Amaths question help?

77th Cloud SG

The binomial expansion of (1+px)^n, where n>0, in ascending powers of x is

1 - 12x + 28p²x² + qx³+ ...

Find n, p, and q

I got np = 12
nC2 = 28

n!/n-2! = 56, how can i solve this? or my path is wrong?

^tamago^ SG

(1+px)^n
= 1 + npx + [n(n-1)/2]p²x² + [n(n-1)(n-2)/6]p³x³+ ...
= 1 - 12x + 28p²x² + qx³+ ...

By comparing,
np = -12 ----(1)
n(n-1)(n-2) = 6q ----(2)

n²-n= 56
(n-8)(n+7)=0
n=8 or -7 (rej. as n>0)

sub n=8 into (1): p= -1.5
sub n=8 into (2): 8×7×6×(-27/8)=6q, q=56×-(27/8)=-189

AndrewPKYap SG

g(x) = |x-3|-4
Find the inverse of g(x)

tanjun SG

[quote]Originally posted by ^tamago^:
(1+px)^n
= 1 + npx + [n(n-1)/2]p²x² + [n(n-1)(n-2)/6]p³x³+ ...
= 1 - 12x + 28p²x² + qx³+ ...

By comparing,
np = -12 ----(1)
n(n-1)(n-2) = 6q ----(2)

n²-n= 56
(n-8)(n+7)=0
n=8 or -7 (rej. as n>0)

sub n=8 into (1): p= -1.5
sub n=8 into (2): 8×7×6×(-27/8)=6q, q=56×-(27/8)=-189[quote]

a small mistake here in bold.

should be [(n)(n-1)(n-2)/6]p^3 = 6q

It didn't really affect the rest of the workings except the
final ans of q should be
q = 8(7)(6)/6(-1.5)^3
= -189

tanjun SG

In this case, g(x) has no inverse function if the domain of g(x) is from -infinity to infinity.

Reason: It is not a one-one function.

^tamago^ SG

p³ was reflected in
sub n=8 into (2): 8×7×6×(-27/8)=6q

n(n-1)(n-2)p³ = 6q

so it remains as -189.

paiseh it's very hard to keep track of all the vars on the small screen. my error correction and checking techniques just didn't come in at this part other than to check that the answer at the end matches. Laughing

spadeTwo SG

tammy ~
i know chiu ish sexpert in amaths. get A1 sumore Laughing

^tamago^ SG

collect a lot of rust liao, need to buah gu you alrd. Laughing Sad Embarassed

spadeTwo SG

gu you not good lah
i want kaya Mr. Green

tanjun SG

lol. I made a mistake too. forget to divide by 6 for the ans.

AMEN567889 SG

Laughing

77th Cloud SG

A bloody motor boat travels in a stright line across a river which flows at 3m/s btwn straight parallel banks, 200m apart. the bloody boat, has speed 6m/s in still water, travels directly frm point a to point b, 150 downstream of a, on the opposite bank. find the time taken to travel frm a to b.

hisoka SG

differential eqn wor, and have to find out the flow profile of the river. and how long the boat is

77th Cloud SG

huh? what do u mean? this question is found on the ten year series.

absol SG

common angle between the velo diag. and dist diag is angle ABX

angle ABX = tan^-1( 200/150)
= 53.1 deg
using sine rule,
3sin53.1 / 6 = sin angle YAB
angle YAB = sin^-1 (0.4)
= 23.6 deg
therefore, angle AYB = 180-23.6-53.1= 103.3 deg
using cos rule, resultant velocity AB = ( 6^2 + 3^2 -2(6)(3)cos103.3)^1/2
resultant velocity AB = 7.30m/s

distance AB = (150^2+200^2)^1/2 (pythagoras theorem)
= 250

time taken = distance AB / resultant speed (also indicated by AB) = 250/7.30
= 34.25084106s
= 34s (nearest sec)

hope this helps...