Final answer:
The image formed by the concave mirror with a focal length of 43 cm and an image that is inverted and five times smaller than the object is located at 17.2 cm in front of the mirror, making option C the correct answer.
Step-by-step explanation:
The question involves finding the position of the image formed by a concave mirror when given the focal length and the size of the image relative to the object.
To solve this, we need to use the mirror equation 1/f = 1/do + 1/di, where f is the focal length, do is the distance of the object from the mirror, and di is the distance of the image from the mirror.
Additionally, the magnification m is given by di/do and for an inverted image that is five times smaller than the object, m would be -1/5, because the negative sign indicates that the image is inverted.
Given that the focal length is 43 cm (which we will consider as positive since it's a concave mirror), we can rewrite the mirror equation in terms of the do and solve for the image distance di considering the magnification.
Substituting m into the equation we get: -1/5 = di/do, therefore do = -5di. Now, substituting do into the mirror equation, we can solve for di. After calculations we find that the image is formed at 17.2 cm in front of the mirror, making option C the correct option.