Let s be the subset of the set of ordered pairs of integers defined recursively by: basis step: (0, 0) ∈ s. recursive step: if (a, b) ∈ s, then (a, b + 1) ∈ s, (a + 1, b + 1) ∈ s, and (a + 2, b + 1) ∈ s. a) list the elements of s produced by the first four applications of the recursive definition. b) use strong induction on the number of applications of the recursive step of the definition to show that a ≤ 2b whenever (a, b) ∈ s. c) use structural induction to show that a ≤ 2b whenever (a, b) ∈ s.

Stefano accidentally dropped his sunglasses off the edge of a canyon as he was looking down. the height, h(t), in meters (as it relates to sea level), of the sunglasses after t seconds, is shown in the table. during its descent, the pair of sunglasses passed by a climber in the canyon 6 seconds after stefano dropped them. to the nearest meter, what is difference in elevation between stefano and the climber? 166 meters 176 meters 230 meters 240 meters its b.176 i took the test 166 is wrong and 176 is correct

Pyotr tchaikovsky sporting goods operates on a 45% overhead based on the selling price, which results in an overhead of $65.34 on the newest version of an air hockey game set. if the air hockey game set costs pyotr tchaikovsky sports $49.32, find the selling price, the markup, and the net profit.

Hardest math question of all time can you solve the equation. check for extraneous solutions.9∣9-8x∣ = 2x+3