currysauce
Actuary in the making
1. The chord PQ of the parabola x²=12y passess through the fixed point (4, -3). Show that if the tangents at P and Q meet at T, then the locus of T is the straight line 3y-2x=9.
2.Seven people enter one train carriage in which there are 10 seats, 5 facing forward, 5 backward.
In how many ways can they take their places if
(i) any person can occupy any seat
(ii) two particular people A, B sit facing the front
(iii) A sits near the window
(iv) B sits in the corner of the carriage
(v) A and B sit near the window
(vi) A and B sit facing eachother
3. If y=1/x , d^(n)y/dx^(n) = (-1)^n n!/ x^(n+1) . Show this by induction.
THANKS!
2.Seven people enter one train carriage in which there are 10 seats, 5 facing forward, 5 backward.
In how many ways can they take their places if
(i) any person can occupy any seat
(ii) two particular people A, B sit facing the front
(iii) A sits near the window
(iv) B sits in the corner of the carriage
(v) A and B sit near the window
(vi) A and B sit facing eachother
3. If y=1/x , d^(n)y/dx^(n) = (-1)^n n!/ x^(n+1) . Show this by induction.
THANKS!