Question Number 101085 by ajfour last updated on 30/Jun/20 Commented by ajfour last updated on 30/Jun/20 $${x}\:{in}\:{terms}\:{of}\:{b}\:{and}\:{c},\:{given}\:{any} \\ $$$${real}\:{b}\:{and}\:{c}. \\ $$$$\left({what}\:{seems}\:{a}\:{right}\:{angle}\:{is}\:\right. \\ $$$$\left.{indeed}\:{a}\:{right}\:{angle}\right) \\ $$…
Question Number 166611 by cortano1 last updated on 23/Feb/22 $$\:\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{polynom}\:\mathrm{give}\:\mathrm{the}\: \\ $$$$\:\mathrm{remainder}\:\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\mathrm{1}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\: \\ $$$$\:\mathrm{x}^{\mathrm{4}} +\mathrm{4}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\:\mathrm{divided}\:\mathrm{by}\:\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{2}. \\ $$ Terms of Service Privacy…
Question Number 101062 by bemath last updated on 30/Jun/20 Answered by MJS last updated on 30/Jun/20 $$\mathrm{after}\:“\mathrm{many}\:\mathrm{times}''\:\mathrm{implies}\:\mathrm{that} \\ $$$${p}=\frac{\mathrm{10}}{\mathrm{25}}=\frac{\mathrm{2}}{\mathrm{5}}\pm\mathrm{0} \\ $$$$\Rightarrow\:\mathrm{there}\:\mathrm{are}\:\frac{\mathrm{25}}{{p}}=\mathrm{62}.\mathrm{5}\approx\mathrm{60}\:\mathrm{candies}\:\mathrm{in}\:\mathrm{the}\:\mathrm{jar} \\ $$ Commented by…
Question Number 101056 by bemath last updated on 30/Jun/20 $$\mathrm{If}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}\left(\mathrm{5}{x}+\mathrm{1}\right)+{p}^{\mathrm{2}} =\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{one}\:\mathrm{root}\:\mathrm{equals}\:\mathrm{to}\:\mathrm{two}\:\mathrm{more} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{other},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${p}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\_\_\_ \\ $$ Commented by bemath last updated…
Question Number 166592 by Ari last updated on 22/Feb/22 Answered by nurtani last updated on 23/Feb/22 $${x}^{\mathrm{2}} =\mathrm{17}{x}+{y}…\left({i}\right) \\ $$$${y}^{\mathrm{2}} ={x}+\mathrm{17}{y}…\left({ii}\right) \\ $$$$\left({i}\right)−\left({ii}\right): \\ $$$$\blacksquare\:\:{x}^{\mathrm{2}}…
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Question Number 101052 by 1549442205 last updated on 30/Jun/20 $$\mathrm{Given}\:\mathrm{a}=\:^{\mathrm{3}} \sqrt{\mathrm{7}+\sqrt{\mathrm{50}}},\mathrm{b}=\:^{\mathrm{3}} \sqrt{\mathrm{7}−\sqrt{\mathrm{50}}}.\mathrm{Prove} \\ $$$$\mathrm{that}\:\mathrm{a}^{\mathrm{7}} +\mathrm{b}^{\mathrm{7}} \mathrm{is}\:\mathrm{an}\:\mathrm{even}\:\mathrm{number}. \\ $$ Answered by MJS last updated on 30/Jun/20…
Question Number 35481 by JOHNMASANJA last updated on 19/May/18 $${if}\:{x}^{{p}} {y}^{{p}} =\left({x}\:+\:{y}\right)\:^{{p}\:+{q}} \:\:\: \\ $$$${prove}\:{that}\:\frac{{dy}}{{dx}}=\frac{{y}}{{x}} \\ $$ Commented by math1967 last updated on 19/May/18 $${plz}\:{check}\:{x}^{{p}}…
Question Number 35475 by Apostle last updated on 19/May/18 $${Is}\:{Rational}\:{Number}\:{Countable}? \\ $$$${If}\:{yes}\:{how}\:{do}\:{we}\:{count}\:{it}\:{with}\:{one}\:{to}\:{one}\:{correspondence}\:{with}\:{set}\:{of}\:{natural}\:{number}\:\mathbb{N}? \\ $$ Answered by MJS last updated on 19/May/18 Terms of Service Privacy…
Question Number 166526 by mathlove last updated on 21/Feb/22 Answered by MJS_new last updated on 21/Feb/22 $$\Rightarrow \\ $$$${x}^{\mathrm{4}} +\frac{\mathrm{7}}{\mathrm{2}}{x}^{\mathrm{3}} +\frac{\mathrm{9}}{\mathrm{2}}{x}^{\mathrm{2}} +\frac{\mathrm{7}}{\mathrm{2}}{x}−\frac{\mathrm{5}}{\mathrm{2}}=\mathrm{0} \\ $$$$\left({x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}\right)\left({x}^{\mathrm{2}}…