The math help thread

Another question -
A light moving at 3 ft/s approaches a 6 ft. man standing 12 ft from a wall. The light is 3 ft above the ground. How fast is the tip P of the man's shadow moving when the light is 24 ft from the wall?

The shadow is on the wall, if you didn't understand my wording =x

y = the height in feet of the shadow (as the triangle ABC is proportional with the triangle ADE (double in size), we can deduce that the height of the triangle is 6 feet. Add 9 in the end.)
x = the length in feet from the wall

we have that


we want to find


For y, how can we make a function that's describing its height? At least we know that for y(0) = 9. We also know that the triangles ABC and ADE are proportional to eachother. However, the proportionality changes. If we find a general formula for the proportionality to those triangles...



So in reality, all we have to do is to find a way of describing Dy, then we've solved this issue.

The small triangle is of size


And the big triangle is of size


We know that


Which means that


Therefore, let's just differentiate the height of the big triangle!


Insert for t = 0 and you'll receive 3/4, or 0.75 ft/s.

Edit: Ninja'd, it seems.

Noah