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Sample Answer to largest area question: "Geometry" 1) 1st triangle is equilateral (3 sides are equal), therefore all angles are = 60 degrees. 2nd area of triangle = 0.5*base*height 3rd height = the projection of one side on the perpendicular line to any of the other two sides= (1/3) sin 60, therefore, area = 0.5*1/3*1/3*sin60= 0.0481 units^2 2)Area of square= side^2= (1/4) ^2=1/16=0.0625 units^2 3)1st Penta= 5 in latin 2rd sum of angles in pentagon=540 degrees. Therefore,each angle is 108 degrees 3rd the area of a regular pentagon= (5/4)*(side^2)*tan(54)=2.7 units^2 4) Area of circle= pi*radius^2= (22/7)*(0.5^2)=0.785 units^2 Therefore, the correct answer is 3) the pentagon, :)

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I have a PhD degree in Physics and Chemistry, I can do this job. Please review my answer for 5 questions. Q1: A container is kept at temperature of 400K. It contains 1L of Oxygen and 2L of Hydrogen. The pressure in the container is 735 Torr. The gas ignites and all Oxygen and Hydrogen react to create water vapor. What will be the pressure in the container after the ignition? A1:490 Torr Because P1V1=n1RT1, P2V2=n2RT2 Where T1=T2=400 K, n2=n1*2/3 (due to 2H2+1O2=2H2O) , V1=V2=3 L, P1=735 torr. So P2=n2RT2/V2=n1RT1/V1*2/3=P1*2/3=490 Torr. Q2: One balloon contains 2 Liters of Nitrogen at a pressure of 735 Torr. Another Balloon contains 1 Liter of Oxygen at a pressure of 1470 Torr. The gas from both balloons is transfered into a third balloon at a pressure of 2940 Torr. Assuming the temperature is 298 K in all Balloons, what will be the volume of the third balloon? A2: 1L Because P1V1=n1RT1, P2V2=n2RT2, P1V1=n1RT1, P3V3=n3RT3 Where T1=T2=T3=298K=T, V1=2L, V2=1L, n1+n2=n3 (no reaction), P1=735 Torr, P2=1470 Torr, P3=2940 Torr, R=constant. So V3=n3RT3/P3=(n1+n2)RT/P3=n1RT1/P3+n2RT2/P3=P1V1/P3+P2V2/P3=735Torr*2L/2940Torr+1470Torr*2L/2940Torr=1L Q3: Which has the largest area? 1) A triangle with three 1/3 meter edges 2) A square with four 1/4 meter edges 3) A pentagon with five 1/5 meter edges 4) A circle with 1/2 meter radius A3: 4) Method 1, simply calculate them and compare. Method 2, for the equilateral polygon with certain circumference, the more the number of edges, the larger the area. When the number of edges up to infinite, the polygon can be regarded as a circle with same circumference. So the area 1)<area 2)<area 3)<…<area circle with circumference of 1 meter=area circle with 1/2pi meter radius Fe2(SO4)3 + H2 A4: 3H2SO4 + 2Fe => Fe2(SO4)3 + 3H2 Q5: Balance the following chemical equation, Burning of Butane C4H10 + O2 à CO2+H2O A5: 2C4H10 + 13O2 à 8CO2+10H2O

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