Alidless shoebox is made of five rectangular pieces of cardboard forming its base and four sides. its dimensions are: base length l = 48 cm, base width w = 25 cm, and side height h = 11 cm. the base lies in quadrant i of the xy-plane, with its length along the x-axis and its width along the y-axis. the box’s sides extend in the positive z-direction. the cardboard is thin and has an area mass density of s = 0.075 g/cm2.(a) what is the x-coordinate, in centimeters, of the center of mass of the shoebox's base?

24 cm

Explanation:

The x coordinate of the center of mass of the base of the shoebox is simply the mid point of the rectangular base of such box. As the box length lies along the x-axis and the whole base is on the first quadrant. Assume that 1 corner of the box is at the origin of the xy-plane, we can calculate the x-coordinate of the center of mass of the base is at

L/2 = 48/2 = 24 cm

  0, 15); y equals one over sixty times x squared plus 15

Step-by-step explanation:

Assuming the halfpipe is only useful if the curve opens upward, the "base" (vertex) must be below the focus, so cannot be at (0, 60).

Apparently, the ground is supposed to be the directrix of the curve. Then the vertex is halfway between the focus and the ground, so is at (0, 15). The focus-vertex distance (p) is then 30-15 = 15, so the coefficient of the squared term is 1/(4p) = 1/(4·15) = 1/60.

For a vertex of (0, 15) and a vertical scale factor of 1/60, the equation of the curve is ...

  y = (1/60)x^2 +15 . . . . matches the last choice