2<span>cos2(θ)−1 = 0
</span><span>2cos2(θ)=1
</span><span>cos2(θ)=1/2
</span><span>2θ=arc cos1/2
</span><span>2θ=60 degrees
</span><span>θ=30 degrees</span>
Answer:
The Ptolemaic model of the universe <u><em>A) explained and predicted the motions of the planets with deferents and epicycles.</em></u>
Explanation:
Ptolemy of Alexandria built an explanation of the observed movements of the planets that remained in force for thirteen centuries. Ptolemy proposed a model of the Universe with the Earth in the center. In the model, the Earth remains stationary while the planets, the Moon and the Sun describe complicated orbits around it. In other words, Ptolemy devised a system in which he used epicycles, deferential and eccentric, and it was necessary to introduce an equating point to reproduce planetary movements. He proposed that:
a) Each planet revolves with constant velocity around a circle called an epicycle.
b) The center of the epicycle is located and moves with constant velocity around another circle called deferential.
c) The center of the deferent is located at a moving point, which travels with constant speed describing another circumference called eccentric.
d) The center of the eccentric coincides with the center of the Universe.
e) Since the Earth is not located in the center of the Universe, but very close to it, it was necessary to introduce an equating point, which is not on Earth, and from which you can see the planet move with constant speed.
However, Ptolemy put forward this geometric theory to explain mathematically the movements and failed to adjust any system of cycles, epicycles and eccentrics that accurately represented the observed movements of the planets.
Finally, <u><em>The Ptolemaic model of the universe A) explained and predicted the motions of the planets with deferents and epicycles.</em></u>
Answer:
Environmental Protection Agency (EPA)
Explanation:
In the United States of America, the agency which was established by US Congress and saddled with the responsibility of overseeing all aspects of pollution, environmental clean up, pesticide use, contamination, natural resources and hazardous waste spills is the Environmental Protection Agency (EPA). Also, EPA research solutions, policy development, and enforcement of regulations through the resource Conservation and Recovery Act.
The Environmental Protection Agency (EPA) is the governmental agency set up to ensure that various industries, factories and people comply with laws and regulations concerning the environment i.e it is an agency established to oversee and enforce environmental compliance by the people.
Hence, the Environmental Protection Agency (EPA) is saddled with the responsibility of enforcing federal and state laws related to environmental and natural resources.
