Science & Mathematics - 25 November 2006

These polys satisfy these conditions:
1) polynomial Tk is of degree k
2)T0(x)= 1, for k=1, 2, ..., coefficient of x^k in Tk equals 2^(k-1)
3) polynomials T0, T1, T2..., Tn form orthogonal basis in space of polynomials Vn(-1, 1; w(x)= 1/(sqrt(1-x^2))
* Vn(a, b; w(x)) stands for the linear space of polynomials degree (< or = to) n endowed with inner product
(P, Q)= integral from a to b of P(x)Q(x)w(x) dx.
In the solution of this problem use the following identities:
1. integral from -1 to 1 of 1/(sqrt(1-x^2)) dx = pi
2. integral from -1 to 1 of (x^(2m))/(sqrt(1-x^2)) dx= ((1x3x5...(2m-1))/(2^m x m!)) x pi for m= 1, 2, 3, ...
3. integral from -1 to 1 of (x^(2m-1)) / (sqrt(1-x^2)) dx = 0, for m=1, 2, ...

a) find the polynomial T1 of degree 1 of the form T1(x) = x + ...that is orthogonal to T0
b) Find the only quad. polynomial T2 of the form T2(x) = 2x^2..that is orthogonal to both T0 & T1
c) show P(x)= 6x^2-5x + 4 can be a linear combo of T0, T1, T2 as follows P= 3T2- 5T1 +7T0

2006-11-25 14:07:41 · 1 answers · asked by Stephanie 2 in Mathematics

Suppose a baseball is shot up from the ground straight up with an initial velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
•16 represents 1/2g, the gravitational pull due to gravity (measured in feet per second2).
•v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
•s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
a)What is the function that describes this problem?

b)The ball will be how high above the ground after 1 second?



c) How long will it take to hit the ground?





d) What is the maximum height of the ball? What time will the maximum height be attained?

2006-11-25 14:06:10 · 5 answers · asked by howsurgrass 1 in Mathematics

The problem is 4x(squared) + 2x - 1 = 0

Choices for answer:

-1+/- (square root)5

(-1+/- (sqaure root)5) / 4 (4 on the bottom)

-1+/-2 (square root)5

(-1+/- 2 (square root)5)4

2006-11-25 14:05:13 · 2 answers · asked by Anonymous in Mathematics

I know that an overdose on most medications do severe liver damage first and then, slowly and painfully, shut down everything else. Do sleeping pills do the same? It's just a question so I don't need anything other than good scientific answers.

2006-11-25 14:05:06 · 6 answers · asked by fromatoms2adam 1 in Medicine

john has 300 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). He wants to maximize the area of his patio (area of a rectangle is length times width). What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation.

Show clearly the algebraic steps which prove your dimensions are the maximum area which can be obtained. Use the vertex formula to find the maximum area.

2006-11-25 14:01:48 · 6 answers · asked by howsurgrass 1 in Mathematics

The problem is 3x(squared) - 8x - 6 = 0

Choices for the answer:

(-4+/-(sqaure root)34) / 3 (meaning the first part is over 3)

(4+/-(square root)34) / 3

-4+/-2(square root)34

4+/-2(square root)34

2006-11-25 14:01:43 · 2 answers · asked by Anonymous in Mathematics

Methanol has been proposed as a fuel of the future for automobiles. Current automotive engines can run on methanol with relatively minor modifications. By what percent would you have to change the size of the gas tank, if you wanted a car to have the same maximum range per tank.

2006-11-25 14:01:37 · 3 answers · asked by koolbreeze 1 in Engineering

2006-11-25 14:00:55 · 12 answers · asked by hope 5 in Physics

I would really appreciate it if anyone could help me with and explanation of the aerodynamics of the catapult. I have a project and I have to creatively explain the aerodynamics, but I am not sure what they are. Please, if you are going to say "Do your own homework", just don't answer. You don't deserve the points. I would really thank anyone that would help me, and you could get ten points, so HELP ME!!!!

2006-11-25 13:57:55 · 3 answers · asked by answerseeker 2 in Engineering

How would you write the net ionic eqations for these?

