Question Number 174806 by cortano1 last updated on 11/Aug/22 $${Given}\:{f}\left({x}\right)={x}^{\mathrm{4}} +{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d} \\ $$$${where}\:{a},{b},{c}\:{and}\:{d}\:{are}\:{real}\:{number} \\ $$$${suppose}\:{the}\:{graph}\:{f}\left({x}\right)\:{intersects} \\ $$$${the}\:{graph}\:{of}\:{y}=\mathrm{2}{x}−\mathrm{1}\:{at}\:{x}=\mathrm{1},\mathrm{2},\mathrm{3}. \\ $$$$\:{Find}\:{the}\:{value}\:{of}\:\:{f}\left(\mathrm{0}\right)+{f}\left(\mathrm{4}\right). \\ $$ Commented by…
Question Number 174800 by AgniMath last updated on 11/Aug/22 $$\mathrm{For}\:\mathrm{which}\:\mathrm{value}\:\mathrm{of}\:{x}\:\mathrm{this}\:\mathrm{cubic}\:\mathrm{equation}\:\mathrm{will} \\ $$$$\mathrm{be}\:\mathrm{0}\:?\:{a}^{\mathrm{3}} \:−\:\mathrm{16}{a}\:−\:\mathrm{3} \\ $$ Answered by MJS_new last updated on 11/Aug/22 $${a}_{\mathrm{1}} =−\frac{\mathrm{8}\sqrt{\mathrm{3}}}{\mathrm{3}}\mathrm{cos}\:\left(\frac{\pi}{\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{3}}\mathrm{arcsin}\:\frac{\mathrm{9}\sqrt{\mathrm{3}}}{\mathrm{128}}\right) \\…
Question Number 174799 by Shrinava last updated on 11/Aug/22 Answered by behi834171 last updated on 12/Aug/22 $${cot}\frac{{A}}{\mathrm{2}}=\sqrt{\frac{{p}\left({p}−{a}\right)}{\left({p}−{b}\right)\left({p}−{c}\right)}}\:\:=\frac{\boldsymbol{{S}}}{\left(\boldsymbol{{p}}−\boldsymbol{{b}}\right)\left(\boldsymbol{{p}}−\boldsymbol{{c}}\right)}= \\ $$$$=\frac{\boldsymbol{{p}}\left(\boldsymbol{{p}}−\boldsymbol{{a}}\right)\:}{\boldsymbol{{S}}}=\frac{\boldsymbol{{p}}−\boldsymbol{{a}}}{\boldsymbol{{r}}}\:\:\:\:\:{and}\:{so}\:{on}… \\ $$$$\Pi\boldsymbol{{cot}}\frac{\boldsymbol{{A}}}{\mathrm{2}}=\frac{\boldsymbol{{S}}^{\mathrm{2}} }{\boldsymbol{{p}}.\boldsymbol{{r}}^{\mathrm{3}} }=\frac{\boldsymbol{{S}}}{\boldsymbol{{r}}^{\mathrm{2}} } \\…
Question Number 43716 by behi83417@gmail.com last updated on 14/Sep/18 Commented by tanmay.chaudhury50@gmail.com last updated on 15/Sep/18 Commented by tanmay.chaudhury50@gmail.com last updated on 15/Sep/18 Commented by…
Question Number 43707 by Tawa1 last updated on 14/Sep/18 $$\mathrm{Simplify}:\:\:\: \\ $$$$\left(\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\right)\left(\mathrm{x}^{−\mathrm{1}} \:+\:\mathrm{y}^{−\mathrm{1}} \:+\:\mathrm{z}^{−\mathrm{1}} \right)\:=\:\left(\mathrm{x}^{−\mathrm{1}} \:\mathrm{y}^{−\mathrm{1}} \:\mathrm{z}^{−\mathrm{1}} \right)\left(\mathrm{x}\:+\:\mathrm{y}\right)\left(\mathrm{y}\:+\:\mathrm{z}\right)\left(\mathrm{z}\:+\:\mathrm{x}\right) \\ $$ Commented by math1967 last updated…
