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Initially m and m and the pulley are at rest and the spring k n m is at its


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1.When 15.0 mL of 3.00 M NaOH was mixed in a calorimeter with 13.0 mL of 3.00 M HCl, both ...

room temperature (22.0 °C), the temperature increased to 29.1 °C. The resultant salt solution had a mass of 18.00 g and a specific heat capacity of 3.74 J K-1 g-1. What is the heat capacity of the calorimeter (in J/°C)? Note: The molar enthalpy of neutralization per mole of HCl is -55.84 kJ mol-1.
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2.A mathematician diagnosed with schizophrenia is fooling himself by playing with a list L containing n distinct integers in just his ...

ng n distinct integers in just his thoughts. He plays turns on the list. In each turn he does the following– He takes a number (in its index’s order ) and swap it with any number in the list including itself i.e. if it swap it with itself it doesn’t move at all (The selection of the number is completely random). He does the same for all the elements in their index’s order in that turn. If initially the list was unsorted, such that, no element was in sorted position, then find the probability that the list is sorted after m such turns. Note : Take the assumption that if an element is not in its sorted position then it can be in any other n − 1 positions equally likely.
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3.. A uniform cylinder of mass M and radius R is initially at rest on a rough horizontal surface. A ...

ght string is wrapped around the cylinder and is pulled straight up with a force T whose magnitude is 0.8 Mg. As a result, the cylinder slips and accelerates horizontally. The moment of inertia of the cylinder is I = 12 MR2 and the coefficient of kinetic friction is 0.4. a. On the diagram above show all the forces applied on the cylinder. b. Determine the linear acceleration a of the center of the cylinder. c. Determine the angular acceleration α of the cylinder. d. Explain the difference in results of linear acceleration a and αR.
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

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