Question Number 71428 by TawaTawa last updated on 15/Oct/19 Answered by ajfour last updated on 15/Oct/19 Commented by ajfour last updated on 15/Oct/19 $${P}\:\left[{r}\mathrm{cos}\:\left(\theta−\phi\right),\:{r}\mathrm{sin}\:\left(\theta−\phi\right)\right] \\…
Question Number 71423 by ajfour last updated on 15/Oct/19 Commented by ajfour last updated on 15/Oct/19 $${MjS}\:{Sir}… \\ $$ Commented by mr W last updated…
Question Number 71410 by TawaTawa last updated on 15/Oct/19 Answered by MJS last updated on 15/Oct/19 $${A}=\begin{pmatrix}{\mathrm{0}}\\{\mathrm{0}}\end{pmatrix}\:\:{B}=\begin{pmatrix}{{p}}\\{\mathrm{0}}\end{pmatrix}\:\:{C}=\begin{pmatrix}{{p}}\\{{q}}\end{pmatrix}\:\:{D}=\begin{pmatrix}{\mathrm{0}}\\{{q}}\end{pmatrix} \\ $$$${DC}:\:{y}={q} \\ $$$${AC}:\:{y}=\frac{{q}}{{p}}{x} \\ $$$${BE}:\:{y}=−\frac{{p}}{{q}}{x}+\frac{{p}^{\mathrm{2}} }{{q}} \\…
Question Number 5825 by Rasheed Soomro last updated on 30/May/16 Commented by Rasheed Soomro last updated on 30/May/16 $$\mathrm{A}\:\mathrm{is}\:\mathrm{the}\:\mathrm{center}\:\mathrm{of}\:\mathrm{arc}\:\mathrm{BC}. \\ $$$$\mathrm{AB}=\mathrm{AE}=\mathrm{AG}=\mathrm{AC} \\ $$$$\mathrm{AB}\:{m}\mathrm{eans}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B} \\ $$$$\mathrm{Similarly}\:\mathrm{AE},\mathrm{AG},\mathrm{AC}\:\mathrm{are}\:\mathrm{also}\:\mathrm{distances}.…
Question Number 5822 by Rasheed Soomro last updated on 30/May/16 $$\mathcal{P}{rove}\:{that}\:{among}\:{all}\:\boldsymbol{{triangles}}, \\ $$$${which}\:{have}\:{same}\:\boldsymbol{{circum}}-\boldsymbol{{radius}}, \\ $$$${the}\:\boldsymbol{{equilateral}}\:\boldsymbol{{triangle}}\:{has} \\ $$$$\boldsymbol{{maximum}}\:\boldsymbol{{area}}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 5816 by Rasheed Soomro last updated on 29/May/16 $$\mathcal{P}{rove}\:{that}\:{among}\:{all}\:{cyclic}\:\:{n}-{gons},\: \\ $$$${which}\:{have}\:{same}\:{radius},\:{regular}\:{n}-{gon} \\ $$$${has}\:{maximum}\:{area}. \\ $$ Commented by Yozzii last updated on 29/May/16 $${Is}\:{induction}\:{possible}\:{for}\:{n}\geqslant\mathrm{3}?…
Question Number 5763 by sanusihammed last updated on 26/May/16 $${Thanks}.\:{please}\:{can}\:{you}\:{show}\:{me}\:{the}\:{rest}\:{solution}.\:{i}\:{want}\:{to}\: \\ $$$${see}\:{the}\:{last}\:{steps}.\:\:\mathrm{2}^{{x}} \:=\:\mathrm{4}{x}\:.\:\:{Thanks}\:{for}\:{the}\:{time}\:{and}\:{the}\: \\ $$$${previous}\:{solution}. \\ $$ Commented by nburiburu last updated on 25/Jun/16 $${graph}\:{the}\:{functions}\:{y}=\mathrm{2}^{{x}}…
Question Number 71265 by ajfour last updated on 13/Oct/19 Commented by ajfour last updated on 13/Oct/19 $${Find}\:{radius}\:{of}\:{yellow}\:{sphere}\:{x}, \\ $$$${that}\:{touches}\:{the}\:{other}\:{sphere}, \\ $$$${lateral}\:{surface}\:{of}\:{cone}\:{and}\: \\ $$$${cone}\:{cover}\:{plate}. \\ $$…
Question Number 71255 by ajfour last updated on 13/Oct/19 Commented by MJS last updated on 13/Oct/19 $$\mathrm{the}\:\mathrm{maximum}\:\mathrm{area}\:\mathrm{depends}\:\mathrm{on}\:{a} \\ $$$$\mathrm{the}\:\mathrm{area}\:\mathrm{for}\:\theta=\mathrm{90}°\:\mathrm{is}\:\frac{\pi}{\mathrm{4}}{b}\:\mathrm{and}\:\mathrm{this}\:\mathrm{value}\:\mathrm{is} \\ $$$$\mathrm{again}\:\mathrm{reached}\:\mathrm{st}\:\theta=\mathrm{45}°.\:\mathrm{this}\:\mathrm{is}\:\mathrm{only}\:\mathrm{possible} \\ $$$$\mathrm{if}\:{a}=\sqrt{\mathrm{2}}{b}\:\mathrm{at}\:\mathrm{least}.\:\mathrm{for}\:{b}\leqslant{a}\leqslant\sqrt{\mathrm{2}}{b}\:\mathrm{the}\:\mathrm{maximum} \\ $$$$\mathrm{area}\:\mathrm{is}\:\frac{\pi}{\mathrm{4}}{b};\:\mathrm{for}\:{a}>\sqrt{\mathrm{2}}{b}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{is}\:\mathrm{at}\:{r}={a}…
Question Number 5704 by sanusihammed last updated on 24/May/16 $${Show}\:{that}\:… \\ $$$$ \\ $$$${Limit}\:\:\:\:\:\:\left[\frac{\mathrm{3}^{{x}} \:−\:\mathrm{3}^{−{x}} }{\mathrm{3}^{{x}\:} \:+\:\mathrm{3}^{−{x}} }\right]\:=\:−\:\mathrm{1} \\ $$$${x}\:\rightarrow\:−\infty \\ $$ Answered by FilupSmith…