Math Problems from Rocket City
10:25 PM
Muhammad Yusuf
, Posted in
1. Tux is camping
on Plotu, and his campsite is in the shape of a circle. The base of his tent is in the shape of a
square, which happens to be inscribed in the circle. If the side length of the square is the
positive solution for x in the equation 3x2=13x+30, then what is the area of
the region outside his tent, but inside his campsite (the shaded region between
the circle and the square)?
(3
points)
2. How many solutions of the form (x,y), with x
and y both being positive integers, are there to the equation 2x + 10 = 2010?
(3
points)
3. Dis, a galactic mail carrier, wants to get
from his house (Point A) to the post office (Point B) located on the 3 x 3
grid. Evil Ed, an especially bothersome alien, is located on Point C. If Dis
can only move right and down along grid lines, how many different paths can he
take from his house to the post office while avoiding Evil Ed?
(4
points)
