Triple Integral For Moment Of Inertia

[Air]

I have general question which need to be answered before I can understand steps which I have to do. There are:

• When you are told that a solid is bounded by the coordinate plane and the plane $$x+10y + 2z = 5$$, are the limits considered to be $$0-1$$ for $$x$$-axis, $$0-10$$ for the $$y$$-axis and $$0-2$$ for the $$z$$ axis. What is the $$=5$$ used for in this question?
• If you are told that the density is directly proportional to the distance from the $$y-z$$ axis, does that mean that the density is $$kx$$?

Could you help clear my mind? Thanks in advance.

 

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• When you are told that a solid is bounded by the coordinate plane and the plane $$x+10y + 2z = 5$$, are the limits considered to be $$0-1$$ for $$x$$-axis, $$0-10$$ for the $$y$$-axis and $$0-2$$ for the $$z$$ axis. What is the $$=5$$ used for in this question?

Draw a picture. The solid in question is tetrahedral in shape, while the limits you give describe a rectangular brick. The equation they gave describes a plane with normal vector (1, 10, 2) that intersects the axes at the points (5, 0, 0), (0, 1/2, 0) and (0, 0, 5/2). Have you taken multivariable calculus yet?

• If you are told that the density is directly proportional to the distance from the $$y-z$$ axis, does that mean that the density is $$kx$$?

Did they say y-z axis, y=z axis or yz-plane ? I'm not sure what they could mean by y-z axis.

 

[Air]

Draw a picture. The solid in question is tetrahedral in shape, while the limits you give describe a rectangular brick. The equation they gave describe a plane with normal vector (1, 10, 2) that intersects the axes at the points (5, 0, 0), (0, 1/2, 0) and (0, 0, 5/2). Have you taken multivariable calculus yet?

Yes, I've taken multivariable calculus. I understand the further process to work out the moment of inertia but the limits and the density function that I have to insert confuses me.

Did they say y-z axis, y=z axis or yz-plane ? I'm not sure what they could mean by y-z axis.

Sorry for the confusion. It said $$y-z$$ plane.