# Tutor profile: Sag P.

## Questions

### Subject: SAT

Albert is staying at a hotel that charges $200 per night plus tax for a room. A tax of 9% is applied to the room rate, and an additional onetime untaxed fee of $11.00 is charged by the hotel. What is the total charge, in dollars, for staying x nights?

109/100 (200x) + 11 = 1.09 (200x) + 11 = 218x + 11

### Subject: Applied Mathematics

An archer is practicing archery. He may hit the target A with a probability of 0.7 and target B with a probability of 0.2, and the probability that he misses his shot is 0.1. If he hits the target, A, he may earn a reward prize with probability 0.4 and if he hits the target B, he may earn a reward with probability 0.5. If he did earn the reward, find the probability that it was by hitting target A.

Event A: He hits the Target A Event B: He hits the Target B Event M: He misses. Event R: He earns the reward. Total probability of the archer earning the reward is: P(A)PR/A) + P(B)P(R/B) + P(M)P(R/M) = (0.7)(0.4) + (0.2)(0.5) + (0.1)(0.0) = 0.28 + 0.1 = 0.38 Probability that he hit A, given the fact that he did earn a reward, as per Baye's theorem of apriori probabilities is P (A/R) = P(A) [P(R/A)] / P(A)P(R/A) + P(B)P(R/B) + P(M)P(R/M) = 0.28 / 0.38 = 0.737 That is our final answer.

### Subject: Physics

There is a block of mass m = 2 kgs, moving with a velocity 10 m/s kept on the ground as seen from a stationary reference frame. Friction exists and due to the friction on the ground. the block stops moving. Case 1: We observe from a reference frame that has zero velocity. The loss of kinetic energy is \frac{1}2{}mv^{2} = 100 J. Due to the friction on the ground. the entire 100 J energy is dissipated, thus resulting in 100 J of thermal effects - say the warming of the surrounding air, which is measured by a thermometer kept nearby. Case2: When this same phenomenon was observed from a reference frame moving with a velocity of 5 m/s say in a car that was moving at 5 m/s velocity, it was seen that the initial velocity of the block was 5 m/s and after the block stopped, it was -5 m/s. The change in KE was 0 in this second case, and thus the kinetic energy dissipated was zero. The ambient thermometer in this case doesn't register any temperature rise. As per the Work - Kinetic Energy Theorem, the work done by friction force (which is the only horizontal force present in the situation) should be equal to the change in the kinetic energy of the system. In Case 1, 100 J of heat was released, in Case 2, 0 J of heat was released, however, when we note that we are talking about the very same phenomenon, we ought to get the very same amount of heat evolved as the answer. Explain the discrepancy.

This situation is a classic illustration of an assumption gone wrong. If we assume the block on earth to be a block on block type of a system, and then solve for the heat evolved, considering momentum conservation and Heat = change in KE of the entire system, we get the same answer. by looking at the system from either reference frame. Here, its a mistake to assume that the earth is stationary.

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