Category: Arithmetic

Question Number 215232 by Mingma last updated on 01/Jan/25 Answered by devdutt last updated on 01/Jan/25 $$\ln 3\sqrt{5}+\ln x\log {}_{45}x=2\ln x$$$$\Rightarrow \ln 3\sqrt{5}+\frac{\ln {}^{2}x}{\ln 45}=2\ln x$$$$\Rightarrow\:\mathrm{ln}\:^{\mathrm{2}} {x}\:−\:\mathrm{2ln}\:\mathrm{45}\:\mathrm{ln}\:{x}\:+\:\mathrm{ln}\:\mathrm{3}\sqrt{\mathrm{5}}\:\mathrm{ln}\:\mathrm{45}\:=\:\mathrm{0} \…

Question Number 214622 by Frangg last updated on 13/Dec/24 Answered by Rasheed.Sindhi last updated on 14/Dec/24 $$\underset{―}{Iftodeterminex:}$$$$△\mathrm{ABE}\sim △\mathrm{DCE}$$$$\frac{\mathrm{AB}}{\mathrm{DC}}=\frac{\mathrm{AE}}{\mathrm{DE}}$$$$\frac{19}{6}=\frac{2\mathrm{x}+8}{\mathrm{x}-2}$$$$\mathrm{19x}−\mathrm{38}=\mathrm{12x}+\mathrm{48}…

Question Number 213802 by efronzo1 last updated on 17/Nov/24 Answered by A5T last updated on 17/Nov/24 $$t_1=k-1;t_2=k$$$$t_3=\frac{5k+1}{25k-25};t_4=\frac{\frac{10k-4}{5k-5}}{25k}=\frac{10k-4}{125k(k-1)}$$$${t}_{\mathrm{5}}…

Question Number 213522 by efronzo1 last updated on 07/Nov/24 $$\mathrm{The}\mathrm{two}\mathrm{corner}\mathrm{points}\mathrm{of}\mathrm{a}\mathrm{square}$$$$\mathrm{lie}\mathrm{on}\mathrm{curve}\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^2-2\mathrm{x}-3\mathrm{and}$$$$\mathrm{the}\mathrm{other}\mathrm{two}\mathrm{corner}\mathrm{points}\mathrm{lie}\mathrm{on}$$$$\mathrm{curve}\mathrm{g}\left(\mathrm{x}\right)=-{\mathrm{x}}^2+2\mathrm{x}+3.\mathrm{It}\mathrm{is}\mathrm{known}$$$$\mathrm{that}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{a}\mathrm{square}\mathrm{can}\mathrm{be}$$$$\mathrm{expressed}\mathrm{by}\mathrm{p}+\mathrm{q}\sqrt{\mathrm{r}},\mathrm{for}\mathrm{a}\mathrm{natural}$$$$\:\mathrm{number}\:\mathrm{p},\mathrm{q}\:,\mathrm{r}\:\mathrm{where}\:\mathrm{r}\:\mathrm{is}\:\mathrm{not}\:\mathrm{divisible}\: \…

Question Number 213100 by MathematicalUser2357 last updated on 30/Oct/24 $$\mathrm{Find}\mathrm{this}\mathrm{numeric}\mathrm{expression}\mathrm{using}:$$$$\mathrm{The}\mathrm{arithmetic}\mathrm{division}\mathrm{rule}a\mathbf{÷}b\left(c\right)=a\mathbf{÷}b\times c,$$$$\mathrm{The}\mathrm{solvable}\mathrm{incorrect}\mathrm{syntax}\mathrm{rule}\left(a\right)b=a\times b,\mathrm{where}b\mathrm{is}\mathrm{a}\mathrm{number}:$$$$12\mathbf{÷}4(10-8+1)2\mathbf{÷}6\times 2=?$$ Commented by A5T last updated on 30/Oct/24…