Reference no: EM132608183

Question 1. What is the graph of 3x² + y² = 18? What are its lines of symmetry? What are the domain and range?

Question 2. Prove that for all integers n > 10,

n - 2 < n² - n/12

Question 3. Solve the equation sin (Π/4 - x) - sin (x + Π/4) = 1 for 0 ≤ x ≤ 2Π. Explain each step and substantiate your conclusions.

Question 4. The office needs cabinets. The price for the first type of cabinet is $10, it needs 6 ft² of floor space, and it has a storage volume of 8 ft³. The price for the second type of cabinet is $20, it needs 8 ft² of floor space, and it has a storage volume of 12 ft³. The company wants to spend no more than $140 and the office can hold up to 72 ft² of cabinets. How can the storage volume be maximized?

Question 5. Prove that 5 +8+ 11 + ..... + (3n + 2) = n(3n + 7)/2 is valid for every positive integer n. Explain each step.