A Plane Lamina with Constant Density $\rho ( x , y ) = 6$

question 34

Multiple Choice

A plane lamina with constant density $\rho ( x , y ) = 6$ occupies a region in the $x y$ -plane bounded by a simple closed path $C$ . Its moments of inertia about the axes are $I _ { x } = - \frac { \rho } { 3 } \int _ { C } y ^ { 3 } d x \text { and } I _ { y } = \frac { \rho } { 3 } \int _ { C } x ^ { 3 } d y$
Find the moments of inertia about the axes, if $C$ is a rectangle with vertices $( 0,0 ) , ( 4,0 )$ , $( 4,5 )$ and $( 0,5 )$ .

• A) \(( - 2,880,1,200 )\)
• B) \(( 1000,640 )\)
• C) \(( - 1,280,1,280 )\)
• D) \(( 2,000 , - 1,280 )\)
• E) \(( - 2,000,1,280 )\)

Understand the characteristics and processes of asexual reproduction in plants.

Recognize the technology and techniques used in the propagation of commercial plants, such as tissue culture.

Identify the environmental and biological triggers of flowering in plants, including the role of vernalization and photoperiods.

Distinguish between the different structures involved in asexual reproduction in plants.

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Definitions:

Surface-Area-To-Volume Ratio

The proportion between the surface area of a body to its volume, affecting rates of heat loss, material exchange, and metabolic rates.

Absorption

The process by which substances are taken up and assimilated into the body of an organism.

Gas Exchange

The biological process by which gases (such as oxygen and carbon dioxide) are transferred between living organisms and the environment, typically occurring in the lungs in humans and across the surfaces of leaves in plants.

Endosymbiosis

A theory explaining the origin of eukaryotic cells from prokaryotic organisms through a symbiotic relationship.