1. AlCl3 + NaCl -> AlCl3 + NaCl

2. FeCl3 + NaOH ->Fe(OH)3 + 3NaCl3

3. AgNO3 + NaCl -> AgCl +NaNO3

2006-11-25 13:57:01 · 1 answers · asked by ? 2 in Chemistry

please explain how u got the answer clearly!!!

thanx for thee help!!!!

2006-11-25 13:56:12 · 4 answers · asked by i<3PiNK 1 in Mathematics

2006-11-25 13:53:22 · 7 answers · asked by don 1 in Mathematics

This is the present, that is the past, now this is the present..Andso on.To anyone time goes by exactly like that.I feel that time is something that only exists if you are aware of it.I think that travel to the past and future is possible.You have to think about it this way.This is the present, that is the past, now this is the present.This is your perspective of time it's different for everyone.I believe everyone is born at the same time.If you are one year older than someone then you live 1 year in their past.That way there is always someone to be aware of the time which creates the constant present.I feel this is how time travel happens, you move faster than normal, eventually you move to another persons present and the ages are equal then after that add the difference. Travel to past is opposite subtract the difference you can do anything but alter the past because it has happend already unlike the future.The future is constantly making the present and the perspective is diverse.

2006-11-25 13:52:50 · 12 answers · asked by theonerm2 3 in Physics

2006-11-25 13:50:01 · 4 answers · asked by Steven I 1 in Chemistry

2006-11-25 13:49:40 · 20 answers · asked by Innocuous pen... 4 in Other - Science

ls

2006-11-25 13:49:29 · 8 answers · asked by Tat 2 in Zoology

theta varies from 0 to 2pi. How many petals are generated?

2006-11-25 13:47:28 · 3 answers · asked by Anonymous in Mathematics

2006-11-25 13:46:49 · 4 answers · asked by Anonymous in Biology

use heron's formula

2006-11-25 13:43:29 · 6 answers · asked by Anonymous in Mathematics

????HELP ME?????

2006-11-25 13:42:56 · 12 answers · asked by caitlin s 1 in Mathematics

2006-11-25 13:38:56 · 21 answers · asked by Tat 2 in Physics

I have some ceramic powder which exhibit some very useful characteristics. I would like to know the size of these powder particles size which I believe is smaller than 100 nanometers. How to measure it? Are there any institutions who certifies nano technology?

2006-11-25 13:38:45 · 1 answers · asked by William X 1 in Physics

2006-11-25 13:38:43 · 5 answers · asked by Anonymous in Biology

2006-11-25 13:37:42 · 11 answers · asked by Morris Jude M 2 in Geography

2006-11-25 13:37:06 · 3 answers · asked by Rosita D 2 in Chemistry

2006-11-25 13:35:14 · 3 answers · asked by Debbie S 1 in Chemistry

Why is it that humans are so weak? We don't have fangs. We don't have claws. We aren't strong compared to animals. We have the brains and the thumbs. But what good are those in a fight for your life?

Why are humans so weak compared to animals?

If a human was to find himself in a fight with a wild animal/predator (i.e. bear, wolf, couger, etc...) is there anyway he could win with his natural resources? (no weapons. just fists/teeth/feet/knees/etc...)

2006-11-25 13:35:07 · 10 answers · asked by supermanpj4444 2 in Zoology

2006-11-25 13:34:36 · 18 answers · asked by Anonymous in Geography

Ok, obviously, we all know that you're gonna die if you fall in lava. BUT! my question is, what exactly happens to the body? do you die instantly? or does your flesh literally melt off your bones? any ideas?

FOR THE RECORD: I'm not sick and twisted, its just that i just watched LOTR, u know, return of the king, and Gollum fell in, so, u know, gears started turning.

2006-11-25 13:33:30 · 11 answers · asked by pharos91 3 in Physics

I need sites with articles and or magazines that talk about the following chemistry unit
1. Organic Chemistry
2. Structure and Properties
3.Energy rates and and rates of Reaction
4.Chemical System and Equilibrium
5.Electrochemistry.

2006-11-25 13:32:46 · 1 answers · asked by ayok 2 in Chemistry