Find the mass and the center of mass of a wire loop in the shape of a helix (measured in cm: x = t, y = 4 cos(t), z = 4 sin(t) for 0 ≤ t ≤ 2π), if the density (in grams/cm) of the wire at any point is equal to the square of the distance from the origin to the point

Mass

Center of mass

Coordinate x

Coordinate y

Coordinate z

Step-by-step explanation:

Let W be the wire. We can consider W=(x(t),y(t),z(t)) as a path given by the parametric functions

x(t) = t

y(t) = 4 cos(t)

z(t) = 4 sin(t)  

for 0 ≤ t ≤ 2π

If D(x,y,z) is the density of W at a given point (x,y,z), the mass  m would be the curve integral along the path W

The density D(x,y,z) is given by

on the other hand

and we have

The center of mass is the point

where

We have

so

the correct answer is b) histograms can be used to exhibit the shape of distributions. this is because histograms count the frequency of each possible answer, so one is able to see which results are more common and which are less common.

step-by-step explanation:

when the line is solid:

when the line is dashed:

this > inequality sign means:

this < inequality sign means:

this > inequality sign means:

this < inequality sign means:

about the problem:

srry i'm not done ! i'll