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# College algebra #11

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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?

_____?

idenny  Apr 12, 2017
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#1
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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)

$$\large \frac{the \ Veracruz \ quake}{the \ East \ unknown \ quake}=\frac{10^{6.5}}{10^{x}}=\frac{1}{3}$$

$$10^x= 3\cdot10^{6.5}$$

$$x=log3+6.5=6.98$$

$$A \ quake \ of \ magnitude \ 6.98 \ would \ be \\three \ times \ as \ powerful \ as \ the \ Veracruz \ quake.$$

!

asinus  Apr 12, 2017
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Wow!

tertre  Apr 12, 2017
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Hi tertre, thank you for your Wow! asinus :- )

asinus  Apr 12, 2017

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