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sec._15.5__applications_of_multiple_integrals___math_2163__section_61998__fall_2019___webassign.pdf

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11/25/2019
Sec. 15.5: Applications of Multiple Integrals – MATH 2163, section 61998, Fall 2019 | WebAssign
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MATH 2163, section 61998, Fall 2019
INSTRUCTOR
Ning Ju
Sec. 15.5: Applications of Multiple Integrals
(Homework)
Northern Oklahoma
College
Current Score
QUESTION
1
POINTS
–/1
2
3
4
5
6
7
TOTAL SCORE
–/2
–/1
–/2
–/2
–/2
–/2
–/12
0.0%
Due Date
DECEMBER 14
11:50 PM CST
Description
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Scoring
Assignment Submission
For this assignment, you submit
answers by question parts. The number
of submissions remaining for each
question part only changes if you
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Sec. 15.5: Applications of Multiple Integrals – MATH 2163, section 61998, Fall 2019 | WebAssign
g
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Your best submission for each question
part is used for your score.
–/1 points
1.
RogaCalcET3 15.5.001.
My Notes
Find the total mass M of the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 assuming a mass density of
δ(x, y) = 10×2 + 4y2.
M=
–/2 points
2.
RogaCalcET3 15.5.006.
My Notes
Find the total mass M of the solid region W defined by x ≥ 0, y ≥ 0, x2 + y2 ≤ 16, and
x ≤ z ≤ 32 − x (in centimeters) assuming a mass density of δ(x, y, z) = 4y g/cm3.
M=
g
–/1 points
3.
RogaCalcET3 15.5.009.
My Notes
Assume that the density of the atmosphere as a function of altitude h (in kilometers) above sea level is
δ(h) = ae−bh kg/km3, where a = 1.225 × 109 and b = 0.21. Calculate the total mass M of the
atmosphere contained in the cone-shaped region
x2 + y2 ≤ h ≤ 3. (If you enter your answer in
scientific notation, round the decimal value to three decimal places. Use equivalent rounding if you do
M=
kg
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Sec. 15.5: Applications of Multiple Integrals – MATH 2163, section 61998, Fall 2019 | WebAssign
–/2 points
4.
RogaCalcET3 15.5.011.
My Notes
Find the centroid of the given region assuming the density δ(x, y) = 1.
Region bounded by y = 1 − x2 and y = 0
x, y =
–/2 points
5.
RogaCalcET3 15.5.016.
Find the y-coordinate of the centroid of the sector in the figure below. Assume that R =
My Notes
22 and
θ = π.
y=
6.
4
–/2 points
RogaCalcET3 15.5.017.
My Notes
Find the centroid of the given solid region assuming a density of δ(x, y, z) = 1.
x2 + y2 + z2 ≤ 49, z ≥ 0
x, y, z =
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7.
Sec. 15.5: Applications of Multiple Integrals – MATH 2163, section 61998, Fall 2019 | WebAssign
–/2 points
RogaCalcET3 15.5.019.
My Notes
Find the centroid of the given solid region assuming a density of δ(x, y, z) = 1.
The “ice cream cone” region W bounded, in spherical coordinates, by the cone ϕ = π and the
3
sphere ρ = 5
x, y, z =
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