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3 years ago

Vertical asymptote of 8tan(πx). Use n as an arbitrary integer if necessary

Mathematics

1 answer:

aliya0001 [1]3 years ago

4 0

There's a vertical asymptote for every integer n/2
Tan(x) is undefined every nPi/2

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I believe it is 816... But I'm not exactly quite sure

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3 years ago

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3 years ago

The number of motor vehicles registered in millions in the US has grown as follows:

zysi [14]

Answer:

a) Figure attached

b) $r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=10 $\sum x = 75.819, \sum y = 43.5231, \sum xy = 330.0321, \sum x^2 =574.8598, \sum y^2 =192.8274$

$r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.819)^2][10(192.8274) -(43.5231)^2]}}=0.989$

So then the correlation coefficient would be r =0.989

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

Solution to the problem

Part a

Year (x): 1940, 1945 1950, 1955, 1960, 1965, 1970, 1975, 1980, 1985

Vehicles (Y): 32.4, 31.0, 49.2, 62.7, 73.9, 90.4, 108.4, 132.9, 155.8, 171.7

After apply natural log for the two variables and create the scatterplot in excel we got the following result on the figure attached.

Part b

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=10 $\sum x = 75.819, \sum y = 43.5231, \sum xy = 330.0321, \sum x^2 =574.8598, \sum y^2 =192.8274$

$r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.81948)^2][10(192.8274) -(43.5231)^2]}}=0.989$

So then the correlation coefficient would be r =0.989

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3 years ago

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MatroZZZ [7]

Answer:

Step-by-step explanation:

Multiply each term of the first polynomial with the second polynomial. Then combine the like terms.

(3a² + 5a - 2)* (5a² -3a + 4)

= 3a² *(5a² -3a + 4) + 5a*(5a² -3a + 4) - 2*(5a² -3a + 4)

=3a²*5a² - 3a*3a² + 4*3a² + 5a*5a² - 3a*5a + 4*5a + 5a²*(-2) - 3a*(-2) + 4*(-2)

=15a⁴ - 9a³ + 12a² + 25a³ - 15a² + 20a - 10a² + 6a - 8

= 15a⁴ - 9a³ + 25a³ + 12a² - 15a² - 10a² + 20a +6a - 8

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Answer:

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=57.2cm

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