Math Forum / Mathematics / Undergraduate Math / June 2005

Two circles C1 and C2 meet at the points A and B. P is a point on the circumference of C1 such that PA is tangent to C2 at A. Q is a point on the circumference of C2 outside C1. QA is produced to meet C1 again at T
so that anglePBT = 75 degrees. Find the size of angleABQ.

I am trying to prove this by induction, but have so far failed.
I note that:
b1 = 1, r1 = 7
b2 = 7, r2 = 13

I have something here called a linear translation
(x,y) -> (x+3,y+5) this can not be done as linear mapping using regular coordinants because
(a1, b1) -> (c1,d1) as well as (a2,b2) -> (c2,d2) it would that according to linearity
(a1 + a2, b1 + b2) -> (c1 + c2, d1+d2)

This question is from the Accuplacer Test (sample exam question)
The equation x2 + 2ix - 4 = 0 has as its roots:
A. Ö5 - 1 , - Ö5 -1
B. Ö5 - i , Ö5 + i

i need help, here the question:
1. From a point on the ground the angle of elevation to a ledge on a building is 27°, and the distance to the base of the building is 45 meters. How many meters high is the ledge?
meters high is the ledge?
        the correct answer is 45/tg 27 degree.  ...

1*2*3-2^3+3*4*5-4^3+...+9999*10000*10001-10000^3.
All i have is, any help as always is appreciated;
If I split the entire series into two parts
(1*2*3+3*4*5+.........)-(2^3+4^3+.......)

not sure if this is right, but can you guys look it over.
2^-3+5^0
( _________) 1/2
2^-5

True or False:
If F(6) and LIM X->6 F(X) both exist, then their vlaues must be approximately equal.
I said this was true but my teacher took of points claiming the answer was false because continuity is not given.
Doesn't F(6) and LIM X->6 F(X) both existing imply continuity?

Im going to study number theory by myself this summer ( my first course in
number theory). In my university they use
Elementary number theory By Burton, fifth edition.
I read good reviews about it on amazon. anybody used another book and think

These seem to be popular at the moment, so I thought I'd chip in:
Limit[(1 - Cos[x])/(x Sin[x]), x -> 0]
(that is, the limit of (1-cosx)/xsinx as x tends to 0)
I'd appreciate any assistance, cos I'm really bad at these. Thanks in

These seem to be popular at the moment, so I thought I'd chip in:
Limit[(1 - Cos[x])/(x Sin[x]), x -> 0]
(that is, the limit of (1-cosx)/xsinx as x tends to 0)
I'd appreciate any assistance, cos I'm really bad at these. Thanks in advance.

I'm trying to solve this problem that has me stumped. Basically, it's a trajectory problem with two twists.
It takes place on a crazy planet where gravity is equal to the vector function
g(t) = (-2 + sin(t))i + (-32 + cos(t))j
(essentially, it always points downward and away from ...

Ok, this is more an algebra question.  Given the equations h/x = tanA1
and h/(x+d) = tanA2, how do I solve for h?  A1, A2, and d are known, x
is unknown.  I know that
h = x * tanA1 and also h = (x + d) * tanA2

I was just wondering if there is an equation or something that can find the number of different posiibilities for a " n " digit code using " m " different figures?
For example if it were a 10 digit alphanumeric code. n=10 m=36 (26 letters + 10 numbers)
Thanks.

Hi, to everyone
I found this "strange" integral.
The exercise says:
Study the following improper integral