Preliminary mathematics marathon (1 Viewer)

[hscishard]

Re: another question

sin 2x + sin 4x = sin 3x
sin (3x - x) + sin (3x + x) = sin 3x
sin 3x cos x - sin x cos 3x + sin 3x cos x + sin x cos 3x = sin 3x
2sin 3x cos x = sin 3x
sin 3x (2cos x - 1) = 0

cos x = 1/2
=> x = 2nπ ± π/3 for integer n

sin 3x = 0
=> 3x = kπ
=> x = kπ/3 for integer k

Nice. That's much quicker

 

[hscishard]

Re: another question

New Question:

a=4 b=5

 

[random-1005]

Find integral 5Cos^2 (x/5) dx

Solve (x^2- 9 )/x <=0

 

[hscishard]

25/4 x sin[(2/5)x] + (5/2)x

 

[hscishard]

x<=-3, 0 <= x <= 3

 

[random-1005]

x<=-3, 0 <= x <= 3

tricked ya, you must always check denominator isnt equal to zero

 

[hscishard]

I went from all < than then all <=, still didn't see that

 

[random-1005]

integral sinx / ( 4 + 5cosx) dx

also integral sin(2x)cos(2x) dx

 

[hscishard]

2nd one is (-1/8)cos4x

 

[random-1005]

2nd one is (-1/8)cos4x

yes

first one is always a little tricky, bit hard to see at first glance

and its not 4unit i promise

 

[hscishard]

1st is (-1/5)log(4+5cosx) + C

Oh yea + C for the other one as well.

 

[random-1005]

use one application of newtons method to find a solution to 2sinx=x, use x=1.6 as the first approximation

 

[random-1005]

prove for simple harmonic motion

acceleration= d/dx(1/2 v^2)

 

[hscishard]

Lol...
Umm

1.6 - [2sin(1.6)-1.6]/[2cos(1.6)-1]

 

[random-1005]

Lol...
Umm

1.6 - [2sin(1.6)-1.6]/[2cos(1.6)-1]

as a number lol

 

[hscishard]

Accerleration is the change in velocity...
Let acceleration = x
Integrating acceleration = 1/2 x a^2 = velocity

 

[random-1005]

Accerleration is the change in velocity...
Let acceleration = x
Integrating acceleration = 1/2 x a^2 = velocity

a= dv/dt = dv/dx * dx/dt
= dv/dx *v
= dv/dx * d/dv( 1/2 v^2) (cancel dv's)
= d/dx (1/2 v^2)

thats the correct way

 

[hscishard]

as a number lol

Wtf..3.1

 

[random-1005]

find the exact value of tan( 2 arccos(12/13))

 

[random-1005]

Wtf..3.1

just checking, make sure u need radian mode on calculator, you were in degrees!