+216 On April 7, 2011, an earthquake of magnitude 6.5 on the Richter scale struck Veracruz, Mexico. On August 23, 2011, an earthquake of magnitude 5.8 on the Richter scale shook the East Coast of the United States. (Round your answers to two decimal places.)
(a) How did the power of the East Coast and Veracruz quakes compare?
The Veracruz quake was ___? times as powerful as the East Coast quake.
(b) What would be the magnitude of a quake three times as powerful as the Veracruz quake?
_____?
+15000 On April 7, 2011, an earthquake of magnitude 6.5 on the Richter scale struck Veracruz, Mexico. On August 23, 2011, an earthquake of magnitude 5.8 on the Richter scale shook the East Coast of the United States. (Round your answers to two decimal places.)
(a) How did the power of the East Coast and Veracruz quakes compare?
The Veracruz quake was ___? times as powerful as the East Coast quake.
(b) What would be the magnitude of a quake three times as powerful as the Veracruz quake?
(a)
\(\large \frac{the \ Veracruz \ quake}{the \ East \ Coast \ quake}=\frac{10^{6.5}}{10^{5.8}}=\color{blue}5.05\)
The Veracruz quake was 5.05 times as powerful as the East Coast quake.
(b)
\(\large \frac{the \ Veracruz \ quake}{the \ East \ unknown \ quake}=\frac{10^{6.5}}{10^{x}}=\frac{1}{3}\)
\(10^x= 3\cdot10^{6.5}\)
\(x=log3+6.5=6.98\)
\(A \ quake \ of \ magnitude \ 6.98 \ would \ be \\three \ times \ as \ powerful \ as \ the \ Veracruz \ quake.\)
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