Recent content by Amer

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    MHB How to make wolfarmalpha solve h(v−t)=h(v+t)

    Okay thanks again (Yes)
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    MHB How to make wolfarmalpha solve h(v−t)=h(v+t)

    Hello, I want wolfarmalpha solve this $h(v-t) = h(v+t)$ for $v$ where $h(x) = ax^2 +bx +c $. It is the vertex I want the students to figure out the vertex of the quadratic function. If $a,b $ and $c$ are numbers wolfarmalpha can solve that for any $t$. Any thoughts? Thanks
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    MHB How about this? What is the inverse of a permutation cycle?

    How about this? reverse the order $(a b c d ) (d c b a ) $ a goes to b from the first then the second send b to a. So $(a_1 a_2 a_3 a_4 \cdots a_n) (a_n a_{n-1} \cdots a_2 a_1 ) = 1 $
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    MHB Does this imply infinite twins?

    What is the function $f(n)$?
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    MHB Find $\angle BPC$ in Triangle ABC with $\angle ACB=\angle ABC=80^\circ$

    I understand the question in a wrong way I will edit my post :)
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    MHB Find $\angle BPC$ in Triangle ABC with $\angle ACB=\angle ABC=80^\circ$

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    MHB Trig Assistance for CNC Machining/Engineering

    yea I see it but it dose not affect the solution. "c" is the intersection between the tangent and the horizontal line "rs". and "ra " is perpendicular to the tangent it is a theorem the angle $acr = y$ I used sine definition to come up with $\sin y = \frac{23.5}{rc} \rightarrow rc =...
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    MHB Trig Assistance for CNC Machining/Engineering

    you mean ch ? it is typo I meant $dh$. ch is perpendicular to SR so we have a right triangle $\tan y = \frac{86}{hd} $ $hd + dR + cr = 126$
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    MHB Trig Assistance for CNC Machining/Engineering

    I edited my post
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    MHB Trig Assistance for CNC Machining/Engineering

    I redraw the picture. you mean by DIA ( diameter ) right ?. you can notice that the two triangles the one with the big circle and the one with small circle are similar. $dR = \frac{39}{\sin y}, cr = \frac{23.5}{\sin y}, ch = \frac{86}{\tan y}$ now $dR + cr + ch = 126 $ hence $126 =...
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    MHB One-to-one & Onto Function: $f$ from $A$ to $B$

    If $f$ is a function then if $f(a) = x$ and $f(a) = y$ then $x=y$ function definition If $f$ is one to one then if $f(a) = f(b)$ then $a = b$. And we have $|A| = |B|$ and each are finite You begin with the right implication suppose $f$ is one to one want to prove it is onto. You can prove by...
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    MHB Properties of gcd's and relatively prime integers

    what is the ring ? is it $\mathbb{Z}$ integers ?
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    MHB History of Sum of Squares: Pythagoras & Beyond

    I would like to know some history on the subject like who is the first to think about sum of squares of integers and what he/she was thinking about. I think maybe it is related to Pythagorean triples. Thanks
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    MHB Proof Noetherian Ring: $M^2 \ne M$

    yea commutative with 1
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    MHB Proof Noetherian Ring: $M^2 \ne M$

    Can you check my Work or mention a link for a proof. Let $R$ be Noetherian ring. Then if $M$ is a maximal ideal in $R$. Prove that $M^2 \ne M$. Proof: Since $R$ is Noetherian ring then $M$ is finitely generated. Thus $M = (a_1, a_2 , \cdots, a_k)$ we can choose the $a_i's $ which are minimal...