Question Number 14724 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 03/Jun/17 Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 03/Jun/17 $${AB}=\mathrm{13},{BC}=\mathrm{16},{AC}=\mathrm{15} \\ $$$${AD}={DC},{DE}\bot{AC}\:\: \\ $$$$……………………………. \\ $$$$\:\:\:\:\:\:\:{DE}=? \\ $$…
Question Number 80222 by mr W last updated on 01/Feb/20 Commented by mr W last updated on 01/Feb/20 $${A}\:{round}\:{steel}\:{plate}\:{with}\:{radius}\:{R}\:{has} \\ $$$${a}\:{round}\:{hole}\:{with}\:{radius}\:{r}\:{as}\:{shown}. \\ $$$${Was}\:{is}\:{the}\:{maximal}\:{area}\:{of}\:{the}\:{ellipse} \\ $$$${which}\:{can}\:{be}\:{cut}\:{off}\:{from}\:{the}\:{plate}?…
Question Number 14661 by ajfour last updated on 03/Jun/17 Commented by ajfour last updated on 03/Jun/17 $$\boldsymbol{{Prove}}\:\boldsymbol{{Pythagoras}}\:\boldsymbol{{theorem}} \\ $$$${with}\:{the}\:{aid}\:{of}\:{image}\:{above}\:. \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last…
Question Number 14630 by Don sai last updated on 03/Jun/17 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{eqn} \\ $$$$\mathrm{dr}/\mathrm{d}\theta=\left[\mathrm{r}\left(\mathrm{a}^{\mathrm{2}} −\mathrm{r}^{\mathrm{2}} \right)/\mathrm{a}^{\mathrm{2}} +\mathrm{r}^{\mathrm{2}} \right]\mathrm{cot}\theta \\ $$$$\mathrm{hint}.\:\mathrm{let}\:\mathrm{a}^{\mathrm{2}} +\mathrm{r}^{\mathrm{2}} =\mathrm{a}^{\mathrm{2}} −\mathrm{r}^{\mathrm{2}} +\mathrm{2r}^{\mathrm{2}} . \\…
Question Number 14502 by ajfour last updated on 01/Jun/17 Commented by ajfour last updated on 01/Jun/17 $${Find}\:\boldsymbol{{x}},\boldsymbol{{y}},\:{and}\:\boldsymbol{{z}}\:\:{in}\:{terms}\:{of}\: \\ $$$$\boldsymbol{{a}},\boldsymbol{{b}},\:{and}\:\boldsymbol{{c}}\:{using}\:{parameters} \\ $$$$\boldsymbol{{h}},\:{and}\:\boldsymbol{{k}}.\: \\ $$ Commented by…
Question Number 145573 by mnjuly1970 last updated on 06/Jul/21 Answered by Olaf_Thorendsen last updated on 06/Jul/21 $${p}\:=\:{half}\:{perimeter} \\ $$$${p}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+\mathrm{2}{r}+\mathrm{2}+\mathrm{2}{r}+\mathrm{3}+\mathrm{2}{r}\right)\:=\:\mathrm{3}\left({r}+\mathrm{1}\right) \\ $$$${p}−{a}\:=\:\mathrm{3}\left({r}+\mathrm{1}\right)−\left(\mathrm{1}+\mathrm{2}{r}\right)\:=\:{r}+\mathrm{2} \\ $$$${p}−{b}\:=\:\mathrm{3}\left({r}+\mathrm{1}\right)−\left(\mathrm{2}+\mathrm{2}{r}\right)\:=\:{r}+\mathrm{1} \\ $$$${p}−{c}\:=\:\mathrm{3}\left({r}+\mathrm{1}\right)−\left(\mathrm{3}+\mathrm{2}{r}\right)\:=\:{r}…
Question Number 145575 by mnjuly1970 last updated on 06/Jul/21 Answered by ajfour last updated on 06/Jul/21 Commented by ajfour last updated on 06/Jul/21 $${Let}\:{the}\:{intersection}\:{be}\:{the} \\…
Question Number 80015 by mr W last updated on 30/Jan/20 Commented by mr W last updated on 30/Jan/20 $$\mathrm{1}.\:{Prove}\:{that}\:{both}\:{equilaterial}\:{triangles} \\ $$$${touch}\:{each}\:{other}\:{in}\:{the}\:{square}\:{as}\:{shown}. \\ $$$$\mathrm{2}.\:{Find}\:{r}_{\mathrm{1}} /{r}_{\mathrm{2}} \\…
Question Number 14384 by ajfour last updated on 31/May/17 Commented by ajfour last updated on 31/May/17 $${only}\:{find}\:{S}={x}+{y}+{z} \\ $$$${in}\:{terms}\:{of}\:\boldsymbol{{a}},\:\boldsymbol{{b}}\:,\:\boldsymbol{{c}}\:\:{which}\:{are} \\ $$$${sides}\:{of}\:\bigtriangleup{ABC}. \\ $$ Commented by…
Question Number 14364 by RasheedSindhi last updated on 31/May/17 $$\mathrm{Modification}\:\mathrm{of}\:\mathrm{Q}#\mathrm{14157} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{xy}=\mathrm{a}^{\mathrm{2}} \\ $$$$\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} −\mathrm{yz}=\mathrm{b}^{\mathrm{2}} \\ $$$$\mathrm{z}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} −\mathrm{zx}=\mathrm{c}^{\mathrm{2}} \\ $$$$\mathrm{Pl}\:\mathrm{discuss}\:\mathrm{also}\:\mathrm{geometrical}/ \\…