Final answer:
Using the mirror equation with the given radius of curvature (50.0 cm), we find that the coils of the electric room heater must be placed approximately 27.0 cm from the concave mirror to produce an image 3.00 m away.
Step-by-step explanation:
The question at hand involves determining the position of the coils relative to a concave mirror based on the given radius of curvature and the distance of the image formed by the mirror. Using the mirror equation 1/f = 1/do + 1/di, where f is the focal length, do the object distance (distance of the coils), and di the image distance (3.00 m from the mirror), we can solve for do. Since the radius of curvature is given as 50.0 cm, we know that the focal length f will be half of that, 25.0 cm or 0.25 m (f = R/2). We can then rearrange the mirror equation to find do.
The mirror equation becomes 1/do = 1/f - 1/di, which gives us 1/do = 1/0.25 m - 1/3.00 m. Solving for do, we find that do is approximately 0.27 m. Therefore, the coils are about 27.0 cm from the mirror, meaning that is how far apart the radiant heaters (the coils) are from the concave mirror.