Mathematics - 29 August 2007

The direction cosines of a vector are the cosines of the angles it makes with the coordinate axes. The cosine of the angles between the vector and the x, y, and z axes are usually called in turn alpha, beta, and gamma. Prove that alpha^2 + beta^2 + gamma ^2 = 1, using either geometry or vector algebra.
(more interested in how to prove it with vector algebra, but geometry is fine too.)

2007-08-29 22:38:34 · 3 answers · asked by tyj8tim 1

show that 27 x 23^n + 17 x 10^2n is divisble by 11 for all positive integers n.

Appreciate if anyone can assit. Thanks

2007-08-29 22:33:29 · 5 answers · asked by silent 1

Find the sum to n terms of the series
Cos^2 a + Cos^2 2a+Cos^2 3a+………..

Find Sina - Sin2a + Sin3a - Sin4a ………. n terms.

2007-08-29 22:24:27 · 2 answers · asked by TiMe_on_WeeLz 2

Can anyone give me a hint on prove this
Summation from k=1 to n
log(n!/(n-k)!)*log(n-k)

is larger than this

Summation from k=2 to n
log((k-1)!)*log(k+1)

2007-08-29 21:18:24 · 1 answers · asked by Mgccl 1

A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted?
[1] 16 [2] 8 [3] 12 [4] 24

similarly how can find the number of cubes with 1 face painted and 0 face painted etc/?....?? please explain,,, give me the general formula........

2007-08-29 20:05:05 · 5 answers · asked by vaidehi 2

A salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. Once, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs. 1148, but the inventory reduced by 54.

1.What is the actual price per piece?
[1] 82 [2] 41 [3] 56 [4] 28
2. What is the actual quantity sold?
[1] 28 [2] 14 [3] 82 [4] 41

2007-08-29 19:52:21 · 4 answers · asked by vaidehi 2

Not looking for just Answers but help. I am not trying to gain answers because I am lazy but could actually use some assistance in solving these. Thanks in advance

2007-08-29 19:47:23 · 4 answers · asked by Anonymous

I need some help with one problem, thanks in advance.

Please show the verification that the function is a solution to the differential equation.
y'-2ty=1; y=e^(t^2) ∫e^(-s^2)ds+e^(t^2)

The upper bound for the integral is t and the lower bound is 0.

2007-08-29 19:45:25 · 2 answers · asked by Digital Olive 2

again ^2 is an exponent
the slash/ is division

2007-08-29 19:44:24 · 7 answers · asked by olive 3

2007-08-29 19:42:14 · 3 answers · asked by jen b 1

2007-08-29 19:41:48 · 2 answers · asked by jen b 1

2007-08-29 19:41:15 · 3 answers · asked by jen b 1

2007-08-29 19:38:22 · 5 answers · asked by xxbabycheekzix 1

I need the formula basically, similarly for cuboid ... if two sides are mentioned....

2007-08-29 19:36:53 · 13 answers · asked by vaidehi 2

2007-08-29 19:32:38 · 3 answers · asked by jennifer f 1

2007-08-29 19:31:41 · 4 answers · asked by jennifer f 1

2007-08-29 19:31:11 · 5 answers · asked by jennifer f 1

2007-08-29 19:30:44 · 3 answers · asked by jennifer f 1

2007-08-29 19:30:37 · 8 answers · asked by Nia 3

A floor plan of a house has been drawn to a scale of 1: 200.

a. If a lounge room is actually 4m by 3.5m, what would its dimensions be on the plan? Give your answer in mm.

b. Would a car 1.8m wide and 5m long fit in the garage if on the plan the garage is 15mm by 30mm?

2007-08-29 19:24:59 · 6 answers · asked by tom_fredd93 1

bike company makes unicycles, bicycles, and tricycles. last week they made 88 more bicycles than unicycles, and 5 times as many tricycles as unicycles. if they made 40 more bicycles than tricycles, how many unicycles did they have.

pleez help!

2007-08-29 19:08:08 · 9 answers · asked by Anonymous

Pump A can unload a ship in 30h and pump B can unload it in 24h. If both pumps were used, How long would it take to empty the ship?

2007-08-29 19:04:35 · 4 answers · asked by steviewanger 1

Complete the statement using the (a) Distributive property (b) Commutative property of addition (c) Commutative property of multiplication : 6 * (5+4) =

2007-08-29 18:54:10 · 6 answers · asked by yeahyeahyeah 4

the sum of 2 numbers is 24. 7 times the smaller number is the same as 5 times the larger number. find the smaller number.

2007-08-29 18:45:12 · 6 answers · asked by Anonymous

Find the exact answers:

2cos^2 x - cosx = 0
0 <= x < 2(pi)

That first "x" is not connected to the exponent (it's just the cos variable). I don't know what to do! An explanation would be just lovely.

2007-08-29 18:11:21 · 5 answers · asked by Anonymous

I'm completely lost on these 2...

1. ln(5-2x)= -3

2. 2lnx=ln2 + ln(3x-4)

2007-08-29 18:06:51 · 4 answers · asked by popngirl_14 2

Factor Completely.

1) ax+bx-a-b

2) c^3+c^2d^2-cd-d^3

Thank you so much.=)

2007-08-29 18:04:35 · 3 answers · asked by Anonymous

or some people write, 5+3 (2-9)^

how do you do that one too I recently posted a question and I finally understood it, I got 392 and its wrong

2007-08-29 17:57:12 · 9 answers · asked by Question Asker 1

A jet airliner is cruising at a speed of 510 miles per hour at a bearing of N16W. There is a 77 mph crosswind striking it from a bearing of S42W. What is the resultant speed and course of the aircraft?

2007-08-29 17:56:48 · 2 answers · asked by Anonymous

since irrational numbers that never end and if you divide 3 by 17 im sure the numbers dont stop ? because i got to the thousandth and it didn't seem like it was going tno stop any time soon.

2007-08-29 17:52:46 · 6 answers · asked by ioaewjfkl 1