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== Divide Ten into Two Parts ==
 
== Divide Ten into Two Parts ==

Revision as of 16:55, 7 October 2022

30 into 4 parts
Category Comment Link Annotated text
word problem/divide a number30 into 4 partsספר_דיני_ממונות#7fd8232) Question: make me four parts out of 30, such that the ratio of the fourth to the third is as the third to the second and as the second to the first. רלב) שאלה תעשה לי מל' ד' חלקים שיהיה יחס הד' אל הג' כג' לב' וכב' לא‫'


Divide Ten into Two Parts

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=4\sdot\left(a\sdot b\right)\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\left(1+\frac{1}{2}\right)\sdot\left(a\sdot b\right)\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=16\sdot a^2\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=\left(6+\frac{1}{4}\right)\sdot a^2\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=5\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=4\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=9b\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot b=21\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=2+\frac{1}{6}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}-\frac{b}{a}=3+\frac{3}{4}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-a^2=50\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\frac{1}{4}b\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2=20+\frac{1}{4}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(b-a\right)^2-a^2=32\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle3a=b\sdot\sqrt{8}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot a=\left(20+\frac{1}{4}\right)a\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot b=\left(20+\frac{1}{4}\right)b\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a\sdot b\right)\sdot a=21a\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot\left(7+\frac{1}{9}\right)=\left(a\sdot b\right)^2\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left[\left(a\sdot b\right)+a^2\right]\sdot a=\left[a\sdot\left(\frac{1}{2}\sdot a\right)\right]^2+36\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-a^2=80\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=4+\frac{1}{4}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}-\frac{b}{a}=\frac{5}{6}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=4+\frac{1}{4}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle6a+\frac{1}{3}\sdot\frac{6a}{b}=56\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}+a=5+\frac{1}{2}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+b\right)\sdot a=30\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}\sdot b=9\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}\right)^2\sdot a=32\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}\sdot\left(b-a\right)=24\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}\right)\sdot b=34\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot a=46\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot b=69\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}+10\right)\sdot a=73\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}-\frac{b}{a}\right)\sdot a=5\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}\right)\sdot a=25-2a\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+a\right)\sdot\left(\frac{b}{a}+b\right)=35\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot\left(\frac{a}{b}+10\right)=122+\frac{2}{3}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot\left(10-\frac{a}{b}\right)=107+\frac{{\color{red}{1}}}{3}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a\sdot b}{b-a}=\sqrt{6}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-\left(a\sdot\sqrt{8}\right)=40\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot\sqrt{10}=b^2\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=\sqrt{5}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}\right)^2+\left(\frac{b}{a}\right)^2=3\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}-\frac{a}{b}=\frac{5}{6}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}\right)^2-\left(\frac{a}{b}\right)^2=2\end{cases}
no such category found: #divide 10 into two parts



\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a+2\sqrt{a}=b-2\sqrt{b}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{10}{a}+\frac{10}{b}=6+\frac{1}{4}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{10}{a}\sdot\frac{10}{b}=6+\frac{1}{4}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{40}{a}\sdot\frac{40}{b}=100\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{50}{a}\sdot\frac{40}{b}=125\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left({\color{red}{\frac{10}{a}\sdot\frac{10}{b}}}\right)^2=20+\frac{1}{4}\end{cases}
no such category found: #divide 10 into two parts


\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{40}{a}\right)^2+\left(\frac{40}{b}\right)^2=625\end{cases}
no such category found: #divide 10 into two parts


Divide Thirty into Two Parts

\scriptstyle\begin{cases}\scriptstyle a+b=30\\\scriptstyle\frac{a}{b}=27\end{cases}
Category Comment Link Annotated text
word problem/divide a numbera+b=30;a/b=27מלאכת_המספר#RDUfExample: as we took 5 as the quotient for 10, we take 27 as the quotient for thirty. המשל כי כמו שלקחנו לחלק ה' מי' נקח לחלק כ"ז משלשים


Divide Ten into Three Parts

\scriptstyle\begin{cases}\scriptstyle a+b+c=10\\\scriptstyle a^2+b^2=c^2\\\scriptstyle a\sdot c=b^2\end{cases}
no such category found: #divide 10 into three parts
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