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#1 Help Me ! » Circle Problems » 2017-05-05 11:09:07

ABC1234
Replies: 1

Circle C1 has equation (x+2)^2 + (y+4)^2 = 64 and circle C2 has equation (x-h)^2 + (y-1)^2 = 81.
The distance between the center of the circles is 13.
1. Find all possible values of h
2. If a segment connecting the centers is drawn, let A be the intersection of the segment with C1 and B be the intersection of the segment with C2. Find AB.
3. Find the equation of the two circles that have the same center as C1 and are tangent with C2.

For part 1, I've already found out that h=-14, 10.  Could you please help me with the rest?  Thanks!  (Please include steps, not just the answers)

#2 Re: Help Me ! » Functional Equations » 2017-04-14 09:36:58

ABC1234

I also need some help on this problem:
Find all functions

that satisfy
for all nonzero x.

I know I'm supposed to substitute (x-1)/x for x, but I don't seem to be getting anywhere with that. Thanks in advance!

#3 Re: Help Me ! » Functional Equations » 2017-04-13 10:15:01

ABC1234

for Q2 I got

but it wasn't right...am I still doing something wrong?

UPDATE:
Never mind, I just had to simplify it big_smile

#4 Re: Help Me ! » Functional Equations » 2017-04-12 10:39:41

ABC1234

for question 2 I got

. Is that right?

For Q1 I'm getting that y=4/3

#5 Help Me ! » Functional Equations » 2017-04-11 12:31:10

ABC1234
Replies: 12

Please help on the following:

1) Suppose that f(x) and g(x) are functions which satisfy f(g(x)) = x^2 and g(f(x)) = x^3 for all x >= 1. If g(16) = 16, then compute

. (You may assume that f(x) >= 1 and g(x) >= 1 for all x >= 1.)

2) The function

satisfies
for all real x. Find f(x).

3) Suppose we have the following identity:

Find the minimum of

Thanks for the help!

#6 Re: Help Me ! » Intermediate Algebra » 2017-02-09 13:27:12

ABC1234

They do not mind

#7 Re: Help Me ! » Intermediate Algebra » 2017-02-09 10:37:56

ABC1234

I'm not sure what Brilliant is.  These problems are from an online math class I take.

#8 Help Me ! » Intermediate Algebra » 2017-02-08 10:33:26

ABC1234
Replies: 8

1) Let

for
  There is a unique ordered pair (c,d) such that
is the closed form for sequence
.  Find c using the Fibonacci and Lucas number sequences.

2) A closed form for the sum

is
where a, b, and c are integers.  Find a+b+c.

Thanks for the help!

#9 Re: Help Me ! » Geometric Sequences » 2017-01-27 12:30:00

ABC1234

I think that the only possible value of r is 0 though.  I'm not sure how to go about proving that though.

#10 Re: Help Me ! » Geometric Sequences » 2017-01-27 12:22:21

ABC1234

I don't really understand the above explanation either

#11 Help Me ! » Geometric Sequences » 2017-01-26 12:18:18

ABC1234
Replies: 4

Please Help:

Determine all nonnegative integers r such that it is possible for an infinite geometric sequence to contain exactly r terms that are integers. Prove your answer.

Thank you in advance!

#12 Re: Help Me ! » Multivariable Polynomials » 2017-01-18 09:36:03

ABC1234

I need help on this one as well:

Find all real x that satisfy

#13 Re: Help Me ! » Multivariable Polynomials » 2017-01-10 12:03:35

ABC1234

Thank you!  I'm still kinda unsure how you solved for 2 though

#14 Help Me ! » Multivariable Polynomials » 2017-01-09 12:48:12

ABC1234
Replies: 8

1) If (x,y) satisfies the simultaneous equations

and
, where x and y may be complex numbers, determine all possible values of
.

2)Determine a constant k such that the polynomial

is divisible by x+y+z.

Thank you!

#15 Re: Help Me ! » Intermediate Algebra » 2016-12-27 04:14:08

ABC1234

I know how to find the sum of roots using vieta's, but how am I supposed to find the coefficients?

#16 Re: Help Me ! » Intermediate Algebra » 2016-12-25 08:00:11

ABC1234

I see after using substitution but what about -4x+3?

#17 Re: Help Me ! » Intermediate Algebra » 2016-12-24 07:54:27

ABC1234

1) I got -8 too after completing the square: 2m^2-4m-6 -> 2(m^2-2m-3) -> 2((x-1)^2-4).  Thanks!
2) I'm not sure about this problem though.  All I know so far is that for

, we can turn it into

#18 Help Me ! » Intermediate Algebra » 2016-12-23 09:52:01

ABC1234
Replies: 10

Please help on following:

1) Suppose r and s are the values of x that satisfy the equation

for some real number m. Find the minimum real value of
.
Using vieta's I used the coefficients of the quadratic to express
as
, but I don't know what to do after that.

2) Let

and let
be the roots of f(x).  Compute
.

Thank you

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