Tutor profile: Ashwin R.
Subject: Linear Algebra
Solve the system of linear equations. x + 2y = 0 3x - 5y = 3
The solutions are x = 6/11; y = -3/11 This can be found by finding an expression for y in terms of x in the first equation --> y = -x/2 This value of y is now substituted in the second equation to give --> 11x/2 = 3 --> x = 6/11 This value of x is now substituted in either of the 2 equations to give --> y = -3/11 This solution represents the intersection point of the two lines x + 2y = 0 and 3x - 5y = 3, when drawn on a graph.
This question has two blanks. Given how BLANK the shortcomings of the standard economic model are in its portrayal of human behavior, the failure of many economists to respond to them is astonishing. They continue to fill the journals with yet more proofs of yet more BLANK theorems. Others, by contrast, accept the criticisms as a challenge, seeking to expand the basic model to embrace a wider range of things people do. The options for the blanks are as follows. Blank 1 options: (A. overlooked, B. occasional, C. patent) Blank 2 options: (D. comprehensive, E. improbable, F. pervasive)
The answers for the two blanks are PATENT and IMPROBABLE, respectively. Blank 1: If the shortcomings were OVERLOOKED or OCCASIONAL, it wouldn't be astonishing that many economists aren't responding to them. PATENT means 'obvious', which would be the right fit, since it would be astonishing that economists aren't responding to such an obvious issue. Blank 2: Both COMPREHENSIVE and PERVASIVE imply 'wide-ranging'. If either of these words are used, there would be no contrast between the type of economists being referred to in the 2nd sentence and the type in the 3rd sentence. IMPROBABLE is a good fit, since then the 2nd and 3rd sentences highlight two different schools of thought.
Subject: Mechanical Engineering
In a closed room which is airtight, what happens when a refrigerator is switched on with its door open?
The temperature of the room goes up. This question can be solved by applying basic energy conservation - Energy cannot be created or destroyed, but can be transformed from one form to another. Energy transfer can be through 2 primary forms in thermodynamics - heat and work. When the room is treated as a closed box, the only energy entering it is in the form of electricity supply to the refrigerator through the wall socket. This energy has to be utilized within the room, as heat or work. The refrigerator door, when closed, separates the room from the refrigerated compartment. Here, the electricity is used to drive the compressor which indirectly enables heat transfer from the refrigerated compartment to the room outside, thereby cooling the inside. This is according to the second law of thermodynamics. When the door is left open, there is no separation between the inside of the refrigerator and the room outside. The refrigerator can be visualized as exchanging heat from the room, to the room. But the electricity still has to be utilized in some form, and is seen as an increase in the temperature of the room. This is the same thing that would happen if you kept a window Air-conditioning unit COMPLETELY inside a closed room and switched it on.
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