Preliminary mathematics marathon (3 Viewers)

hscishard

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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
 

random-1005

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

Solve (x^2- 9 )/x <=0
 
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random-1005

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

random-1005

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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
 

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