Why is it important foe scientists to know how many valence electrons a given element has

Because the number of valence electrons of an element determines the properties and in particular the reactivity of that element.

In fact, elements of the first group (i.e. only one valence electron) have high reactivity, because they can easily give away their valence electron to atoms of other elements forming bonds. On the contrary, elements of the 8th group (noble gases) have their outermost shell completely filled with electrons, so they do not have valence electrons, and they have little or no reactivity at all.

The reflection of the candle in the concave mirror formed an upside-down virtual image that is smaller than the candle.in other words. the answer is the third option, c