Q.1 Find the equation of the hyperbola at the origin, having vertices at (0,-√15),(0,-√15) and asymptotes y= √15/4x,y=-√15/4x
Q.2 The number of moose in northern Maine is increasing at a rate of 3% per year. It is estimated in one county that there are now 2000 moose. If the growth rate remains unchanged, how many years will it be until there are 2600 moose in that county?
Q.3 Use principle of mathematical induction to show 1.3+2.4+3.5+....+n(n+2)=n(n+1)(2n+7)/6.
Q.4 Solve for the real roots of x2/5+x1/5 -2 =0
Q.5 A pendulum swings through an arc of 2 feet. On each successive swing, the length of the arc is 0.9 of the previous length.
(a) What is the length of the arc of the 10th swing?
(b) On which swing is the length of the arc first less than 1 foot?
(c) After 15 swings, what total length would the pendulum have swung?
(d) When it stops, what total length would the pendulum have swung?