While walking through a fictional forest, you encounter three trolls guarding a bridge. Each is either a knight, who always tells the truth, or a knave, who always lies. The trolls will not let you pass until you correctly identify each as either a knight or a knave. Each troll makes a single statement: Troll 1: If I am a knave, then there are exactly two knights here.
Troll 2: Troll 1 is lying.
Troll 3: Either we are all knaves or at least one of us is a knight.
Which troll is which?
Answers
Troll 1: Knight
Troll 2: Knave
Troll 3: Knight
The following information should be considered:
- Troll 3's statement should be true since they can only be knights or knaves, till all of them are knaves, at least one must be a knight.
- In the case when Troll 2 is a knight, so Troll 1 is knave, but if that were the case Troll 1's statement should be true, and since knaves do not tell the truth, this assumption is incorrect.
- In the case when Troll 2 is a knave, Troll 1 is a knight and his statement can be disregarded.
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Answer:
Troll 1: Knight
Troll 2: Knave
Troll 3: Knight
Step-by-step explanation:
Troll 3's statement must be true because if they can only be knights or knaves, unless all of them are knaves, at least one must be a knight. Thus, Troll 3 is a knight.
If Troll 2 is a knight, then Troll 1 is knave, but if that were the case Troll 1's statement would be true, and since knaves do not tell the truth, this assumption is incorrect.
If Troll 2 is a knave, Troll 1 is a knight and his statement can be disregarded since it is conditioned to the possibility of him being a knave.
Therefore, Trolls 1 and 3 are knights and Troll 2 is a knave.
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Over the last 100 business days, harry had 20 customers on 30 of those days, 25 customers on 20 days, 35 customers on 30 days, 40 customers on 10 days, and 45 customers on 10 days. what is the variance of the number of harry's customers?
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30°
249
126
Answers
Answer:
30 - Acute
249 - Obtuse
126 - Obtuse
Step-by-step explanation:
Less than 90 - Acute
90 - Right
More than 90 - Obtuse
Answers
1pint ------> 2cups
x -----------> 440 cups
Clearing x we have:
x = (440/2) * (1)
x = 220 pint containers.
Answer:
Paul needs about:
x = 220 pint containers.
440/2 =220
Because 1 pint = 2 cups
Answers
Final answer:
In damped harmonic motion, we calculate damping coefficient γ by comparing the periods of damped and undamped motion. For the given situation where the quasi-period is 90% greater than the undamped period, the damping coefficient is approximately 0.7416.
Explanation:
The subject of this question involves Damped Harmonic Motion, a concept in Physics, related to vibrations and waves. The equation given, u'' + γu' + u = 0, describes the motion where γ denotes the damping coefficient. Here, we have to calculate this damping coefficient when the quasi period of the damped motion is 90% greater than the period of the corresponding undamped motion.
To solve this, we must use the relationship between damped and undamped periods. The quasi-period T' of a damped harmonic motion relates to the undamped period T as: T' = T/(sqrt(1 - (γ/2)^2)). Now, given that T' = 1.9T, we can but these two equations together:
1.9 = 1/(sqrt(1 - (γ/2)^2))
Solving this for γ, we get γ ≈ 0.7416. Hence, the damping coefficient γ for which the quasi period of the damped motion is 90% greater than the period of the corresponding undamped motion is approximately 0.7416.
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Final answer:
The value of the damping coefficient γ for which the quasi period of the damped motion is 90% greater than the period of the undamped motion is the one that satisfies γ=2*ω*0.9, where ω is the natural frequency of oscillation.
Explanation:
The given equation is for a damped harmonic oscillator, a physical system that oscillates under both a restoring force and a damping force proportional to the velocity of the system. The damping coefficient γ determines the behavior of the system and in this case, we need to find the value of γ such that the quasi period of the damped motion is 90% greater than the period of the undamped motion.
The period of the undamped motion, T₀, is calculated by the formula T₀=2π/sqrt(ω), where ω is the natural frequency of oscillation. The quasi period of the damped motion, Td, is increased by a factor of 1+η (in this case, 1.9 as the increase is 90%) and calculated by the formula Td=T₀(1+η) = T₀*1.9.
The damping ratio η is determined by the damping coefficient γ as η=γ/2ω. Therefore, by combining these expressions and rearranging the terms, we extract γ from these formulas as γ=2ω*η => γ=2*ω*(0.9). Thus, the value of the damping coefficient γ for which the quasi period of the damped motion is 90% greater than the period of the corresponding undamped motion is the one which satisfies γ=2*ω*0.9.
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Answers
11 members and we have to pick three without replacement.
= 165
There are 165 possible sets of officers
Answers
Answer:
x + 3.5
Step-by-step explanation:
You are adding
hopefully this helps you:)