Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers) of the quake below the surface at the epicenter. x 2.8 3.9 3.3 4.5 2.6 3.2 3.4y 4.7 9.6 11.2 10.0 7.9 3.9 5.5(a) Make a scatter diagram of the data.Flash Player version 10 or higher is required for this question. You can get Flash Player free from Adobe's website. Then visualize the line you think best fits the data. (b) Use a calculator to verify that Σx = 23.7, Σx2 = 82.75, Σy = 52.8, Σy2 = 447.56 and Σxy = 184.28. Compute r. (Round to 3 decimal places.) As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.Given our value of r, we can not draw any conclusions for the behavior of y as x increases.Given our value of r, y should tend to remain constant as x increases. Given our value of r, y should tend to decrease as x increases.Given our value of r, y should tend to increase as x increases.
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers) of the quake below the surface at the epicenter.
x 2.8 3.9 3.3 4.5 2.6 3.2 3.4
y 4.7 9.6 11.2 10.0 7.9 3.9 5.5
(a) Make a
Flash Player version 10 or higher is required for this question.
You can get Flash Player free from Adobe's website.
Then visualize the line you think best fits the data.
(b) Use a calculator to verify that Σx = 23.7, Σx2 = 82.75, Σy = 52.8, Σy2 = 447.56 and Σxy = 184.28.
Compute r. (Round to 3 decimal places.)
As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.
Given our value of r, we can not draw any conclusions for the behavior of y as x increases.
Given our value of r, y should tend to remain constant as x increases.
Given our value of r, y should tend to decrease as x increases.
Given our value of r, y should tend to increase as x increases.
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