If you check the units of your expression, you'll see that they don't work out. Your mistake is in the area element for polar coordinates.Emily Herschbein said:UPDATE: I have converted to polar coordinates, giving density = 1.2 r Cos[theta]+ 0.7 r Sin[theta]. Then I solved the following integral:
This gave me 8.55 g which was incorrect. Where am I going wrong?
A mass given density function is a mathematical representation that describes the relationship between the mass of a substance and its density. It is typically used to calculate the mass of a substance given its density and volume.
A regular density function only describes the relationship between density and volume, while a mass given density function also takes into account the mass of the substance. This allows for more accurate calculations of mass given a known density and volume.
A mass given density function is commonly used in fields such as physics, chemistry, and engineering to calculate the mass of a substance in various scenarios. It is also used in industries such as manufacturing and construction to determine the amount of material needed for a project.
No, a mass given density function is specific to a particular substance or material. Each substance has its own unique density, so a different mass given density function would need to be used for each substance.
Area is not directly related to a mass given density function. However, the concept of density can also be applied to two-dimensional objects, in which case area would be used instead of volume. In this scenario, a mass given density function would describe the relationship between the mass and area of the object.