Question Number 8785 by FilupSmith last updated on 27/Oct/16 Commented by FilupSmith last updated on 27/Oct/16 $${f}\left({x}\right)=\sqrt{{x}^{\mathrm{2}} −\lfloor{x}\rfloor} \\ $$$$\: \\ $$$${x}={N}+{c},\:\:\:\lfloor{x}\rfloor={N}\in\mathbb{Z} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{c}<\mathrm{1} \\…
Question Number 8783 by uchechukwu okorie favour last updated on 27/Oct/16 $${evaluate}\:\int\mathrm{4}^{{x}} {dx} \\ $$ Answered by FilupSmith last updated on 27/Oct/16 $$\mathrm{4}^{{x}} ={e}^{{x}\mathrm{ln}\left(\mathrm{4}\right)} \\…
Question Number 8782 by uchechukwu okorie favour last updated on 27/Oct/16 $${evaluate};\:\int\frac{\mathrm{sin}^{−\mathrm{1}} {x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$ Answered by prakash jain last updated on 27/Oct/16 $$\mathrm{sin}^{−\mathrm{1}}…
Question Number 8781 by tawakalitu last updated on 27/Oct/16 $$\mathrm{Father}\:\mathrm{reduced}\:\mathrm{the}\:\mathrm{quantity}\:\mathrm{of}\:\mathrm{food}\:\mathrm{bought}\:\mathrm{for} \\ $$$$\mathrm{the}\:\mathrm{family}\:\mathrm{by}\:\frac{\mathrm{25}}{\mathrm{2}}\%\:.\:\mathrm{When}\:\mathrm{he}\:\mathrm{found}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{cost}\:\mathrm{of}\:\mathrm{living}\:\mathrm{has}\:\mathrm{increased}\:\mathrm{by}\:\mathrm{15\%}.\:\mathrm{What} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{fraction}\:\mathrm{increase}\:\mathrm{in}\:\mathrm{the}\:\mathrm{family}'\mathrm{s}\:\mathrm{food} \\ $$$$\mathrm{bill}\:\mathrm{now}\:? \\ $$ Terms of Service Privacy Policy…
Question Number 139851 by mnjuly1970 last updated on 01/May/21 $$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:…… \\ $$$$\:\:\:\:\:\:\Phi=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}}\right)}{\:\sqrt{{x}}}{dx}=\mathrm{4}\:{ln}\left(\frac{{e}}{\mathrm{2}}\right)\:…\checkmark \\ $$ Answered by mindispower last updated on 01/May/21…
Question Number 74308 by Learner-123 last updated on 21/Nov/19 Answered by Tanmay chaudhury last updated on 22/Nov/19 $${P}×\mathrm{2}{R}={I}\alpha \\ $$$$\alpha=\frac{{w}−{w}_{\mathrm{0}} }{{t}} \\ $$$$\frac{{w}−{w}_{\mathrm{0}} }{{t}}=\frac{{P}×\mathrm{2}{R}}{{I}} \\…
Question Number 139840 by mnjuly1970 last updated on 01/May/21 Commented by mnjuly1970 last updated on 01/May/21 $${please}\:{prove}::\Uparrow\Uparrow\Uparrow \\ $$ Answered by mr W last updated…
Question Number 139842 by I want to learn more last updated on 01/May/21 Commented by MJS_new last updated on 01/May/21 $$\mathrm{no}\:\mathrm{real}\:\mathrm{solution} \\ $$ Answered by…
Question Number 74300 by ~blr237~ last updated on 21/Nov/19 $${Let}\:{consider}\:\:\gamma\:\::{I}\rightarrow\mathbb{R}^{\mathrm{2}} \:\:{a}\:{parametric}\:{curve}\: \\ $$$$\left.\mathrm{1}\left.\right){Prove}\:{that}\:{if}\:\:{a}<{b}\:\:{and}\:\:\gamma\left({a}\right)\neq\gamma\left({b}\right)\:{then}\:{there}\:{exist}\:\:{t}_{\mathrm{0}} \in\right]{a},{b}\left[\:\:\right. \\ $$$${such}\:{as}\:\:\gamma'\left({t}_{\mathrm{0}} \right)\:\:{is}\:{colinear}\:{to}\:\gamma\left({b}\right)−\gamma\left({a}\right)\: \\ $$$$\left.\mathrm{2}\right){Show}\:{that}\:{if}\:\:\gamma\:{is}\:{regular}\:{and}\:{the}\:\:{function}\:{f}\::{I}\rightarrow\mathbb{R}\:\:\:\:{t}\rightarrow{f}\left({t}\right)=\mid\mid\gamma\left({t}\right)−{O}\left(\mathrm{0},\mathrm{0}\right)\:\mid\mid\:\:{is}\:{maximal}\:{in}\:{t}_{\mathrm{0}} \in{I} \\ $$$${Then}\:\:\mid{K}_{\gamma} \left({t}_{\mathrm{0}} \right)\mid\geqslant\frac{\mathrm{1}}{{f}\left({t}_{\mathrm{0}} \right)}…
Question Number 139838 by EnterUsername last updated on 01/May/21 $$\mathrm{If}\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} \:\mathrm{and}\:{z}_{\mathrm{3}} \:\mathrm{are}\:\mathrm{the}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{a}\:\mathrm{right}-\mathrm{angled}\:\mathrm{isos}- \\ $$$$\mathrm{celes}\:\mathrm{triangle}\:\mathrm{described}\:\mathrm{in}\:\mathrm{counter}\:\mathrm{clock}\:\mathrm{sense}\:\mathrm{and} \\ $$$$\mathrm{right}\:\mathrm{angled}\:\mathrm{at}\:{z}_{\mathrm{3}} ,\:\mathrm{then}\:\left({z}_{\mathrm{1}} −{z}_{\mathrm{2}} \right)^{\mathrm{2}} \:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\: \\ $$$$\left(\mathrm{A}\right)\:\left({z}_{\mathrm{1}} −{z}_{\mathrm{3}} \right)\left({z}_{\mathrm{3}}…