Find the Mass of the Surface $S$ Having the Given Mass Density

question 155

Short Answer

Find the mass of the surface $S$ having the given mass density.
$S$ is part of the plane $x + 7 y + 3 z = 21$ in the first octant; the density at a point $P$ on $S$ is equal to the square of the distance between $P$ and the $x y$ -plane.

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Definitions:

Antigen Presenting Cells

Cells that display foreign antigens complexed with major histocompatibility complex molecules on their surfaces.

Progenitor

An ancestor or parent in a direct line of descent, or a cell that has the capacity to differentiate into a specific type of cell.

Plasma Cell

Cell that secretes antibodies; a differentiated B lymphocyte (B cell).

Dendritic Cells

Antigen-presenting cells that process antigen material and present it on the surface to T cells, playing a crucial role in the immune response.