Question Number 43706 by Tawa1 last updated on 14/Sep/18 $$\mathrm{If}\:\:\mathrm{pqr}\:=\:\mathrm{1} \\ $$$$\mathrm{Hence}\:\mathrm{evaluate}:\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{e}\:+\:\mathrm{f}^{−\mathrm{1}} }\:\:+\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{f}\:+\:\mathrm{g}^{−\mathrm{1}} }\:\:+\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{g}\:+\:\mathrm{e}^{−\mathrm{1}} } \\ $$ Commented by Joel578 last updated on 14/Sep/18 $${p},{q},{r}\:\mathrm{and}\:{e},{f},{g}\:?…
Question Number 43702 by rajesh123456 last updated on 14/Sep/18 $${simplify}\:\:\:\left[\frac{\mathrm{12}^{\mathrm{1}/\mathrm{5}} }{\mathrm{27}^{\mathrm{1}/\mathrm{5}} }\right]^{\mathrm{5}/\mathrm{2}} \\ $$ Answered by Joel578 last updated on 14/Sep/18 $$\left(\frac{\mathrm{12}^{\mathrm{1}/\mathrm{5}} }{\mathrm{27}^{\mathrm{1}/\mathrm{5}} }\right)^{\mathrm{5}/\mathrm{2}} \:=\:\frac{\sqrt{\mathrm{12}}}{\:\sqrt{\mathrm{27}}}\:=\:\frac{\mathrm{2}\sqrt{\mathrm{3}}}{\mathrm{3}\sqrt{\mathrm{3}}}\:=\:\frac{\mathrm{2}}{\mathrm{3}}…
Question Number 43705 by Tawa1 last updated on 14/Sep/18 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{to}\:\mathrm{each}\:\mathrm{quadratic}\:\mathrm{factor}\:\mathrm{in}\:\mathrm{the}\:\mathrm{denominator}\:\mathrm{of}\:\mathrm{the}\:\mathrm{form}\: \\ $$$$\mathrm{ax}^{\mathrm{2}} \:+\:\mathrm{bx}\:+\:\mathrm{c}\:\:\:\mathrm{which}\:\mathrm{does}\:\mathrm{not}\:\mathrm{have}\:\mathrm{linear}\:\mathrm{factors},\:\mathrm{there}\:\mathrm{corresponds}\:\mathrm{to} \\ $$$$\mathrm{a}\:\mathrm{partial}\:\mathrm{fraction}\:\mathrm{of}\:\mathrm{the}\:\mathrm{form}\:\:\:\:\frac{\mathrm{Ax}\:+\:\mathrm{B}}{\mathrm{ax}^{\mathrm{2}} \:+\:\mathrm{bx}\:+\:\mathrm{c}}\:\:\:\mathrm{where}\:\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{constant}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 109237 by bobhans last updated on 22/Aug/20 $$\:\:\frac{\flat{o}\flat{hans}}{\angle\angle\angle\angle\angle} \\ $$$$\begin{cases}{{x}^{\mathrm{3}} +{x}^{\mathrm{2}} {y}\:=\:\mathrm{9}}\\{{y}^{\mathrm{3}} +{y}^{\mathrm{2}} {x}\:=\:\mathrm{25}}\end{cases}.\:{find}\:{x}\:{and}\:{y}. \\ $$ Answered by bemath last updated on 22/Aug/20…
Question Number 109222 by bemath last updated on 22/Aug/20 $$\:\:\:\:\frac{\ldots\flat{em}\mathcal{ATH}\ldots}{\cong\cong\cong\cong\cong\cong} \\ $$$$\sqrt{\mathrm{5}+\sqrt{\mathrm{10}}}\:=\:{x}.\left(\sqrt{\mathrm{5}+\sqrt{\mathrm{15}}\:}\:+\sqrt{\mathrm{5}−\sqrt{\mathrm{15}}}\:\right) \\ $$$${x}\:=? \\ $$ Answered by bobhans last updated on 22/Aug/20 $$\:\:\:\frac{\_\flat{o}\flat\mathcal{HAN}\varsigma\_}{\triangleright\triangleleft} \\…