The solid Q has the moment of inertia I x about yz -plane given by the triple integral ∫ 0 2 ∫ − 4 − y 1 1 2 ( x 2 + y 2 ) 4 − y 1 ( y 2 + z 2 ) ( x 2 + y 2 ) d z d x d y a. Find the density of Q. b. Find the moment of inertia I z about the xy -plane.
The solid Q has the moment of inertia I x about yz -plane given by the triple integral ∫ 0 2 ∫ − 4 − y 1 1 2 ( x 2 + y 2 ) 4 − y 1 ( y 2 + z 2 ) ( x 2 + y 2 ) d z d x d y a. Find the density of Q. b. Find the moment of inertia I z about the xy -plane.
The solid Q has the moment of inertia Ixabout yz-plane given by the triple integral
∫
0
2
∫
−
4
−
y
1
1
2
(
x
2
+
y
2
)
4
−
y
1
(
y
2
+
z
2
)
(
x
2
+
y
2
)
d
z
d
x
d
y
a. Find the density of Q.
b. Find the moment of inertia Izabout the xy-plane.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
The table below indicates the number of years of experience of a sample of employees who work on a particular production line and the corresponding number of units of a good that each employee produced last month.
Years of Experience (x)
Number of Goods (y)
11
63
5
57
1
48
4
54
5
45
3
51
Q.1.1 By completing the table below and then applying the relevant formulae, determine the line of best fit for this bivariate data set.
Do NOT change the units for the variables.
X
y
X2
xy
Ex=
Ey=
EX2
EXY=
Q.1.2 Estimate the number of units of the good that would have been produced last month by an employee with 8 years of experience.
Q.1.3 Using your calculator, determine the coefficient of correlation for the data set.
Interpret your answer.
Q.1.4 Compute the coefficient of determination for the data set.
Interpret your answer.
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