This is done by nuclear fusion in which it converts hydrogen atoms into helium. so the byproduct of nuclear fusion is that in the sun's core is a massive volume of energy that getting release and radiates outward towards of the surface of the sun and into space to the solar systems and a bit beyond. that's kinda all I know hope it helps. =^-^=
Like theories, scientific laws describe phenomena that the scientific community has found to be provably true. Generally, laws describe what will happen in a given situation as demonstrable by a mathematical equation, whereas theories describe how the phenomenon happens.
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A microwaveable cup-of-soup package needs to be constructed in the shape of a cylinder to hold 600 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.02 cents per square centimeter. The top will be made of glued paper, costing 0.05 cents per square centimeter. Find the dimensions for the package that will minimize production costs.
h: height of the cylinder, r: radius of the cylinder
The volume of a cylinder: V=πr2h
Area of the sides: A=2πrh
Area of the top/bottom: A=πr2
The cost of packaging, C=2πrh*0.02+ πr^2*0.02+ πr^2*0.05 subject to the constraint πr^2h=600
C=πr(0.04h+.07r) and the constraint implies h=600/ πr^2
So C=πr(24/πr^2+.07r)=24/r+.07πr^2
C'=-24/r^2+0.14πr=0
r^3=24/0.14π r=3.79 cm
h=600/πr^2=13.3 cm
C=π*3.79*(0.04*13.3+.07*3.79)=9.48cents
C''=0.14π+48/r^3>0 for all r>=0 so our solution is indeed a minimum.
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Answer:
Given:
Th = 270 °C = 270+273 = 543 K, hot temperature
Tc = 210 °C = 210+273 = 363 K, cold temperature
According to the Carnot theorem, the maximum efficiency achievable by a heat engine between a hot and cold temperature is
η = 1 - Tc/Th
= 1 - 363/543
= 0.668 = 11.047 (approx)
Answer: 11.0% (nearest integer)