4. Evaluate the double integral given by [" -dydz

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Do as indicated.
1. A certain province widely cultivates maize crops during the dry season. The average weight (in
tons) of the harvested crops is modelled by h(x, y, z)=240+y²ln(√27-2), where z is the
average amount of rainfall, y is the amount of nitrogen in the soil, and z is the number of plants
infected by several vector-borne viruses.
a. What is the total average weight of the harvested maize crops at the end of the planting
season if y=2.86, z = 32, and 8-e?
b. Compute for h(0,0,0). Justify your result.
c. Find the domain of the function h.
In(4xy)
2. If w
du
- cos(2yz - 3), zlog(t), y4e and zsin(-1). Find dt
3. Use Lagrange multipliers to solve for the dimensions of a closed right circular cylindrical can with
smallest surface area whose volume is 27 in".
4. Evaluate the double integral given by
[f
5. Given the region R on the right, use vertical
strip, SET UP the double integral that will
solve its area.
1
-dydz
I
(1, 1)
y = √z
Z
y=r³
THE
Transcribed Image Text:Do as indicated. 1. A certain province widely cultivates maize crops during the dry season. The average weight (in tons) of the harvested crops is modelled by h(x, y, z)=240+y²ln(√27-2), where z is the average amount of rainfall, y is the amount of nitrogen in the soil, and z is the number of plants infected by several vector-borne viruses. a. What is the total average weight of the harvested maize crops at the end of the planting season if y=2.86, z = 32, and 8-e? b. Compute for h(0,0,0). Justify your result. c. Find the domain of the function h. In(4xy) 2. If w du - cos(2yz - 3), zlog(t), y4e and zsin(-1). Find dt 3. Use Lagrange multipliers to solve for the dimensions of a closed right circular cylindrical can with smallest surface area whose volume is 27 in". 4. Evaluate the double integral given by [f 5. Given the region R on the right, use vertical strip, SET UP the double integral that will solve its area. 1 -dydz I (1, 1) y = √z Z y=r³ THE
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