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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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A bakery slices a loaf of bread. The end face of the loaf (a cross-section) sits on the cutting board as illustrated in the diagram below:
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The height y of the crust above the cutting board is known for the following values:
The bakery wants the cross-sectional area of the end face to estimate the loaf’s volume. The outline of the crust is concave down for 0≤x≤10.
Use the trapezoidal rule with a step size of h=2cm to estimate the cross-sectional area A (in cm2).
The loaf is 18cm long.
Use your result from part (a) to estimate the volume of the loaf (in cm3).
Given the outline is concave down on [0,10], state, with justification, whether the trapezoidal rule overestimates or underestimates the true area.
A precise scan reports the true cross-sectional area is 13.6cm2.
Calculate the percentage error of your estimate from part (a).
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