Which is larger? a) x = 1/3 b) x = 0.333333 c) neither, both are equivalent.
a) is larger; it's infinitely repeating threes all the way down, instead of the truncated threes given in b).
How do you say "give me the book" in Latin? What mood is the word "give"? Identify the cases of the two nouns.
Da mihi librum. Da is the imperative mood—it's a command! Liber, libri is singular, accusative, and masculine. It's the direct object in this scenario, so it's accusative; it's second declension, so -um is the proper ending to use. Mihi is dative, because you're giving a book *TO* someone, and that's the most common usage of the dative.
There is a circle inscribed within a square of side length s=4. What is the perimeter of a square that has the same area as the circle?
The area of the circle is (0.5)*pi*r^2, where r is the radius. r = 2, as the diameter of the circle spans the whole length of the square. Thus, the area of the circle is 2*pi. A square that has an area of 2*pi has a sidelength of s_new = sqrt(2*pi). Thus, the perimeter of the square is 4 * s_new = 4 * sqrt(2*pi), which is approximately equal to 10.03.