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Prove that if a statement can be proved by strong mathematical induction, then it can be proved by ordinary mathematical induction. To do this, let P(n) be a property that is defined for integers n, and suppose the following two statements are true:
1. P(a), P(a + 1), P(a + 2), . . . , P(b).
2. For any integer k ≥ b, if P(i) is true for all integers i from a through k, then P(k + 1) is true. The principle of strong mathematical induction would allow us to conclude immediately that P(n) is true for all integers n ≥ a. Can we reach the same conclusion using the principle of ordinary mathematical induction? Yes! To see this, let Q(n) be the property P(j) is true for all integers j with a ≤ j ≤ n. Then use ordinary mathematical induction to show that Q(n) is true for all integers n ≥ b. That is, prove
1. Q(b) is true. 2. For any integer k ≥ b, if Q(k) is true then Q(k + 1) is true.
Given two chickens in a flock, one of them is dominant. This defines the pecking order of the flock. How can a tournament be used to model pecking order?
manufacturer of mp3 players is preparing to set the price on a new model.demand is thought to depend on the price and
the speed of a stream is 6 mph. if a boat travels 54 miles downstream in the same time that it takes to travel 27 miles upstream, what is the speed of the boat in still water?
Provide a real-world example that shows 2 related sets. List all the members of your sets in set notation. A set can consist of individuals, objects
why the set {T (v1), T (v2), T (v3)} is linearly dependent.
before 1918 approximatelynbsp60nbspof the wolves in the new mexico and arizona region were male andnbsp40nbspwere
The length of time employees have worked at a corporation is normally distributed, with a mean of 11.2 years & sd of 2.1 years. In a company cutback, the lowest 5% in seniority are laid off. What is the maximum length of time an employee could hav..
Find the equation for the plane tangent to the paraboloid z = 2x2 + 3y2 that is also parallel to the plane 4x - 3y - z = 10
Coffee is being poured into the mug at a constant rate. Sketch a graph of the depth of the coffee in the mug as a function of time. Account for the shape of the graph in terms of concavity.
A rope connects two poles that are 80 feet apart. The function .02x^2+15 models the height the rope is above the ground
If the silo is 90 ft high and the man makes exactly three complete revolutions, how much work is done by the man against gravity in climbing to the top?
A motorboat travels 469km in 7 hours going upstream. It travels 493km going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
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