Mathematics - 22 October 2007

1.Prove that a decimal (ie base 10) number a(subscript n)…a(subscript 2), a(subscript 1), a(subscript 0) is divisible by 11 if and only if the number (-1)^n*( a(subscript n)+…+a(subscript 2) - a(subscript 1) + a(subscript 0) is divisible by 11.

2.Evaluate (59/61), (30/59) showing all the steps and naming the laws used at each step. (Hint: Legendre’s symbols.)

3.Prove that if G=, then G=

4. Let G be a finite group, and let g,x∈ G
(a) prove that x and g^-1xg have the same order
(b) Let a,b∈G. Prove that ab and ba have the same order

This is i think the last of my exam help..thanks to everyone. i really appreciate it

Don

2007-10-22 15:00:32 · 1 answers · asked by Anonymous

Wheat is poured through a chute at the rate of 10 ft^3/min and falls in a conical pile whose bottom radius is always half the altitude. How fast will the circumference of the base be increasing when the pile is 8 ft high?
I know that v= (1/3) py r^2 h
because r equals half h so
v= (2/3) py r^3
differentiate: (dv/dt) = 2py (r^2) (dr/dt)
and we also know that the circumference:
(dc/dt) = 2 py (dr/dt)
and then what can I do ??
plz help

2007-10-22 14:58:31 · 1 answers · asked by thatisme 2

What is the cardinality of {o,{o}} where o is the empty set

2007-10-22 14:46:12 · 3 answers · asked by Y1083 1

can somebody explain how I answer write this question? I know what the zeroes are im just not sure about the last two points...

Determine the equation if the zeroes are -2 and 3 and the graph passes through the point (1,4)

Determine the equation if the zeroes are -3, 1 and 2 and the y-intercept is 3

2007-10-22 14:43:51 · 2 answers · asked by Anonymous

It's the sum from K=1 to infinity for (K)/(K!)

It's merely auxillary to another problem (statistics.....poisson distribution).....

But I've forgotten how to do this one, and I don't have a book on integrals and sums with me.

2007-10-22 14:43:43 · 4 answers · asked by Anonymous

I keep getting -9 and its wrong

2007-10-22 14:43:30 · 10 answers · asked by johnniedr3 1

Show that a positive integer is divisible by 11 if and only if the difference of the sum of its decimal digits in even-numbered positions and the sum of its decimal digits in odd-numbered positions is divisible by 11.

2007-10-22 14:27:43 · 2 answers · asked by Anonymous

all i know is something about the horizontal rule or something..

2007-10-22 14:27:29 · 2 answers · asked by jmacsgrl15 2

2007-10-22 14:27:27 · 1 answers · asked by Anonymous

φ(n) is almost always divisible by 4. Describe all the n's for which φ(n) is not divisible by 4.

2007-10-22 14:25:40 · 2 answers · asked by gumy23s 1

2007-10-22 14:25:31 · 1 answers · asked by birmingham927 2

An airplane flies at an altitude of 5miles toward a point directly over an observer. The speed of the plane is 600mph. Find the rate at which the angle of elevation "theta" is changing when the angle is a) theta = 30degrees
b) theta = 60deg
c) theta = 75deg

2007-10-22 14:23:40 · 1 answers · asked by Sean 2

Pls don't jus tgive me the answer, but just give the solution showing the steps involved in solving this problem

2007-10-22 14:21:12 · 2 answers · asked by venky 2

A hint was given to consider the n consecutive integers starting with (n+1)! + 2... but I'm not entirely sure where to go with this problem...

2007-10-22 14:19:37 · 5 answers · asked by Anonymous

PRIME FACTORS OF:56, 67, 72, 85, 92
PRIME FACTORIZATION OF:49, 38, 76, 60, 81, 132, 140, 87

2007-10-22 14:19:24 · 2 answers · asked by Anonymous

If the graph of a polynomial function has four x-intercepts, then it must have at least three points at which its tangent line is horizontal.

True or false? Explain?

2007-10-22 14:18:16 · 2 answers · asked by Daniel B 1

f(x) = 2sinx + sin2x, [0,π]

(hint: cos2x = 2cos²x-1)

2007-10-22 14:09:48 · 1 answers · asked by Daniel B 1

3N/8-3/4=N-4/2 | 5/n+2=3/2n | 5x^2=80 | 4x(x+1)=3

2007-10-22 14:04:48 · 1 answers · asked by Crogdar Gnarhan 3

2007-10-22 14:04:32 · 1 answers · asked by J.T. 1

how do you factor 2x^3+x^2+1

explanation? because im quite confused.

2007-10-22 14:03:25 · 5 answers · asked by Ally 2

2007-10-22 13:57:16 · 12 answers · asked by renato d 1

Find the critical point of (1 + 2 x) exp(2 x).
Please do it step by step so i can follow.. i tried this but made a mistake and im trying to find out where i went wrong. Thanks!

ps/ exp(2x) is the same as e^2x

2007-10-22 13:48:18 · 2 answers · asked by Anonymous

i applied cosx/sinx but i ended up with
(1+cosx)/(1-cosx)
thanks

2007-10-22 13:47:00 · 3 answers · asked by Anonymous

a box is pushed up a ramp with a total effort of 65 newtons .
the efforrt,disregarding friction, is 40 newtons. if the box weighs
280 newtons and if the top of the ramp is 5 meterrs abov the ground.

how long is the ramp.?

how much is the efficency of the ramp?

2007-10-22 13:40:15 · 1 answers · asked by :}smile :} 1

I need help,

the question is: a pool is a 22-ft by 36-ft rectangle that is 5 ft deep, write the number of cubic feet of water the pool will hold

2007-10-22 13:38:57 · 3 answers · asked by fan_cran_z 3

Solve. (x + 4)^2 = 4

2007-10-22 13:36:25 · 9 answers · asked by Anonymous

How do u find the derivative of r= tan^2(3-x)?

If u can please show me step by step cuz i keep getting the wrong answer. I know it involves Chain Rule or something but i jus dont kno how to do it. Thanks!

2007-10-22 13:32:35 · 2 answers · asked by tulipeliza 3

We want to build a box for a cord of wood (unstacked).

2007-10-22 13:31:30 · 10 answers · asked by tailsnnails 3

2007-10-22 13:31:13 · 1 answers · asked by WEINI3000 2

I can not figure out how to solve

20 X 10 to the fifth power + 4 X 10 to the sixth power

I know I seem really stupid, but I came in right when class was dismissed, and she just handed me the worksheet. I don't know how to solve it, and I'm not good at math in the first place. Can anyone help? I don't even need the answer, just if someone could tell me how to go about solving it. Thanks very much! =)

2007-10-22 13:27:07 · 6 answers · asked by Lindsay 2