In the following exercises, consider a lamina occupying the region R and having the density function ρ given in the first two groups of Exercises. a. Find the moments of inertia l x , l y and l o about the x -axis. y -axis, and origin, respectively. b. Find the radii of gyration with respect to the x-axis, y-axis, and origin, respectively. 329. R is the region enclosed by the ellipse x 2 + 4 y 2 = 1 ; ρ ( x , y ) = 1.
In the following exercises, consider a lamina occupying the region R and having the density function ρ given in the first two groups of Exercises. a. Find the moments of inertia l x , l y and l o about the x -axis. y -axis, and origin, respectively. b. Find the radii of gyration with respect to the x-axis, y-axis, and origin, respectively. 329. R is the region enclosed by the ellipse x 2 + 4 y 2 = 1 ; ρ ( x , y ) = 1.
Let I =
f(x) dx, where f is the function whose graph is shown.
4
2
y
f
X
1
2
3
4
(a) Use the graph to find L2, R2 and M2.
R₂
M2
=
=
=
(b) Are these underestimates or overestimates of I?
O 42 is an underestimate.
O 42 is an overestimate.
◇ R2 is an underestimate.
OR2 is an overestimate.
OM2 is an underestimate.
○ M2 is an overestimate.
(c) Use the graph to find T2.
T₂ =
Examine the Variables: Carefully review and note the names of all variables in the dataset. Examples of these variables include:
Mileage (mpg)
Number of Cylinders (cyl)
Displacement (disp)
Horsepower (hp)
Research: Google to understand these variables.
Statistical Analysis: Select mpg variable, and perform the following statistical tests. Once you are done with these tests using mpg variable, repeat the same with hp
Mean
Median
First Quartile (Q1)
Second Quartile (Q2)
Third Quartile (Q3)
Fourth Quartile (Q4)
10th Percentile
70th Percentile
Skewness
Kurtosis
Document Your Results:
In RStudio: Before running each statistical test, provide a heading in the format shown at the bottom. “# Mean of mileage – Your name’s command”
In Microsoft Word: Once you've completed all tests, take a screenshot of your results in RStudio and paste it into a Microsoft Word document. Make sure that snapshots are very clear. You will need multiple snapshots. Also transfer these results to the…
Elementary Statistics: Picturing the World (7th Edition)
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