Suppose s is a recursively defined set, defined by - the number 1 is in s - if n is in s, then so is 3n + 2 - if n is in s, then so is 5n - 1 - if n is in s, then so is n + 7. suppose you want to prove using structural induction that all members of s have a certain property. what do you have to prove in the base step?

The graph shows the distance y, in inches, a pendulum moves to the right (positive displacement) and to the left (negative displacement), for a given number of seconds x. how many seconds are required for the pendulum to move from its resting position and return? enter your answer in the box.

Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).

Find the value of x. give reasons to justify your solutions! c ∈ ae