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Chapter 13: Q. 20 (page 1038)

Explain why the location of the centroid relates only to the geometry of the region and not its mass.

Short Answer

Expert verified

Centroid of the plane figure is defined as the point of intersection of the medians.

Step by step solution

01

Given information

The location of the centroid relates only to the geometry of the region and not it's mass.

02

Calculation

For an example, take a triangle ABCwith vertices (1,1),(2,0),and(2,3)and join them. The point of intersection of medians AD,BEand CFis G

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Most popular questions from this chapter

In Exercises 57–60, let R be the rectangular solid defined by

R = {(x, y, z) | 0 ≤ x ≤ 4, 0 ≤ y ≤ 3, 0 ≤ z ≤ 2}.

Assume that the density of R is uniform throughout, and find the moment of inertia about the x-axis and the radius of gyration about the x-axis.

Evaluate the triple integrals over the specified rectangular solid region.

∭R x2yzdV, whereR={(x,y,z)∣−2≤x≤1,0≤y≤3,and1≤z≤5}

Explain why∑i=1l∑j=1m∑k=1nij2k3=∑j=1m∑k=1n∑i=1lij2k3.

Use Definition 13.4to evaluate the double integrals in Exercises 29–32.

localid="1649936867482" ∬xx2ydA

whereR={(x,y)∣1≤x≤3and0≤y≤2}

Find the volume between the graph of the given function and the xy-plane over the specified rectangle in the xy-plane

f(x,y)=-2x2y3WhereR={(x,y)|-2≤x≤3,-1≤y≤5}
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