mm-499
===
Subject: Re: Past IGCSE Physics Papers
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id i88LKgC28051;
Hello
My name is Zohaib from KSA. I urgently need the IGCSE past
papers of
every subject.
Has any one got any of the Physics past questions for the
>international GCSE Examination ? Where could I get them ?
===
Subject: ma 214
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id i88Mavg02146;
I am in cal 4 but it has been a while since I had cal 2. how
do you
solve 2 2
a(t) = -t^ /2 s^ /2
e^ integral (from o to t) e^ ds
this reads, e raised to the negitive t to the second degree
divided
by 2, then times the integral from 0 to t of e raised to s to
the
second degree divided by 2.
Trying to find if it is a solution of the differential eguation
x''(t) + tx'(t) + x(t0 = 0
I am having trouble taking the derivative od a(t)
===
Subject: Re: ma 214
> 2 2
> a(t) = -t^ /2 s^ /2
> e^ integral (from o to t) e^ ds
> this reads, e raised to the negitive t to the second degree
divided
> by 2, then times the integral from 0 to t of e raised to s
to the
> second degree divided by 2.
f(t) = e^((-t^2)/2); f'(t) = -t.f(t); f(t) = -f(t) + t^2 f(t)
a(t) = f(t) integeral(0,t) f(t) dt
a'(t) = -t.a(t) + f(t)(f(t) - 1)
a(t) = -a(t) - t.a'(t) - 2t.f(t)^2 + t.f(t)
> Trying to find if it is a solution of the differential
eguation
> x''(t) + tx'(t) + x(t0 = 0
f(t) + t.f'(t) + f(t) = 0
> I am having trouble taking the derivative od a(t)
===
Subject: Re: ma 214
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id i89Ie8F10286;
>f(t) = e^((-t^2)/2); f'(t) = -t.f(t); f(t) = -f(t) + t^2 f(t)
>a(t) = f(t) integeral(0,t) f(t) dt
Not correct.
a(t) = f(t).integeral(0,t) dt/f(t)
>a'(t) = -t.a(t) + f(t)(f(t) - 1)
>a(t) = -a(t) - t.a'(t) - 2t.f(t)^2 + t.f(t)
a'(t) = -t.a(t) + f(t)/f(t) = -t.a(t) + 1
a(t) = -a(t) - t.a'(t)
and also
f(t) = -f(t) - t.f'(t)
===
Subject: Re: ma 214
> I am in cal 4 but it has been a while since I had cal 2. how
do you
> solve 2 2
> a(t) = -t^ /2 s^ /2
> e^ integral (from o to t) e^ ds
a(t) = e^((-t^2)/2)
Use chain rule
a'(t) = e^((-t^2)/2)) * (1/2) * (-1) * 2t = -t.a(t)
> Trying to find if it is a solution of the differential
eguation
> x''(t) + tx'(t) + x(t0 = 0
> I am having trouble taking the derivative od a(t)
a(t) = ???
===
Subject: Explanation
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id i88N6RY04860;
Can anyone explain me how/why
1/2 * [(2,-45 degrees) - ( 40,90 degrees)] = (41.43,-88
degrees)
and
how/why
1/2 * [(2,-45 degrees) + ( 40,90 degrees)] = (38.62,88
degrees)?
Pliz can can any1 explain me the working of the above 2
problems and
how we arrive at these 2 answers?
===
Subject: Re: Explanation
> Can anyone explain me how/why
> 1/2 * [(2,-45 degrees) - ( 40,90 degrees)] = (41.43,-88
degrees)
> and
> how/why
 1/2 * [(2,-45 degrees) + ( 40,90 degrees)] = (38.62,88
degrees)?
> Pliz can can any1 explain me the working of the above 2
problems and
> how we arrive at these 2 answers?
Are your ordered pairs, such as (2,-45 degrees), supposed to
be polar
representations of 2d vectors or 2d points or complex numbers?
If so, one way to deal with them is to convert to rectangular
form do
the various operations the convert back.
For example, the polar form (r, theta) for a complex number
converts
to the rectangular form r cos(theta) + i sin(theta)
===
Subject: Re: Explanation
>Can anyone explain me how/why
> 1/2 * [(2,-45 degrees) - ( 40,90 degrees)] = (41.43,-88
degrees)
> and
> how/why
 1/2 * [(2,-45 degrees) + ( 40,90 degrees)] = (38.62,88
degrees)?
