Use the principle of mathematical induction to show that the mathematical statement is true for all natural numbers n.Sn: 2 is a factor of 
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Show S1 is true: 12 - 1 + 2 = 2; 2 is a factor of 2
Assume that Sk is true: 
; 2 is a factor of k2 - k + 2
Show that if Sk is true, then Sk+1 is true:
Sk+1 = (k + 1)2 - (k + 1) + 2 = k2 + k + 2 = (k2 - k + 2) + 2k
(k2 - k + 2) is Sk and 2 is a factor of 2k
Since 2 is a factor of Sk+1 is true, the statement is true for all values of n.
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Find the focus and directrix of the parabola.- 
x2 = y
A. (0, -6); y = 6 B. (-12, 0); x = 6 C. (0, 6); y = -6 D. (0, -6); y = -6
Find the equation of the hyperbola with center (1, 1), vertex (4, 1) and focus (7, 1). ?
A. 
B. 
C. 
D. 
E. none of these
Find an equation of an ellipse satisfying the given conditions.Vertices:(±14, 0); Length of minor axis: 16
A. 
+ 
= 1
B. 
+ 
= 1
C. 
+ 
= 1
D. 
+ 
= 1
Solve the problem.A suspension bridge has twin towers that are 1300 feet apart. Each tower extends 180 feet above the road surface. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cable at a point 200 feet from the center of the bridge.
What will be an ideal response?