- #1

- 64

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## Homework Statement

View attachment 229290

## Homework Equations

## The Attempt at a Solution

I am not sure what equation to use for the volume[/B]

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- Thread starter Jozefina Gramatikova
- Start date

- #1

- 64

- 9

View attachment 229290

I am not sure what equation to use for the volume[/B]

- #2

Chandra Prayaga

Science Advisor

- 650

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1. Understand, from the ranges of x, y and z given by you, the shape of the region you are interested in. In other words, answer the first question and sketch the region. In your graph, you only showed a few isolated points. You did not sketch the region in space.

2. The relevant equation posted by you is not adequate. Density = mass / volume is good only if the density is constant. In your case, the density depends on position (your equation: ρ = 1 + z). Then you must use the differential form:

dm = ρ dV,

and integrate this to get the total mass. It will be a triple integral.

- #3

- 64

- 9

1. Understand, from the ranges of x, y and z given by you, the shape of the region you are interested in. In other words, answer the first question and sketch the region. In your graph, you only showed a few isolated points. You did not sketch the region in space.

2. The relevant equation posted by you is not adequate. Density = mass / volume is good only if the density is constant. In your case, the density depends on position (your equation: ρ = 1 + z). Then you must use the differential form:

dm = ρ dV,

and integrate this to get the total mass. It will be a triple integral.

I hope you can see the picture better now. I was wondering if I need the whole rectangle as a region or just the purple triangle that I sketched there?

Last edited:

- #4

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- #5

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Your sketch is nowhere close to being right. It is a three dimensional solid.I was wondering if I need the whole rectangle as a region or just the purple triangle that I sketched there?

What is the range of z? For some arbitrary z in that range, what does the XY lamina look like?

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