2u Mathematics Marathon v1.0 (2 Viewers)

[ice ken]

Aruguing over the internet over who gets to post a maths question, come on people I kid

go ahead drynxz post rue question

 

[drynxz]

lol ok then my turn!!



prove cot(A+B) = (cot A cot B - 1 ) / ( cot A + cot B)
*might have been typed up previously but too lazy to look through 500 posts -_-

EDIT : the text book has the answers wrong, so i edited the question.

 

[Riviet]

*might have been typed up previously but too lazy to look through 500 posts -_-

From my memory, I don't recall a question like that. So no worries.

 

[pLuvia]

Easy one

int.secxdx

*Hint*

Spoiler

Multiply top and bottom by secx + tanx

 

[SoulSearcher]

Yeah sure, if you're doing 4 unit

 

[Riviet]

Easy one

int.secxdx

I think a hint might be good as a 2 unit student wouldn't be able to spot this easily:

Spoiler

Multiply top and bottom by secx + tanx

 

[pLuvia]

Opps, I didn't think it was specifically for a 4u students. Anyway take Riviet's advice

 

[SoulSearcher]

I didn't say it was for 4 unit students, I said it would be easy for a 4 unit student Now the hint is there, it should be easy now

 

[Forbidden.]

Here's a no doubt easy one ..

Find the gradient of a straight line perpendicular to 5x+2y-10=0


Former HSC students have trouble recalling linear graphs ..

 

[Starcraftmazter]

This?

Spoiler

5x+2y-10=0
m₁ = -A/B
m₁ = -5/2
Using m₁m = -1,
-5/2m = -1
-5m = -2
m = 2/5

Therefor, gradient of line is 2/5

 

[Riviet]

Yep, and pLuvia's question needs answering too.

P.S int. means "integral of".

 

[Starcraftmazter]

Haven't done that yet 8)

btw. I thought it was one question at a time :s

 

[SoulSearcher]

Yeah, well people have been skipping questions lately

 

[Mountain.Dew]

heres my contribution:

HSC 2004 Q9(b)

URL to pdf file here: http://boardofstudies.nsw.edu.au/hsc_exams/hsc2003exams/index4.html#m

 

[DistantCube]

Int. sec x =

Spoiler

ln (sec x + tan x) + c

for reference; work the rest our yourselves.

 

[drynxz]

and no one anwered my question too -_-

 

[SoulSearcher]

I might as well kill 2 birds with one stone. Got nothing else to do at the moment.

prove cot(A+B) = (cot A cot B - 1 ) / ( cot A + cot B)

Spoiler

cot(A+B) = 1/tan(A+B)
= 1/{(tanA+tanB)/(1-tanAtanB)}
= (1-tanAtanB)/(tanA+tanB)
= {(cotAcotB-1)/(cotAcotB)}/{(cotA+cotB)/cotAcotB)}
= (cotAcotB-1)/(cotA+cotB)

int. sec x

Spoiler

int. sec x dx
= int. secx(secx+tanx)/(secx+tanx) dx

d/dx (secx + tanx) = secxtanx + sec²x
= secx(secx+tanx)

Therefore secx(secx+tanx)/(secx+tanx) = f'(x)/f(x), where f(x) = secx+tanx
Therefore int. secx(secx+tanx)/(secx+tanx) dx
= ln (secx+tanx) + C

I'll leave Mountain.Dew's question for someone else to do.

 

[Riviet]

Another question:

Solve e^4x - 4e^2x + 4 = 0

 

[Sober]

Another question:

Solve e^4x - 4e^x + 4 = 0

That is equivalent to solving y⁴ - 4y + 4 = 0 which is beyond the 2 or even 4 unit course. Also, I graphed it using graphing software and it even has no real solutions.

 

[Riviet]

Woops, that wasn't intended. I've fixed it up (now it's solvable).