Mathematics - 9 October 2006

r(t) = ((2^(1/2))t)i + (e^t)j + (e^-t)k is a given verctor-valued function with domain ranging from 0 to 6... I have to find the length of arc... formula for it is...

s = int ( norm ( deri ( r(t)))) with respect to t... upper and lower bounds are given 6 and 0...

r'(t) = (2^(1/2))i + (e^t)j - (e^t)k

||r'(t)|| = (2+(e^4t)+(e^-4t))^(1/2)

when I simplify it, I get...

||r'(t)|| = ((e^2t)+1)/(e^2t)

I am sure I have not made mistakes in simplifying, right???

once I integrate the norm of derivative of r(t), I get...

(t+((e^-2t)/-2))... once I apply limits, my answer should be...

13/2 - (e^-12/2)...

so my basic question is, anyway i can simplify this???

btw my given options are following...

1. e^6 +e^-6
2. 2e^-6
3. 2e^6
4. e^6-e^-6
5. e^6

which one am i choose?

2006-10-09 07:44:21 · 3 answers · asked by Faraz S 3

Please can someone show me how

(cos^2(x))(d^2y)/(dx^2) + (2cosx)(sinx)(dy/dx) + 2y = xcos^3(x)

simplifies to

(d^2z)/(dx^2) + z = x

using the substitution

y = zcosx where z is a function of x

2006-10-09 07:26:02 · 3 answers · asked by Anonymous

when a,b,c are the lenghts of an triangle then:
a/(b+c-a)+ b/(c+a-b)+(a+b-c) > or = 3

2006-10-09 07:20:37 · 1 answers · asked by Stiuler E 1

i have a problem for derivatives and it says :
x^3=y^3=y

is this a typo since there are 2 equal signs, or does it mean y is equal to x^3, so the derivative is 3x^2?

2006-10-09 07:04:06 · 11 answers · asked by Anonymous

i hate school and that stupid mathematics never goes into my brain.

2006-10-09 06:43:19 · 23 answers · asked by Anonymous

2006-10-09 06:36:45 · 6 answers · asked by angeleyes3789 1

curve is - r(t) =

i got r'(0) = <π,3π,0>

and r'(1/2) = <0,0,-π>

what is my next step?

2006-10-09 06:27:45 · 2 answers · asked by Faraz S 3

a=p+prt
how do you solve for p

2006-10-09 06:27:06 · 6 answers · asked by Anonymous

-2(x + 3) - (3x + 5) = ?

A) -5x - 1

B) -5x + 8

C) -5x - 11

D) -9x

2006-10-09 06:26:25 · 20 answers · asked by cak 1

I dont have a calculator off hand.

2006-10-09 06:25:00 · 21 answers · asked by Anonymous

-5(x + 3) - 4x = 6(2x + 3) - 12

After distributing and combining like terms, this problem should read:

A) -9x + 3 = 12x - 9

B) -9x - 15 = 12x + 6

C) -6x = 15x - 12

D) -9x - 15 = 8x - 3

2006-10-09 06:23:49 · 9 answers · asked by cak 1

-5(x + 3) - 4x = 6(2x + 3) - 12

After distributing and combining like terms, this problem should read:

-9x + 3 = 12x - 9

-9x - 15 = 12x + 6

-6x = 15x - 12

-9x - 15 = 8x - 3

2006-10-09 06:23:06 · 5 answers · asked by cak 1

I realise that the distance will depend on the occuipation and leisure activities of the person.

2006-10-09 06:14:14 · 10 answers · asked by pbenquirer 1

But does any one know what 'one over alpha' means? If not my friend had a site to explaine it it is very interesting. (All he wants it a little traffic.) www.oneoveralpha.com

2006-10-09 06:08:44 · 2 answers · asked by Angels Of The Arts 2

2006-10-09 06:08:42 · 10 answers · asked by ned f 1

I know we would use L'hopital's rule but i still can not figure out the answer yet. little help pls!

2006-10-09 05:53:09 · 7 answers · asked by Faraz S 3

I have been working on this problem for about an hour now and I still can't get it. Can someone helps me and show your work?

If f(x) = x^2 - x + 2 and h is not equal to 0, find:

1.) f(x + h) - f(x)
2.) f(x + h) - f(x) / h (all over h)

2006-10-09 05:52:41 · 7 answers · asked by Michelle 2

(-2x^2y/5)^-2 / (2x^-2y^3/5)^-3

2006-10-09 05:39:09 · 4 answers · asked by Anonymous

if i have a figure in a cell and want to minus the VAT @ 17.5% how would i create a formula to do this?

2006-10-09 05:37:21 · 7 answers · asked by KT 2

If A, B, and C are sets, prove: (A - B) is a subset of C iff (A - C) is a subset of B.

I've already wasted hours on this problem (I hardly know where to start), so I would appreciate any help. Thank you!

2006-10-09 05:35:59 · 4 answers · asked by Anonymous

2abc^-3/-3a^-2b^2c^-1

2006-10-09 05:29:02 · 3 answers · asked by Anonymous

As expanatory as possible...

2006-10-09 05:24:16 · 3 answers · asked by Anonymous

include how u got there please

(12x)^-1yz^-3 there are fraction bars under each line

-4x^3
y^2z^2

2006-10-09 05:18:27 · 7 answers · asked by Anonymous

2006-10-09 05:13:45 · 3 answers · asked by Anonymous

Me says the answer is -12

Bens says the answer is 160

Who has to pay for lunch?

2006-10-09 05:13:32 · 8 answers · asked by jammerjaws 1

pls tell option 1 or 2 is correct.
Equation of the y axis is given by:

#1. y=constant
#2.y=0

2006-10-09 05:11:56 · 13 answers · asked by jose v 1

2006-10-09 05:06:21 · 8 answers · asked by Anonymous

2006-10-09 05:05:37 · 22 answers · asked by jammerjaws 1

What is the actual distance between Chicago and St. Louis? Use a proportion to solve.

2006-10-09 05:04:25 · 9 answers · asked by jammerjaws 1

will the alien have 31 robots

2006-10-09 05:01:26 · 8 answers · asked by jammerjaws 1