BRIEF ANSWERS FOR TEST 1

• One irrational number between .2616 and .2617 is: .261601001000100001... where the pattern of 0's and 1's continues with larger and larger blocks of 0's.
• [(8*x^8*y^{-2})/(-4*x^{-1}*y^{-5})]^3 simplifies to -8*x^27*y^9.
• (5 x 10^6)^3 in scientific notation is 1.25 x 10^20.
• square_root(x*cube_root(x))*cube_root(x^2) can be rewritten as cube_root(x^4).
• (square_root(3)-square_root(2))/(square_root(3)+square_root(2)) = 5 - 2*square_root(6).
• 3*x^2 - x + 4 divided by x+2 is 3*x-7 with remainder 18.
• 2*y^2+9y-18 = (2*y-3)(y+6).
• (x^4-16)/(x^4 + 8*x^2 + 16) = (x^2-4)/(x^2+4).
• The equation x + square_root(x) = -2 + square_root(x) is INCONSISTENT, since the only potential solution is x=-2, but neither side is defined when x=-2.
• Joe's average speed is (total kilometers)/(total hours) = 5k/((3/15) hr + (2/6)hr) = 9 3/8 k/hr.
• Working together for three hours (from 5-8pm) Della and Don can scrape [((1/10)+(1/15)) yachts/hour]*[3 hours] = 1/2 yacht. Thus Don must scrape 1/2 yacht before Della arrives. Since he scrapes a full yacht in 15 hours, he can scrape 1/2 yacht in 7 1/2 hours. To work for 7 1/2 hours before Della arrives he must start at 5pm - 7 1/2 hours = 9:30am.