Expert: Richard J. Raridon - 6/15/2009

Question
1.   If a varies directly as b, and a = 75 when b = 40, find a when b = 12.
  
2.   A public opinion poll found that out of a sample of 450 voters, 252 favored a school bond issue. If 20,000 people voted, how many are likely to vote for the bond measure?
  
3.   If p varies inversely as the square root of q, and p = 12 when q = 36, find p when q = 16.


4.   Solve given the root indicated:
Equation:  x4 - 5x2 - 10x - 6 = 0
Root:  -1 + i
  
5.   Solve:
|a/2+1| = 3

9.   Assume that y varies directly as x. If y = 3.2 when x = 0.2, find y when x = 1.6.
  
10.   Find all zeros of the polynomial
x^3 - 5x^2 + x - 5
  

11.   Find the distance between the pair of points:
(-a,b) and (2a,4b)

12.   Find an equation of the circle with the center and radius:
(-5,3); r = 0.167

13.   Solve by completing the square:
x^2 - 4x = -3
  
14.   Identify the conic section whose equation is given:
16x^2 + 4y^2 = 16
  

15.   Solve:
c^3 + c^2 - 7c - 3 = 0, given root -3
  
16.   Choose the real solutions of the system:
y^2 = 2x  and  x^2 + y^2 = 8
  
17.   Find the length of a side of each of two squares given that the sum of their perimeters is 44 ft and the sum of their areas is 73 ft2.
  
18.   What is one-third of the perimeter of the square whose area is 36 square units?

19.   Solve:
4^1-x = 8

Answer
1) a = 22.5
2) 11,200
3) p = 18
4) You have to realize that if one root is -1+i then another root is
-x-i.  So if you multiply together (x+1-i) and (x+i+1) you get
x^2+2x+2.  Divide that into x^4-5x^2-10x-6 and you get x^2-2x-3
which you can factor to get (x-3)(x+1) so the other roots are 3,-1
5) a=4 and a=-8
9) y=25.6
10) y = 5, +/-i
11) 3(a^2+b^2)^1/2
12) (x+5)^2 +(y-3)^2 = 1/36
13) x = 1,3
14) ellipse
15) 1 +/-i
16) x=2, y= +/-2
17) 3 & 8
18) 8
19) x= -1/2