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olganol [36]
4 years ago
11

By what factor does the intensity increase for each whole-number increase in the richter scale? use your understanding of logari

thms and the inverse relationship between logarithms and exponents to explain your answer.
Mathematics
2 answers:
Mrac [35]4 years ago
8 0
The factor of intensity increase for each whole number increase in the Richter scale is 10. This is because the Richter scale is a logarithmic scale that has a base of 10. As an example, a Richter scale of 1 increased to 2 will have an intensity increase of 
10^2 / 10^1 = 10
marusya05 [52]4 years ago
3 0

Answer:

The intensity increases by a factor of 10.

The Richter scale uses a logarithm with base 10.

For example, an earthquake with magnitude 2 is 102 times more intense than a standard earthquake, while an earthquake with magnitude 3 is 103 times more intense than a standard earthquake, and 103 = 102 × 10.

Step-by-step explanation:


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3 years ago
Which equation is the inverse of y = 9x2 - 4?
m_a_m_a [10]

Answer:

The inverse will be:

y' = \frac{\sqrt{x+4}}{3}

Step-by-step explanation:

In order to find the inverse of the equation, we do a variable change, since we are finding the inverse, :

f(x)  = 9x^{2} - 4

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x = 9y' ^{2} - 4

Now solve for y'.

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x + 4= 9y'^{2} - 4+4

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Second divide by 9

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y'^{2} = (x + 4)/9

Now you will have to clear y, with the square root.

[tex]y'^{\frac{2}{2}} = \sqrt{x + 4}  / \sqrt{9}[/tex] =

Simplifying terms

y' = \frac{\sqrt{x+4}}{3}

f^{-1}(x)  = \frac{\sqrt{x+4}}{3}

You can check the answer by doing the evaluation of the following equation:

(f o f^{-1} ) (x)

substitute the equation for y' or inverse function f^{-1}

f(\frac{\sqrt{x+4} }{3})

Now substitue the value into f(x)

You will have

= 9(\frac{\sqrt{x+4} }{3}} )^{2}  - 4\\\\Solving\\\\9(\frac{{x+4} }{9}} )  - 4

=x

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3 years ago
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