Hi, here are some questions I hope you can help out. 1. A geometric progression and an airthmetic progression has the common first term, a. The sum of the firs three terms of the geometric progression is 19/27 of the sum to infinity. Find the common ratio, r.
The second and third terms of the geometric progression are increasing consecutive terms of the arithmetic progression respectively. Find the sum of the 1st 55 terms of the arithmetic progression in terms of a.
My confusion:The first sentence of the second paragraph confuses me. I don't understand what they meant by increasing consecutive terms of the arithmetic progression. Is it the first three term? or is it for us to find out?
2. A curve has parametic equations x=1 + 2sin (-) , y=4+ (squareroot 3)( cos (-) )
Determine the rate of change of xy at (-)= pi/6 if x increases at a constant rate of 0.1 unit per second.
My confusion: I don't know how to determine change of xy.
(-) -> theta
3. The equation of three planes P1, P2, P3 are
x + 3y + 2 = 8
3x + y -2=0 and
x + py + qz = 11
If P1, P2 and P3 have no point in common, using the values of a and b found in (iii), comment on the value of p and find an equation relating p and q.
My Confusion: I don't know how to attempt this type of question when 3 planes have no point in common. It's not included in my school notes too.
Hi,
For Q3, please refer to explanations in my slide:
http://www.slideshare.net/weews/how-to-solve-problems-involving-relationships-between-planes
Thanks.
Cheers,
Wen Shih
Hi,
Let's look at Q2.
Given: theta = pi/6, dx/dt = 0.1.
Find: dw/dt, where we let w = xy.
1. Find an expression of dw/dt by implicit differentiation, with respect to t.
2. Apply chain rule on dy/dt, so that you may use the information dx/dt = 0.1. You also need to find the value of dy/dx when theta = pi/6.
Thanks.
Cheers,
Wen Shih
Hi,
Let's deal with Q1.
Increasing: Common difference is positive.
Consecutive: Not necessarily first 3 terms. See them as k-th, (k + 1)-th, (k + 2)-th terms.
Thanks!
Cheers,
Wen Shih