Science & Mathematics - 15 December 2007

A previous question asked about a root of:
f(x) = 4x^7 +6x^6 +3x^5 +250x^4 +1000x^3 +75x^2 -20x +17

Can you estimate or generalize approximately about the roots, using only, pencil and paper, factorizations or approximations? (no calculators, computers, solvers or Newton-Raphson. See how far you can get using your head!).
Can you at least bound the regions in which each root lies, by identifying the zero-crossings of f?

Two ideas: a) since all terms other than "-20x" are positive, most roots will be negative.
Hence it might make it algebraically easier to substitute u→(-x) and consider
f(u) = -4u^7 +6u^6 -3u^5 +250u^4 -1000u^3 +75u^2 +20u +17

b) I'm thinking one promising way might be to regard it as the superposition of two (or more) polynomials, a high-order one and a lower-order one.

Your thoughts?

[ http://answers.yahoo.com/question/index?qid=20071215210154AAY3BhC ]

2007-12-15 17:15:55 · 2 answers · asked by smci 7 in Mathematics

2007-12-15 17:13:22 · 14 answers · asked by Calvin K 1 in Astronomy & Space

EXPLAIN IN TERMS OF ARCHIMEDES PRINCIPLE

2007-12-15 17:10:22 · 7 answers · asked by Handiman 3 in Physics

This is the 2nd time Ive posted this, but only got one answer the last, wld like more. Actually back in hospital now. In October (4th I think) my mates and I were mucking around in a tree and I slipped and fell three metres or so out onto the hard concrete ground. I was unconscious and my mate called an ambo. It came and I woke up in it, screaming in pain, thrashing around, was given something and then was in and out of it for the next few minutes. Woke up like a week later, was told I had been in an induced coma, had had brain swelling/minor bleeding and had my skull drilled to relive pressure, and had 13 pins and a rod in my foot as it was smashed. Had amnesia from the day of the accident and barely remember the trip. 2 nights ago I remembered a night there and 'felt' the doctor put a tube in throat & the doctor pinning my foot. Would they have used anaesthetic for my 2 operations, or being in a coma was enough?

2007-12-15 17:06:53 · 4 answers · asked by Anonymous in Medicine

When you roll (or slide) something through a loop-de-loop, why do you have to start the track higher than the top of the loop?

I'm not talking about something that propels itself, like a toy race car with a motor.

Imagine a track with zero friction. You have a track that leads down into a loop-de-loop. The loop reaches a height of 1 meter. The part of the track that leads down has to start HIGHER than 1 meter, even considering zero friction. I remember this fact from physics, but I don't understand why.

Can anybody explain this to me? It doesn't matter whether the object slides (like a small block) or rolls, as long as you assume zero friction.

2007-12-15 17:06:52 · 10 answers · asked by Nicholas Barry 2 in Physics

2007-12-15 17:04:48 · 16 answers · asked by Anonymous in Astronomy & Space

An aircraft with a constant speed in still air travels 4800 km with a constant tailwind in 4 hours. With the same wind now against the aircraft, it takes 5 hours to make the return trip. What was the speed of the wind, in km/hr?

a. 100

b. 110

c. 120

d. 125

e. 900

f. 990

g. 1080

h. 1125

i. none of these

I get to the point of
4800/4=1200
4800/5=960
then i don't know how to go from there

2007-12-15 17:04:23 · 3 answers · asked by Lili S 1 in Mathematics

2007-12-15 16:57:37 · 9 answers · asked by Y.S.C B 2 in Biology

please write out the problem

2007-12-15 16:55:24 · 6 answers · asked by dirtycav21 1 in Mathematics

9x^-4=0? trying to figure it out for hours

2007-12-15 16:53:04 · 14 answers · asked by Anonymous in Mathematics

2007-12-15 16:52:02 · 0 answers · asked by Anonymous in Biology

the teacher didn't provide a correct answer.. the one i came up with was 3 square root of 3/2, dunno if it's right.. and please put your work process in your answer :)

2007-12-15 16:50:23 · 6 answers · asked by Anonymous in Mathematics

please help me!!!! i looked on the spectrum.net and mangatraders. and other countless sites

2007-12-15 16:50:12 · 1 answers · asked by Anonymous in Astronomy & Space

a.causes for deposition.
b.shapes of deposition.
c.sizes of sediment grains.
d.angles of slope.

2007-12-15 16:49:33 · 4 answers · asked by bammmmmmmmmmmmmm 1 in Earth Sciences & Geology

2007-12-15 16:48:47 · 2 answers · asked by ! :) 2 in Earth Sciences & Geology

as india is progressing we can expect that to be there in next few years.

2007-12-15 16:47:47 · 15 answers · asked by bhaskar999 1 in Astronomy & Space

The house has two heat pumps and two 250 ft deep vertical closed loop wells. The only think I don't know is whether or not the wells are exclusive to the individual pumps. There are two separate air handlers (two thermostats obviously controling the air handlers.) I'm wondering if it will damage the system if one pump is run to cool one side of the house for those who like it cold at night and the other pump heats the other side of the house for those who like it warm. Thanks!

2007-12-15 16:47:23 · 3 answers · asked by Peter J 1 in Engineering

can you help with this.....
find the equation of the parabola with vertex(1,5) and passing the point (2,7)

2007-12-15 16:47:22 · 1 answers · asked by mathhelp 3 in Mathematics

a) √7(B+C)

b) ABC - pie, pie = 3.14159

2007-12-15 16:43:36 · 3 answers · asked by matchamatics 1 in Mathematics

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2007-12-15 16:40:18 · 3 answers · asked by Y Y 1 in Engineering

1. DNA polymerase adds complementary base pairs to each strand of DNA
2. DNA polymerase "proofreads" the molecule to make sure that each molecule is a perfect copy of the original DNA.
3. DNA is "unzipped" as the hydrogen bonds between base pairs are broken and two molecules of DNA separate.

2007-12-15 16:38:30 · 2 answers · asked by Anonymous in Biology

Bewildering Math assignment


A vertical radio antenna is to be built on a hill which makes an angle of 6 (degrees) with the horizontal. If guy wires are to be attached at a point that is 75.0 m up on the antenna and at points 50.0 m from the base of antenna what will be the length of guy wires which are positioned up and directly down the hill ?

This is all that i have . =( if possible could u show some working out

2007-12-15 16:37:19 · 2 answers · asked by Anonymous in Mathematics

with SOURCE/S to prove your answer :) thanksss

2007-12-15 16:33:29 · 3 answers · asked by ilovepink 2 in Biology

2007-12-15 16:30:14 · 2 answers · asked by acemie 1 in Chemistry

2007-12-15 16:28:39 · 5 answers · asked by dirtycav21 1 in Mathematics

At a specific engine rpm, an automobile engine provides a constant force that is applied to the automobile. If the car is traveling on a horizontal surface, does the car accelerate when this force is applied? Explain.

My answer: F = ma. Since F is constant and m is constant, then a is also constant. So, I guess the car DOES NOT accelerate? Is this right? Is the explanation right? I'm not sure... =|

Thanks!

2007-12-15 16:28:03 · 8 answers · asked by Anonymous in Physics

2007-12-15 16:25:16 · 14 answers · asked by Anonymous in Earth Sciences & Geology

wintery mix/ wind mean snow? or slush? or what?

2007-12-15 16:23:30 · 5 answers · asked by Anonymous in Weather

1.x+3y=5
x+4y=6

2.p-3q=-1
5p+16q=5

3. 300x-y=130
200x+y=120

2007-12-15 16:21:20 · 2 answers · asked by Frannie 2 in Mathematics