a wooden cube, whose edges are one centimeter long, rests on a horizontal surface. illuminated by a point source of light that is x x centimeters directly above an upper vertex, the cube casts a shadow on the horizontal surface. the area of the shadow, which does not include the area beneath the cube, is 48 48 square centimeters. find the greatest integer that does not exceed 1000 x . 1000x. (1996,

The area of a shadow is the amount of surface area that is covered by the shadow. It is the two-dimensional projection of an object onto a surface.

Let the distance between the point source of light and the horizontal surface be h. Since the shadow is a projection of the cube onto the horizontal surface, the shadow has the same proportions as the cube. Therefore, the height of the shadow is h/x times the length of the shadow, which is 48x. The area of the shadow is then:

48x * h/x = 48h

Since the area of the shadow is 48x^2, we have:

48h = 48x^2

h = x^2

We are asked to find the greatest integer that does not exceed 1000x. Substituting the expression for h into the equation, we get:

1000x = 1000x^2

x = 1/1000

Hence, The greatest integer that does not exceed 1000x is 1. the value of x is approximately 0.001.

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