> Pliz can can any1 explain me the working of the above 2
problems and
>how we arrive at these 2 answers?
Those appear to be ordered pairs, first summed, and then
multiplied by half.
They each seem to be both wrong. Are you trying to multiply
each sum and
difference by half?
For the first, I would take path:
(1/2) *[(-38, 45 degrees)] = (-19, 24.5 degrees)
Maybe I have misunderstood what you expressed.
G C
===
Subject: Re: Explanation
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id i89BsDS03622;
>Can anyone explain me how/why
> 1/2 * [(2,-45 degrees) - ( 40,90 degrees)] = (41.43,-88
degrees)
> and
> how/why
 1/2 * [(2,-45 degrees) + ( 40,90 degrees)] = (38.62,88
degrees)?
> Pliz can can any1 explain me the working of the above 2
problems
and
>how we arrive at these 2 answers?
>Those appear to be ordered pairs, first summed, and then
multiplied
by half.
>They each seem to be both wrong. Are you trying to multiply
each sum
and
>difference by half?
>For the first, I would take path:
>(1/2) *[(-38, 45 degrees)] = (-19, 24.5 degrees)
>Maybe I have misunderstood what you expressed.
>G C
Yes the sum and difference of these polar coordinates are being
multiplied by half.
Geometrically, i have been able to come up with how the
answers were
===
Subject: Re: Explanation
>Can anyone explain me how/why
> 1/2 * [(2,-45 degrees) - ( 40,90 degrees)] = (41.43,-88
degrees)
> 1/2 * [(2,-45 degrees) + ( 40,90 degrees)] = (38.62,88
degrees)?
> Those appear to be ordered pairs, first summed, and then
multiplied by
half.
> They each seem to be both wrong. Are you trying to multiply
each sum and
> difference by half?
> For the first, I would take path:
> (1/2) *[(-38, 45 degrees)] = (-19, 24.5 degrees)
> Maybe I have misunderstood what you expressed.
No, he's being a jerk expecting us to read his mind, for are
not we, like
him and everybody else in his class, totally knowledgeable, as
tho it was
our
native language, what jargon he's using? Now I ask you and
him, am I
psychic? Is he using polar coordinates, like (5 ft, North by
NorthWest)
and vector addition?
===
Subject: Re: Pre-calc
>I haven't taken math since high scool and I forgot
everything, can
>someone please explain this problem for me.(Difference
quotient)
>f(x)= 2x+5
[f(x+h) - f(x)] / h
[ 2(x+h)+5 - (2x+5) ] / h
[ 2x+2h+5 - 2x - 5 ] / h
2h/h
2
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com
You want an intelligent conversation? Do what I do: talk to
yourself. It's the only way. -- /Torch Song Trilogy/
===
Subject: Re: simplifying large square roots
> When simplifying square roots, then it is possible to find a
square
number
> which is a factor of the number to be 'square rooted', and
so simplify
the
> square root by 'bringing' the square root of the square
number outside of
> the root..... if that makes sense.
> For instance, sqr(32) is equal to sqr(16 x 2) = 4sqr(2).
> So, is there a way to determine whether a number to be
rooted has a
square
> number as a factor? is there an algorithm (other than the
most obvious
way
> to go through each square number in turn) that can find
square number
> factors?
It's easy to read off the square and squarefree parts of an
integer
from its factorization into primes, e.g. p q^2 r^3 s^4 ->
pr(qrs^2)^2.
Currently no feasible (polynomial time) algorithm is currently
known
for recognizing squarefree integers or for computing the
squarefree
part of an integer. In fact it may be the case that this
problem
is no easier than the general problem of integer factorization.
The latter problem is important because one of the main tasks
of computational algebraic number theory reduces to it (in
deterministic polynomial time). Namely the problem of computing
the ring of integers of an algebraic number field depends upon
the square-free decomposition of the polynomial discriminant
when computing an integral basis, e.g. [3] S.7.3 p.429 or [2]
This is due to Chistov [1]. See also Problems 7,8, p.9 in [4],
which lists 36 open problems in number theoretic complexity.
-Bill Dubuque
[1] A. L. Chistov. The complexity of constructing the ring of
integers
of a global field. Dokl. Akad. Nauk. SSSR, 306:1063-1067, 1989.
