A woman who is 6 feet tall stand near a light that is 13 feet tall. Find a function for the length of her shadow in term of her distance from the base of the lamp.

If x is the distance from the lamp, and s is the length of her shadow, then using similar triangles,

13/(x+s) = 6/s
s = 6/7 x

To find a function for the length of the woman's shadow in terms of her distance from the base of the lamp, let's consider the similarity of triangles formed by the woman, her shadow, and the light.

We can set up a proportion to find the ratio of the length of the woman's shadow to her distance from the base of the lamp:

(Height of the woman's shadow) / (Distance from the base of the lamp) = (Height of the woman) / (Height of the light)

Let's assign variables to the different quantities involved:

Let s represent the length of the woman's shadow.
Let d represent the distance from the base of the lamp to the woman.
Let h represent the height of the woman.
Let H represent the height of the light.

Based on the given information, we have:
s/d = h/H

Substituting the values into the equation:
s/d = 6/13

Therefore, the function for the length of her shadow in terms of her distance from the base of the lamp would be:
s(d) = (6/13)d