Question Number 9060 by tawakalitu last updated on 16/Nov/16 Answered by mrW last updated on 17/Nov/16 $$\left.{b}\right) \\ $$$$\mathrm{60}^{\mathrm{2}} =\mathrm{40}^{\mathrm{2}} +\mathrm{92}^{\mathrm{2}} −\mathrm{2}×\mathrm{40}×\mathrm{92}×\mathrm{cos}\:\alpha \\ $$$$\mathrm{cos}\:\alpha=\frac{\mathrm{40}^{\mathrm{2}} +\mathrm{92}^{\mathrm{2}}…
Question Number 140129 by mathdanisur last updated on 04/May/21 $${x};{y}\in\mathbb{R}^{+} \:;\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{2} \\ $$$${proof}:\:\mathrm{3}−{xy}\geqslant\left({x}+{y}\right)\sqrt{{xy}}+\left({x}−{y}\right)^{\mathrm{2}} \geqslant\mathrm{2}{xy} \\ $$ Answered by mr W last updated on…
Question Number 74594 by ajfour last updated on 27/Nov/19 Commented by ajfour last updated on 27/Nov/19 $${Reposted}:\:{Q}.\mathrm{74557} \\ $$$${A}\:{particle}\:{of}\:{mass}\:{m}\:{tied}\:{to}\:{O} \\ $$$${with}\:{a}\:{string}\:{of}\:{length}\:{b}\:{and} \\ $$$${released}\:{at}\:{t}=\mathrm{0}\:{at}\:{the}\:{rim}\:{of} \\ $$$${a}\:{hollow}\:{hemisphere}\:{crucible}.…
Question Number 9057 by sandipkd@ last updated on 16/Nov/16 Answered by aydnmustafa1976 last updated on 16/Nov/16 $${nsin}\frac{\mathrm{1}}{{n}}={lim}\frac{{sin}\frac{\mathrm{1}}{{n}}}{\frac{\mathrm{1}}{{n}}}={lim}\frac{{sint}}{{t}}=\mathrm{1}\:{therefore}\:\:\mathrm{4}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx}=\mathrm{4}.{arctgx}\mid_{\mathrm{0}} ^{\mathrm{1}} =\mathrm{4}\left(\frac{\Pi}{\mathrm{4}}−\mathrm{0}\right)=\Pi \\ $$ Commented…
Question Number 74590 by Aditya789 last updated on 27/Nov/19 Answered by MJS last updated on 27/Nov/19 $${n}=\mathrm{7} \\ $$$$\mathrm{the}\:\mathrm{coefficients}\:\mathrm{then}\:\mathrm{are}\:\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}\:\mathrm{with}\:{n}=\mathrm{7};\:\mathrm{0}\leqslant{k}\leqslant\mathrm{7} \\ $$$$\begin{pmatrix}{\mathrm{7}}\\{\mathrm{0}}\end{pmatrix};\:\begin{pmatrix}{\mathrm{7}}\\{\mathrm{1}}\end{pmatrix};\:\begin{pmatrix}{\mathrm{7}}\\{\mathrm{2}}\end{pmatrix};\:\begin{pmatrix}{\mathrm{7}}\\{\mathrm{3}}\end{pmatrix};\:\begin{pmatrix}{\mathrm{7}}\\{\mathrm{4}}\end{pmatrix};\:\begin{pmatrix}{\mathrm{7}}\\{\mathrm{5}}\end{pmatrix};\:\begin{pmatrix}{\mathrm{7}}\\{\mathrm{6}}\end{pmatrix};\:\begin{pmatrix}{\mathrm{7}}\\{\mathrm{7}}\end{pmatrix} \\ $$$$\mathrm{1}\:\mathrm{7}\:\mathrm{21}\:\mathrm{35}\:\mathrm{35}\:\mathrm{21}\:\mathrm{7}\:\mathrm{1} \\ $$…
Question Number 74591 by Aditya789 last updated on 27/Nov/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 74589 by Aditya789 last updated on 27/Nov/19 Answered by MJS last updated on 27/Nov/19 $${a}\left({b}−{c}\right){x}^{\mathrm{2}} +{b}\left({c}−{a}\right){xy}+{c}\left({a}−{b}\right){y}^{\mathrm{2}} =\mathrm{0} \\ $$$${x}^{\mathrm{2}} +\frac{{b}\left({c}−{a}\right){y}}{{a}\left({b}−{c}\right)}{x}+\frac{{c}\left({a}−{b}\right){y}^{\mathrm{2}} }{{a}\left({b}−{c}\right)}=\mathrm{0} \\ $$$${x}={t}−\frac{{b}\left({c}−{a}\right){y}}{\mathrm{2}{a}\left({b}−{c}\right)}…
Question Number 74587 by lalitchand last updated on 27/Nov/19 $$\mathrm{If}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{n}\:\mathrm{arithmetic}\:\mathrm{means}\:\mathrm{between}\: \\ $$$$\mathrm{two}\:\mathrm{number}\:\mathrm{is}\:\mathrm{20}.\mathrm{if}\:\mathrm{last}\:\mathrm{mean}\:\mathrm{is}\:\mathrm{double} \\ $$$$\mathrm{of}\:\mathrm{1st}\:\mathrm{mean}\:\mathrm{and}\:\mathrm{one}\:\mathrm{is}\:\mathrm{three}\:\mathrm{times}\:\mathrm{of} \\ $$$$\mathrm{another}\:\mathrm{number}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{numbers}. \\ $$$$ \\ $$ Terms of Service Privacy Policy…
Question Number 9049 by Rasheed Soomro last updated on 16/Nov/16 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{every}\:\mathrm{even}\:\mathrm{number}\:\mathrm{can}\:\mathrm{be}\: \\ $$$$\mathrm{expressed}\:\mathrm{as}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two}\:\mathrm{primes}\:\mathrm{or} \\ $$$$\mathrm{give}\:\mathrm{an}\:\mathrm{counter}\:\mathrm{example}. \\ $$ Commented by FilupSmith last updated on 16/Nov/16 $$\mathrm{2}{n}={p}_{\mathrm{1}}…
Question Number 9048 by tawakalitu last updated on 16/Nov/16 Answered by Rasheed Soomro last updated on 16/Nov/16 $$\left.\mathrm{a}\right)\:\:\mathrm{Straight}\:\mathrm{line}:\:\mathrm{y}=\mathrm{mx}+\mathrm{c} \\ $$$$\:\:\:\:\:\:\:\mathrm{Circle}:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{2gx}+\mathrm{2fy}+\mathrm{C}_{\mathrm{1}} =\mathrm{0} \\ $$$$\mathrm{For}\:\mathrm{intersection}\:\mathrm{we}\:\mathrm{have}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{above}…