Hints and Solutions for last spring exam

1) Multiply both sides by 12(x+3) and solve the resulting equation. You get x=-3. This is not allowed therefore the original equation has no solution
2) a) x=-3 b) y=-4x-13
3) a) R=50x; C=65000 + 10x; P=40x-65000. b) x=1625
4) a) domain of f: x different than -1; domain of g: all reals;
b) (6x-3)/(3x-1); c) (4x+1)/(x+1); d) f^{-1}(x)=(x-1)/(2-x); e) g^{-1}(x)=(x+2)/3;
5) a) (1,4); b) x=3,-1 c) y=3;
6) y = (x+5)^2+2
7) a) 1st row: -6 -16 -8 2nd row: -2 -8 -4
b) not possible
c) 1st row: 20/3 -1/3 -8/3 2nd row: 1/3 1/3 -1/3 3rd row: -2 0 1
d) 1st row: 8 3 2 2nd row 3 5 5
8) a) no solution b) x=28; y=-17; z=1;
9) x= cord type; y= cord less type a) corners: (0,200); (200,100); (400,0)
b) maximization of profit at (200,100)
10) a) omitted b) the resulting quadratic equation gives x= 6 or -8. However only x=6 is allowed since for x=-8 the terms log (x) and log (x+2) don't make sense
11) the general term of the sequence is a_n=-8 + (n-1)4; the sum of the first 100 terms is 19,000
12) Use the formula A_n=R(1-(1+i)^-n)/i and solve for n. This becomes a logarithmic equation and it is not typical for this kind of problem. You may disregard this for the final
13) Use the formula S=R((1+i)^n-1)/i and solve for R