English Translation: Soviet Math. Dokl., 39:597-600, 1989.
90g:11170
http://citeseer.nj.nec.com/context/464298/0
[2] Lenstra, H. W., Jr. Algorithms in algebraic number theory.
Bull. Amer. Math. Soc. (N.S.) 26 (1992), no. 2, 211-244.
93g:11131
http://www.ams.org/bull/pre-1996-data/199226-2/lenstra.pdf
http://www.ams.org/bull/pre-1996-data/199226-2/Lenstra
[3] Pohst, M.; Zassenhaus, H. Algorithmic algebraic number
theory.
Cambridge University Press, Cambridge, 1997.
[4] Adleman, Leonard M.; McCurley, Kevin S.
Open problems in number-theoretic complexity. II.
Algorithmic number theory (Ithaca, NY, 1994), 291-322,
Lecture Notes in Comput. Sci., 877, Springer, Berlin, 1994.
95m:11142
http://citeseer.nj.nec.com/168265.html
===
Subject: Re: Maths software and line-of-best-fit
> I need to ascertain, from a data set, precisely the point at
which a
> line of best fit crosses the X-axis.
> I know how to draw it free hand I'm just worried its not
accurate!
> Consequently I'd be gratful if anyone could recommend a
suitably
> accurate software package, apparantly many, e.g. Excel arent
very
> accurate.
There are several formulas in the method of least-square
regression that
will enable you to compute the least-square regression line
(aka the
line-of-best-fit) from your (x,y)-pairs of data. Excel will
crank out
those formulas and give you the slope and the y-intercept of
that line.
Call
the slope m and the y-intercept b. Then, the regression line is
given
by the equation: y = m x + b. Again, Excel computes what m and
b
are
from the data you entered.
Now, to determine where this line crosses the x-axis, you just
set y=0, and
solve for x. If you do that, you'll find out that the
x-intercept is
located
at the point (-b/m, 0). Excel is accurate enough for most
mundane
applications (unless you are doing nuclear physics).
Shedar
===
Subject: Re: Consecutive Terms in math
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id i89DmQJ14776;
Arturo you !never! did give me an equation for solving
consecutive
!Multiplied! terms and that's what I've been searching for...
===
Subject: Re: Consecutive Terms in math
days. My association with the Department is that of an alumnus.
>Arturo you !never! did give me an equation for solving
consecutive
>!Multiplied! terms and that's what I've been searching for...
Brock! I !never! claimed to give you an equation.
I gave you a ->METHOD<- for bounding the possible solutions to
a
manageable set.
And then I said I had given you a method.
Do you know the difference between equation and method? Here's
a
hint: an EQUAtion must have an EQUAL sign somewhere in it...
--
It's not denial. I'm just very selective about
what I accept as reality.
--- Calvin (Calvin and Hobbes)
Arturo Magidin
magidin@math.berkeley.edu
===
Subject: Domain of inequality quadratic
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id i89DmQY14796;
State the domain for n
then state the domain for which cases it isn't true. (use
domain of t)
(n^2)+n<20
My problem is that because of the less than they don't need the
quadratic to come out and I can't solve... maybe you can help?
===
Subject: Re: Domain of inequality quadratic
> State the domain for n
> then state the domain for which cases it isn't true. (use
domain of t)
> (n^2)+n<20
> My problem is that because of the less than they don't need
the
> quadratic to come out and I can't solve... maybe you can
help?
Bring everything to one side:
n^2 + n - 20 < 0
Factor:
(n + 5)(n - 4) < 0
Now, what can you say about *that* inequality?
--
Rich Carreiro rlcarr@animato.arlington.ma.us
===
Subject: 25 of March and 28 of October
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id i89ENNF18413;
Hello people.. I recently found out that what happens is that
25 of
March and 28 of October have the same day, every year. e.g if
25 of
March 1980 is Monday , then 28 of October is Monday also..
I' m trying for the proof but I have difficulties.
Can you please give me some help?
Have you ever seen that with some other dates maybe?
===
Subject: Re: 25 of March and 28 of October
> Hello people.. I recently found out that what happens is
that 25 of
> March and 28 of October have the same day, every year. e.g
if 25 of
> March 1980 is Monday , then 28 of October is Monday also..
