Stuck on some maths

smiles

Well, i've been trying to learn my entire honors maths course and it's fun i tell you! (started last week :P )

Ran into a few problems and if anyone an help i'll be eternally grateful - and i need methods, not answers

1. In how many ways an 4 students be chosen out of a group of 12 to go on a trip if a brother amd sister will only go if both are selected?

[i seriously think there's info missing from that one]

2. Find the equation of the circles which contain the point (0,6), have their centres on the line x + y = 3, and which have the line 4x + y - 23 = 0 as tangent.

Oh, and if anyone can explain how to do those ****in simple trigonometry questions ( if SinA = 2/4, what is Sin(4A) ) and that type, the ones without tables or calculator use - my brain just refuses to understand them atm.

I'll be very grateful!

<< Fio >>

Ruaidhri

ok if i remember this right....
1)
you want to choose (effectivly) 3 ppl from a group of 12.(if the brother will go ONLY if the sister will,we will treat them as a pair,one unit)so that means we can go something like this

[1*1]*10*9

the bit in the bracket is the brother and sister..
so now that gives us 90 ways,BUT you can arrange the brother and sister 2 ways(factorial 2..the bit in the brackets)
so we get
90*2=180

i'm not sure..if anyone would check my answer?
does it make any sense?
pm me with any questions

smiles

Originally posted by Ruaidhri
ok if i remember this right....
1)
you want to choose (effectivly) 3 ppl from a group of 12.(if the brother will go ONLY if the sister will,we will treat them as a pair,one unit)so that means we can go something like this

[1*1]*10*9

the bit in the bracket is the brother and sister..
so now that gives us 90 ways,BUT you can arrange the brother and sister 2 ways(factorial 2..the bit in the brackets)
so we get
90*2=180

i'm not sure..if anyone would check my answer?
does it make any sense?
pm me with any questions

The answer's 255.

I mean i think you need something to do with the number of brothers or something. i dunno

<< Fio >>

Gordon

Sounds like they are talking about a specific brother and sister.

Have you tried just whittling down the numbers and calculating them manually then test your hypothesis with that framework?

ie if you have 4 people and only these two can go and you need two people to go etc.

Ruaidhri

hmm..i'm stumped..tried the (n!)/((n-r)!) formalue and got 220?i've NO idea(and i just finished my maths exam last week )

Paulj

ok ...here's how the answer:
10c4 + (10c2)(2c2)=210+(45)(1)=255

ie.
either [the brother and sister] dont go on the trip
or
[the brother and sister] do go on the trip

if they dont go: there are 10 other students left from which to select 4 to go. ie 10c4 (the number of selections of 10 objects taking 4 at a time)

if they do go: there is only on way of selecting the brother and sister to go. ie 2c2=1
and there are 10 people left from which to select the other 2. ie 10c2.
=>the number of ways of selecting the 4 if the bro and sister go is: (10c2)(2c2)=45

Remember that this is a "selections" question. So that means that taking the brother then the sister is the same as taking the sister then the brother.

Paulj

For your second question you gotta form three equations which contain the variables g,f and c. And then use simultaneous eq's to solve for g,f and c and then sub these values into the general circle equation which is:

x^2 + y^2 + 2gx + 2fy +c = 0

To form the three eq's in g,f and c do the following:

a: sub (0,6) into the general circle equation as x and y.

b: sub (-g,-f) into x+y=3 (since the centre of the circle is (-g,-f) and this will satisfy the eq)

c: find the slope of the line 4x+y-23=0. Then find the slope of the line which would be perpendicular to this. (ie m2=-1/m1). Then form the equation of the line perpendicular to 4x+y-23=0 and going through the centre using this slope and the point (-g,-f).

I think thats the jist of it anyway.:)

Paulj

The third question is tackled like this:

Notice that Sin4A is a double angle (see p9 of tables).
ie. Sin4A=2sin2Acos2A
=2(2sinAcosA)([cosA]^2-[sinA]^2)

now all you have to do is find cosA.
This is done using the fact the sinA=4/2=opposite/hypotenuse

Then draw out a right angled triange. Mark in the angle A. Let the opposite side = 4 ; let the hypotenuse = 2. Then use pythagoras's t-rum to find the adjacent side (which is = \/12 [root12]=2\/3)). So then you can say that CosA = \/3/2. Just sub the values for cosA and sinA into the eq above then and u find sin4A = \/3/2.

PiE

God I hate maths.

sc317

I take it this is higher maths???

Please, please tell me it is!

smiles

Originally posted by Paulj
The third question is tackled like this:

Notice that Sin4A is a double angle (see p9 of tables).

IT says not to use log tables or calculators... does that count?

<< Fio >>

Thanks for the other solutions, looking through them now.

and yes, it's higher maths

Nietzschean

smiles i've done all the paper 2's now and i've yet to see a question where it says not to use the tables, i think you will find you have misread that it should be something similar to :

given Sin2A = 5/4 find Sin4A without finding the value of Sin2A or something similar...they want you to use the tables not avoid them only other way would be to use maclarian series......find 2A double it and so on...but i doubt its that

Paulj

I'd say what they mean is not to use the table on page 9 of the log tables however im sure your allowed to use the standard trigonometric proofs. ie. sin2a=2sinAcosA. This means that you never actually know the value of A.

alex122

I think Paulj is right

smiles

Originally posted by Serialkiller
smiles i've done all the paper 2's now and i've yet to see a question where it says not to use the tables, i think you will find you have misread that it should be something similar to :

given Sin2A = 5/4 find Sin4A without finding the value of Sin2A or something similar...they want you to use the tables not avoid them only other way would be to use maclarian series......find 2A double it and so on...but i doubt its that

It's not from the Exam papers.

Some of the other questions like it are:

"If Sin A = 3/5 and cosB = 7 /25, A and B acute, find the value of tan (A + without using tables or a calculator"

or

"Given than tan(A + = 1 and that tan (A - = 1/7., find without using the tables or a calculatior a value for tan A and tan B."

<< Fio >>

lazer

why have u only taking up higher math now..

Nietzschean

smiles then its not on the lc course...there is no trig questions like that on our course...and without using maclarian series i don't think they can be done..

Keeks

Those trig questions are all done (from what i remeber of LC maths) using page 9 of the table book (the page no. is imprinted in my brain).

Lo time since i did LC maths, but thats what it looks lke to me. Would try and calculate them, but I don't have a table book, and couldn't be ar$ed anyway

smiles

Originally posted by lazer
why have u only taking up higher math now..

I didnt only take up higher maths now.

They are on the ourse, they're out of one of the Maths Books.

They dont tend to come up on the papers but i just wanted to know how to dothem just in case.

<< Fio >>

Molly

They are on the ourse, they're out of one of the Maths Books.

No there not on the course. Theres a hell of amount of extra crap in the Maths books.

Nietzschean

chill smiles.....just work at stuff you know is lightly to come up now...too late to be doing something so obscure...just going to stress yourself........

and if nothing else don't be posting that scaring the bejesus outa the rest of us