Two brothers build a pyramid-shaped fort. If the fort is 8 feet wide at its base, what expression could be used to calculate the
2 answers:
Answer:
Step-by-step explanation:
We know that the base is 8 feet wide. The height of the pyramid is at the middle of this width, which forms a right triangle, with the angles formed by one side of the pyramid and the base.
Now, to find the expression of the height, we can use these given information and the trigonometric reasons. Specifically, we would use the tangent from the trigonometric reasons, because the height is the opposite leg to the angle, and the adjacent leg would be 4. So, the expression would be:
Therefore, the expression is
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Answer:
Step-by-step explanation:
a) The game tree for k = 5 has been drawn in the uploaded picture below where C stands for continuing and S stands for stopping:
b) Say we were to use backward induction we can clearly observe that stopping is optimal decision for each player in every round. Starting from last round, if player 1 stops he gets $3 otherwise zero if continues. Hence strategy S is optimal there.
Given this, player 2’s payoff to C is $3, while stopping yields $4, so second player will also chooses to stop. To which, player 1’s payoff in k = 3 from C is $1 and her payoff from S is $2, so she stops.
Given that, player 2 would stop in k = 2, which means that player 1 would stop also in k = 1.
The sub game perfect equilibrium is therefore the profile of strategies where both players always stop: (S, S, S) for player 1, and (S, S) for player 2.
c) Irrespective of whether both players would be better off if they could play the game for several rounds, neither can credibly commit to not stopping when given a chance, and so they both end up with small payoffs.
i hope this helps, cheers
