pxc3110
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$v\frac{dv}{dt}={\alpha'}\cdot{\alpha''}$ $\frac{dv}{dt}=\frac{\alpha'\cdot\alpha"}{|\alpha'|}$ $\kappa^2v^4=\frac{|\alpha'\times\alpha''|^2}{|\alpha'|^6}\cdot v^4=\frac{|\alpha'|^2|\alpha''|^2\sin^... View answer 3 votes Let$u$and$v$be functions of$t$. then$(uv)'=u'v'\iff u'v+uv'=u'v'\iff u'(v-v')+v'u=0\iff u'+\frac {v'}{v-v'}u=0$Let u be the unkown function, then multiply both sides by$e^{\int \frac{...

Proof: Let p be an odd prime number. Consider the group $U_p=${equivalent classes of $a$|$p>a>0$, $gcd(a,p)=1$} (equivalent relation:$a\equiv b \pmod p$, binary operation:[a][b]=[ab]...

$\int \frac1ydy=ln|y|+c=6x$, therefore $e^{ln|y|+c}=e^{6x}$, or $|y|e^c=e^{6x}$ or $|y|=e^{6x}e^c$ (we write $e^{-c}$ as $e^{c}$ since both $-c$ and $c$ represent an arbitrary constant.) or $y=\pm ... View answer 1 votes Differentiating both sides, we get:$2x+2yy'=2(2x^2+2y^2-x)*(4x+4yy'-1)$. Plugging in$x=0, y=\frac 12$, we get:$y'=2y'-1$, or$y'=1$. Therefore,$y-\frac 12=y'(0)(x-0)=x$. This will be transformed ... View answer 1 votes Using the pigeonhole principle: Consider the set$A=${$ab|b\in G$}, where$a\in G $is fixed. If$a\notin A$, then since$a\in G$and all elements in$A$is in$G$,$A\subset G$. then consider the ... View answer 1 votes$\int \frac{2x^2+1}{(2x)^2}dx=\int \frac12+\frac 1{(2x)^2}dx=\frac 12x+\frac14 \int x^{-2}dx=\frac 12 x-\frac 1{4x}+C$View answer 1 votes (I) Let$x\in \mathbb R, x>0$. Maclaurin series for$e^x$:$e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+...$, So$e^x-x=1+\frac{x^2}{2!}+\frac{x^3}{3!}+...>0$or$e^x>x$or$x>log(x)$. When$x\...

It can be shown that neither $h(g,g)$ or $g(g)$ halt. Hence you can solve $g(g)$ by building a second halting machine $h'$ that returns $0$ if input is $(g,g)$ and calls $h$ otherwise. I don't have a ...

Since cyclic groups are isomorphic to additive groups, set of all proofs of this theorem is "isomorphic", in a sense, to set of all proofs of CRT. Hence, find a constructive proof of CRT, which ...

Proof: Let p be an odd prime number. Consider the group $U_p=${equivalent classes of $a$|$p>a>0$, $gcd(a,p)=1$} (equivalent relation:$a\equiv b \pmod p$, binary operation:[a][b]=[ab]...

You can save time by doing it another way: By Euler :$3+7i=e^{iarctan\frac 73}$, which means $(3+7i)^5=e^{i5arctan\frac 73}$ Now use a calculator to evaluate $5arctan \frac 73$. If we know that $... View answer 0 votes Maybe you should use Green theorem to evaluate$I:=\int_{\gamma} P(x,y)dx+Q(x,y)dy$, and I seriously doubt the validity of your formula. I'm not sure if it is wrong though. View answer 0 votes To show that the two definitions for being onto is equivalent: 1. If for$\forall t\in T$,$\exists s\in S|f(s)=t$, then$T\subseteq f(S)$, and for$\forall a\in f(S), a\in T$,so$f(S)\subseteq T\$. ...