/sci/ - Science & Math

>>8614965
>After squinting, I see that 'Mathematics' is God Tier

>>8610743
In base 3, I can write it as 0.1

>>8610600
tau

>>8547906

>>8544404
>>8544447
It was Inspection. Thanks for the Rational Root theorem.

>>8544304
[math]u=x-1,dx=du\\
ln(|x^2-1|)-\frac{3}{x-1}+C[/math]

>>8544156
[math]\frac{2x^2+x+3}{x^3-x^2-x+1} = \frac{2x^2+x+3}{(x+1)(x-1)^2}\\
\frac{2x^2+x+3}{(x+1)(x-1)^2} = \frac{A_0}{x+1}+\frac{A_1}{x-1}+\frac{A_2}{(x-1)^2}\\
2x^2+x+3 = A_0(x-1)^2+A_1(x-1)(x+1)+A_2(x+1)\\
2x^2+x+3 = A_0(x-1)^2+A_1(x^2-1)+A_2(x+1)\\
\left\{ \begin{array}{ccc}
x=+1 & 2+1+3 = 2A_2 \\
x=-1 & 2-1+3 = 4A_0 \end{array} \right.\\
\left\{ \begin{array}{ccc}
x=+1 & 6 = 2A_2 \\
x=-1 & 4 = 4A_0 \end{array} \right.\\
\left\{ \begin{array}{ccc}
x=+1 & 3 = A_2 \\
x=-1 & 1 = A_0 \end{array} \right.\\
x=0 \hspace{4 mm} 0+0+3 = A_0 -A_1 + A_2\\
x=0 \hspace{4 mm} 3 = 1 -A_1 + 3\\
x=0 \hspace{4 mm} -1 = -A_1\\
x=0 \hspace{4 mm} A_1 = 1\\
\frac{2x^2+x+3}{(x+1)(x-1)^2} = \frac{1}{x+1}+\frac{1}{x-1}+\frac{3}{(x-1)^2}\\
\int \frac{1}{x+1}\,dx + \int \frac{1}{x-1}\,dx + \int \frac{3}{(x-1)^2}\,dx\\
ln(x+1) + ln(x-1) + \int \frac{3}{u^2}\,du ; \hspace{4 mm} u=x+1, dx=du\\
ln(x+1) + ln(x-1) + \frac{3}{u}\frac{1}{-1} + C\\
ln(x+1) + ln(x-1) - \frac{3}{x+1} + C\\
[/math]

>>8532683
https://www.youtube.com/watch?v=SrU9YDoXE88

>>8532595
What's this? It works in the viewer but not the post. I think /sci/ has broke.

>>8532229
[math]\frac{d^2x}{dt^2}=-w^2x\\
\frac{dx}{dt}=\sqrt{2}\sqrt{\frac{-w^2x^2}{2}+C}\\
\frac{dx}{dt}=\sqrt{-w^2x^2+C}\\
\frac{dx}{dt}=w\sqrt{-x^2+C}\\
\frac{dx}{dt}=w\sqrt{-x^2+A^2}\\
\frac{dx}{dt}=w\sqrt{A^2-x^2}[/math]

I put >>8531825 into the viewer.

>>8509848
I don't want the small angle approximation, I want something that applies to all θ

>>8509387

>>8509292
>Me not reading properly for the millionth time

[math]\cos{\theta} = \frac{\frac{4}{2}}{\frac{5}{2}} = \frac{4}{5}[/math]
[math]\theta = \arccos{\frac{4}{5}} = 36.87[/math]

[math]686.7N=2∗T∗\sin{36.87}[/math]
T=\frac{686.7N}{2∗sin{36.87}}=572.3N

>>8509252
I dabble

>>8509270
[math]e^A = \sum_{k=0}^{\infty} \frac{A^k}{k!}[/math]

>>8509263
[math[e^A = \sum_{k=0}^{\infty} \frac{A^k}{k!}[/math]

>>8483342
[math] e^A = \sum_{k=0}^{\infty} \frac{A^k}{k!} [\math]

ftfy

Function of θ with respect to t when?

>>8508935

[math]70\mathrm{kg}*9.81\mathrm{ms^{-1}}=686.7\mathrm{N}[/math] <-- Weight on rope.
The tensions on either side will cancel out the weight.

By resolving vertically,
[math]686.7\mathrm{N}=2*\mathrm{T}*\sin{5.0\textdegree}[/math]
[math]\mathrm{T}=\frac{686.7\mathrm{N}}{2*\sin{5.0\textdegree}}=3939\mathrm{N}[/math]

>>>/wsr/ for future reference.

>>8509157
[math]E=mc^2[/math] means an object's extra energy becomes its mass.

When an object moves, its kinetic energy adds to its mass.

>>2715765
Then why not build the best we can build?

>>2715655
There are three basic conclusions. The first is that there exists on the North American Continent a physical potential in resources to produce a high standard of goods and services for all citizens, and that the high-speed technology for converting these resources to use-forms in sufficient volume is already installed, and that the skilled personnel for operating it are present and available. Yet we have unprecedented insecurity, extensive poverty and rampant crime.

The second conclusion of Technocracy is that the Price System can no longer function adequately as a method of production and distribution of goods. The invention of power machinery has made it possible to produce a plethora of goods with a relatively small amount of human labor. As machines displace men and women, however, purchasing power is destroyed, for if people cannot work for wages and salaries, they cannot buy goods. We find ourselves, then, in this paradoxical situation: the more we produce, the less we are able to consume.

The final basic conclusion is that a new distributive system must be instituted that is designed to satisfy the special needs of an environment of technological adequacy, and that this system must not in any way be associated with the extent of an individual's functional contribution to society.