2011 hsc mx1 marathon (2 Viewers)

[bleakarcher]

note: questions may only be posted by the solver of the previous problem
to start off:
d/dx[cos^(-1)[-1/x]]

 

[evanstroeve]

Using chain rule,



Let each arrangement of the letters D E L E T E D be a word.
How many words are there where the D's are separated?

 

[apollo1]

300

ill post question when someone confirms or denies my answer

 

[Deep Blue]

 

[apollo1]

you dont need the 2! because the Ds dont need to be arranged within the group. and also 420-240 = 180

 

[Deep Blue]

you dont need the 2! because the Ds dont need to be arranged within the group. and also 420-240 = 180

Ah, thanks for noticing that.

 

[xblacksheepx]

yeah, its 300.

 

[evanstroeve]

I got 300

 

[apollo1]

ok heres another question

Akram estimates that the probability of his winning any one game of tennis against a particular opponent is 1/3. How many games should they play so that the probability that akram wins at least one game is greater than 0.9 .

 

[evanstroeve]

 

[apollo1]

yep correct. someone post a question.

 

[evanstroeve]

Shit, sorry.

 

[artosis]

<a href="http://www.codecogs.com/eqnedit.php?latex=LHS = (1-sin^2x)^2 @plus;sin^2x \\= 1 - 2sin^2x @plus; sin^4x @plus; sin^2x \\ = sin^2x@plus;cos^2x-2sin^2x@plus;sin^4x@plus;sin^2x \\ = cos^2x @plus;sin^4x \\ =RHS" target="_blank"><img src="http://latex.codecogs.com/gif.latex?LHS = (1-sin^2x)^2 +sin^2x \\= 1 - 2sin^2x + sin^4x + sin^2x \\ = sin^2x+cos^2x-2sin^2x+sin^4x+sin^2x \\ = cos^2x +sin^4x \\ =RHS" title="LHS = (1-sin^2x)^2 +sin^2x \\= 1 - 2sin^2x + sin^4x + sin^2x \\ = sin^2x+cos^2x-2sin^2x+sin^4x+sin^2x \\ = cos^2x +sin^4x \\ =RHS" /></a>

 

[artosis]

shit forgot question

 

[blackops23]

shit forgot question

cos ALPHA = 1-t^2 / 1 + t^2

3/4 = 1-t^2 / 1+t^2

3 + 3t^2 = 4 - 4t^2

7t^2 = 1

t = +/- 1/(sqrt 7) but as ALPHA IS ACUTE t>0 therefore t = 1/sqrt(7) --> tan (alpha/2) = 1/(sqrt(7))]

EDIT: would i get full marks for this solution in an exam?

 

[apollo1]

shit forgot question

1/root(7)

 

[hup]

shit forgot question

A die is rolled 30 times. What is the most likely number of sixes to be rolled?

 

[apollo1]

heres a question:

 

[apollo1]

A die is rolled 30 times. What is the most likely number of sixes to be rolled?

5. hopefully i didnt make a silly mistake.

 

[hup]

heres a question:

View attachment 23277

thats ext 2 induction
and yes 5