Find the Centroid of the Region Bounded by the Given $y=9 x^{3}, 9 x+y=18, x=0$

question 36

Multiple Choice

Find the centroid of the region bounded by the given curves. $y=9 x^{3}, 9 x+y=18, x=0$

• A) \(\left(\frac{7461}{75}, \frac{261}{105}\right)\)
• B) \(\left(\frac{252}{75}, \frac{7452}{105}\right)\)
• C) \(\left(\frac{92}{105}, \frac{9}{75}\right)\)
• D) \(\left(\frac{261}{75}, \frac{7461}{105}\right)\)
• E) None of these

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Definitions:

Pyrimidine

A heterocyclic aromatic organic compound, similar to benzene and pyridine, containing nitrogen atoms at positions 1 and 3 in the ring.

Benzofuran

An organic compound that consists of a fused benzene and furan ring, often serving as a core structure in various pharmaceuticals and organic materials.

Indole

An aromatic heterocyclic organic compound with a bicyclic structure, consisting of a benzene ring fused to pyrrole.

Aromatic

Refers to organic compounds that contain one or more planar rings of atoms with delocalized pi electrons, exhibiting special stability.