1 , which is not a natural number. Conclusion: The set of natural numbers has a multiplicative identity but lacks an additive identity, additive inverse, and multiplicative inverse.