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The magnitude M of an earthquake on the Richter scale is defined as a function of the energy, in joules, E released by the earthquake:
Using this equation, it can be shown that
Find the value of a and the value of b.
On July 22, 2023, Taylor Swift fans in Seattle registered a 2.3 magnitude earthquake. The largest earthquake ever recorded, the 1960 Valdivia earthquake off the coast of Chile, had a 9.5 magnitude.
Find the number of "Swift Quakes" needed to match of energy of the Valdivia earthquake. Give your answer in the form c×10k, where 1≤c<10 and k∈Z.
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The area swept out by Earth's orbit each day is 1.92×1014km2. The height of the Empire State Building is 443m.
Find the radius of Earth's orbit (assume it to be circular).
Hence, determine the number of Empire State buildings that could be placed between the Earth and the Sun. Round your answer to 3 significant figures.
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