MHB Richter Scale Earthquake Magnitude Question?

kjeanch
Messages
2
Reaction score
0
Hello. I am doing a review sheet for my Pre-Calculus final and one of the questions has me stumped. I'm going through our notes and we never did a problem like this in class. Any help would be greatly appreciated. Thank you.

Find the Richter scale magnitude of an earthquake that releases energy of E= 1000 E_0 . Then find the energy released by an earthquake that measures 5.0 on the Richter scale given that that E_0= 10^{4.40}. Finally find the ratio in energy released between an Earthquake that measures 8.1 on the Richter scale and an aftershock measuring 5.4 on the scale. Use the formula R = 2/3 log E/Eo

A) R = 2, E = 7.94 x 10^{11} joules and the ratio E1/E2 = 10200/1
B) R = 2, E = 7.94 X 10^{10} joules and the ratio E1/E2 = 11200/1
C) R = 2, E = 7.94 X 10^{11} joules and the ratio E1/E2 = 11200/1
D) R = 3, E = 7.94 X 10^{11} joules and the ratio E1/E2 11200/1
E) R = 2, E= 5.94 X 10^{11} joules and the ratio E1/E2 = 11200/1

Which answer would be the correct one?
 
Mathematics news on Phys.org
We are told to use the formula:

$$R=\frac{2}{3}\log\left(\frac{E}{E_0}\right)\tag{1}$$

For the first earthquake we are given, we are told $E=1000E_0=10^3E_0$. So, plugging this into (1), there results:

$$R=\frac{2}{3}\log\left(\frac{10^3E_0}{E_0}\right)=\frac{2}{3}\log\left(10^3\right)$$

Now, using the identities $\log_a\left(b^c\right)=c\log(b)$ and $\log_a(a)=1$, what do you find for $R$?
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

Similar threads

Back
Top