Category: Others

Question Number 66746 by John Kaloki Musau last updated on 20/Aug/19 $${A}\:{point}\:{T}\:\:{divides}\:{a}\:{line}\:{AB}\:{internally}\:{in}\:{the}\:{ratio}\:\mathrm{5}:\mathrm{2}.\:{Given}\:{that}\:{A}\:{is}\:\left(-\mathrm{4},\mathrm{10}\right)\:{and}\:{B}\:{is}\:\left(\mathrm{10},\mathrm{3}\right),\:{find}\:{the}\:{coordinates}\:{of}\:{T}. \\ $$ Answered by mr W last updated on 19/Aug/19 $${x}_{{T}} ={x}_{{A}} +\frac{\mathrm{5}}{\mathrm{7}}\left({x}_{{B}}…

Question Number 1208 by 123456 last updated on 14/Jul/15 $$\mathrm{wich}\:\mathrm{statment}\:\mathrm{is}\:\mathrm{true} \\ $$$$\mathrm{1}.\mathrm{if}\:{x}\in\mathbb{Q}\:\mathrm{and}\:{y}\in\mathbb{Z},\:\mathrm{then}\:{xy}\in\mathbb{Q}/\mathbb{Z} \\ $$$$\mathrm{2}.\mathrm{if}\:{x}\in\mathbb{Q}/\mathbb{Z}\:\mathrm{and}\:{y}\in\mathbb{Z},\:\mathrm{then}\:{xy}\in\mathbb{Q}/\mathbb{Z} \\ $$$$\mathrm{3}.\mathrm{if}\:{x}\in\mathbb{R},\:\mathrm{then}\:\exists{y}\in\mathbb{R}\:\mathrm{such}\:\mathrm{that}\:{xy}=\mathrm{5} \\ $$$$\mathrm{4}.\mathrm{if}\:{x}\in\mathbb{N}/\left\{\mathrm{0}\right\},\:\mathrm{then}\:\exists{y}\in\mathbb{Q}\:\mathrm{such}\:\mathrm{that}\:\sqrt{\frac{{y}\left({x}+\mathrm{2}\right)}{{x}\left({x}+\mathrm{1}\right)}}\in\mathbb{Q} \\ $$ Answered by prakash jain last…

Question Number 1196 by 123456 last updated on 13/Jul/15 $$\mathrm{lets}\:{f}:\mathbb{R}\rightarrow\mathbb{Z},\:\mathrm{suppose}\:\mathrm{that}\:\exists{x}\in\mathbb{R}\:\mathrm{and} \\ $$$$\exists{y}\in\mathbb{R}\:\mathrm{with}\:{x}\neq{y}\:\mathrm{such}\:{f}\left({x}\right)\neq{f}\left({y}\right) \\ $$$$\mathrm{can}\:{f}\left({x}\right)\:\mathrm{be}\:\mathrm{conrinuous}? \\ $$ Answered by prakash jain last updated on 14/Jul/15 $${f}\left({x}\right)={a}\in\mathbb{Z}…

Question Number 1192 by 123456 last updated on 13/Jul/15 $$\mathrm{lets}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{and}\:{g}:\mathbb{Z}\rightarrow\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$${f}\left({x}\right)={g}\left({x}\right),{x}\in\mathbb{Z} \\ $$$$\mathrm{given}\:{a}\in\mathbb{Z},\:\mathrm{then}\:\mathrm{proof}\:\mathrm{or}\:\mathrm{give}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\:\mathrm{that} \\ $$$$\underset{{x}\rightarrow{a}} {\mathrm{lim}}{f}\left({x}\right)={g}\left({a}\right) \\ $$ Commented by prakash jain last updated…

Question Number 1155 by 123456 last updated on 05/Jul/15 $$\mathrm{what}\:\mathrm{the}\:\mathrm{min}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{60}{x}+\mathrm{120}{y}+\mathrm{1250}{z} \\ $$$$\mathrm{if} \\ $$$${x}+{y}+\mathrm{5}{z}=\mathrm{150} \\ $$$${x}\in\left\{\mathrm{0},…,\mathrm{150}\right\} \\ $$$${y}\in\left\{\mathrm{0},…,\mathrm{150}\right\} \\ $$$${z}\in\left\{\mathrm{0},…,\mathrm{30}\right\} \\ $$ Answered…