> I' m trying for the proof but I have difficulties.
> Can you please give me some help?
> Have you ever seen that with some other dates maybe?
If, and only if, the number of days between 2 dates (counting
one date
but not the other) is a multiple of 7 (days per week) then the
dates are
on the same day of the week.
This will be a fixed number of days from any date on or after
1 March of
any year up to and including 28 February of the following year.
Periods containing a day in February and a day in the
following March
are subject to leap year variations.
===
Subject: Re: 25 of March and 28 of October
X-RFC2646:  Original
> Hello people.. I recently found out that what happens is
that 25 of
> March and 28 of October have the same day, every year. e.g
if 25 of
> March 1980 is Monday , then 28 of October is Monday also..
> I' m trying for the proof but I have difficulties.
> Can you please give me some help?
> Have you ever seen that with some other dates maybe?
Show that the number of days between 25MAR and 28OCT is
divisible by 7.
--
-- Geo. Michael Henry
No! Bad dog! I said sit! anonymous
===
Subject: Re: subbasis for the topology of a set
> Now in fact (1) isn't quite true as you've stated the
> theorem: in order to prove (1), you have to know that G
> covers X, i.e., that every point of X is in at least one
> member of G. (Another way to say this: U{A : A in G} = X.)
> I don't know whether you've misstated the problem, or
> whether it was poorly stated in your source. However, (2)
> is still true, and I suspect that it's the main point of the
> exercise.
perhaps i left something out. that was a passage (not a
theorem)
of a book called ``topology'' by Klaus Janich which I might
have
omitted something important. before i write the passage here,
let describe my notation:
/ means intersection and / means union. so for example:
n
B = { / s_i such that s_i, ..., s_n is in S}
i=1
means B is the set of all intersection of sets s_i from 1 to n
such that every s_i a member of the collection of sets S. does
anyone have a better notation? words might be misleading. and i
use ``_{}'' as my notation for subscript when the subscript is
more than one letter. the braces act as parentesis.
and here's the passage:
``Definition (subbasis): Let X be a topological space. A set S
of open sets is called a subbasis for the topology if every
open
set is a union of finite intersections of sets in S.
Of course the word ``finite'' here does not mean that the
intersection should be a finite set, but that is the
intersection of finitely many sets. This includes the
intersection of zero sets (that is, an empty family of sets),
which by a meaningful convention is defined to be equal to the
whole space (since in this way the formula
(/_{i in I} S_i) / (/_{u in U} S_u)
=
(/_{v in I / U} S_v)
still holds). Analogously, the union of an empty family of sets
is suitably defined as the empty set.
With these conventions we then have that if X is a set and S
and
arbitrary set of parts of X, there is exactly one topology T(S)
on X such that S is a subbasis for T(S) (the topology generated
by S). It consists exactly of the unions of finite
intersections
of sets in S.''
i am trying to show that the last paragraph is true. before,
let
me give you in my words, what I understand as a subbasis.
let X be a topological space. let S be a collection of open
sets. S is a subbasis for the topology of X if and only if
n
B = { / s_i such that s_i, ..., s_n is in S}
i=1
is a basis for the topology of X. is this correct?
and what I need to show to prove that passage from klaus janich
is (as you said) that there is some topology on X that has S as
a subbasis and if T_1 and T_2 are topologies on X such that
both
have S as subbasis, then T_1 = T_2.
proof:
we must show that there is T_1(S) on X such that S is a
subbasis. this is first thing. we also must show that if T_2(S)
is a topology on X such that S is a subbase for open sets of
(X,T_2), then T_2 = T_1.
i'm trying to use ``S as a subbase'' instead of show that T_1
is
a subset of T_2 and T_2 is a subset of T_1 as you advised. i
think it's easier this way.
define T_1(S) = {/_{i in I} b_i | for every i in I, b_i is in
B}. claim T_1(S) is a topology. let A_j be in T_1(S) for every
j
in J. now, I must show that /_{j in J} A_j is in T_1(S). so,
for every j in J, there's an I_j such that for every i in I_j,
there is B_i ``with respect to j'' in B such that
A_j = /_{i in I_j} B_i ``with respect to j''.
now, if I show that /_{j in J} A_j is in T_1(S), i believe that
means that T_1(S) = T_2(S).
i tried my best with the notation. sorry if it's hard to read.