Question Number 12883 by FilupS last updated on 05/May/17 $$\mathrm{for}\:\:\:\:\:−\mathrm{128}\leqslant{x}\leqslant\mathrm{127} \\ $$$$\mathrm{and}\:\:\:−\mathrm{127}\leqslant{y}\leqslant\mathrm{128} \\ $$$$\mathrm{where}\:\:\:{x},{y}\in\mathbb{Z} \\ $$$$\: \\ $$$$\mathrm{Point}\:{P}\left({x},{y}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{cartesian}\:\mathrm{plane}. \\ $$$$\: \\ $$$$\mathrm{From}\:\mathrm{the}\:\mathrm{origin},\:\mathrm{angle}\:\theta\:\mathrm{is}\:\mathrm{made}\:\mathrm{counter} \\…
Question Number 143952 by akolade last updated on 19/Jun/21 Answered by Olaf_Thorendsen last updated on 20/Jun/21 $$\mathrm{C}\:=\:\int\frac{\mathrm{cosh}{x}}{\mathrm{cosh}{x}+\mathrm{sinh}{x}}\:{dx} \\ $$$$\mathrm{S}\:=\:\int\frac{\mathrm{sinh}{x}}{\mathrm{cosh}{x}+\mathrm{sinh}{x}}\:{dx} \\ $$$$\mathrm{C}+\mathrm{S}\:=\:\int{dx}\:=\:{x}+\mathrm{cst}\:\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\mathrm{C}−\mathrm{S}\:=\:\int\frac{\mathrm{cosh}{x}−\mathrm{sinh}{x}}{\mathrm{cosh}{x}+\mathrm{sinh}{x}}\:{dx} \\ $$$$\mathrm{C}−\mathrm{S}\:=\:\int\frac{\left(\mathrm{cosh}{x}−\mathrm{sinh}{x}\right)^{\mathrm{2}}…
Question Number 12881 by kunalshukla95040 last updated on 05/May/17 $$\frac{{lim}}{{x}\rightarrow\mathrm{0}}\frac{\sqrt{\mathrm{1}−\mathrm{cos}\:{x}}}{{x}} \\ $$$${is}\:{equals}\:{to}. \\ $$ Answered by nume1114 last updated on 05/May/17 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{1}−\mathrm{cos}\:{x}}}{{x}} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}}…
Question Number 143951 by lapache last updated on 19/Jun/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{2}{xsin}^{\mathrm{2}} {t}}{{cos}^{\mathrm{2}} {t}+{x}^{\mathrm{2}} {sin}^{\mathrm{2}} {t}}{dt}=…..???? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 12875 by @matikaku last updated on 05/May/17 Commented by @matikaku last updated on 05/May/17 $${if}\:{area}\:{ABCD}\:{is}\:\mathrm{162}.\:{what}\:{is}\:{the}\:{area}\:{of}\:{marked}/{black}\:{space}?\:{thks} \\ $$ Commented by RasheedSoomro last updated on…
Question Number 12874 by tawa last updated on 04/May/17 Answered by mrW1 last updated on 05/May/17 $$\frac{{dy}}{{dx}}=\mathrm{6}{x}−\mathrm{5} \\ $$$${y}=\int\left(\mathrm{6}{x}−\mathrm{5}\right){dx}=\mathrm{3}{x}^{\mathrm{2}} −\mathrm{5}{x}+{C} \\ $$$$\mathrm{5}=\mathrm{3}×\mathrm{2}^{\mathrm{2}} −\mathrm{5}×\mathrm{2}+{C} \\ $$$$\Rightarrow{C}=\mathrm{3}…
Question Number 12873 by tawa last updated on 04/May/17 $$\mathrm{How}\:\mathrm{many}\:\mathrm{flouride}\:\mathrm{ion}\:\mathrm{are}\:\mathrm{there}\:\mathrm{in}\:\mathrm{1}.\mathrm{46}\:\mathrm{mole}\:\mathrm{of}\:\mathrm{aluminium}\:\mathrm{flouride}\:\mathrm{Alf}_{\mathrm{3}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 78400 by ~blr237~ last updated on 17/Jan/20 $$\mathrm{the}\:\mathrm{convolute}\:\mathrm{function}\:\mathrm{of}\:\mathrm{both}\:\mathrm{f}\:\mathrm{and}\:\mathrm{g}\:\mathrm{is}\:\mathrm{marked}\:\mathrm{f}\ast\mathrm{g} \\ $$$$\mathrm{And}\:\mathrm{define}\:\mathrm{by}\:\:\left(\mathrm{f}\ast\mathrm{g}\right)\left(\mathrm{x}\right)=\int_{\mathrm{0}} ^{\mathrm{x}} \mathrm{f}\left(\mathrm{x}−\mathrm{t}\right)\mathrm{g}\left(\mathrm{t}\right)\mathrm{dt} \\ $$$$\mathrm{Let}\:\mathrm{noted}\:\mathrm{E}=\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{function}\:\mathrm{define}\:\mathrm{on}\:\mathbb{R}_{+} \\ $$$$\left.\mathrm{0}\right)\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{a}\:\mathrm{function}\:\mathrm{f}_{\mathrm{0}} \in\mathrm{E}\:\mathrm{such}\:\mathrm{as}\:\mathrm{for}\:\mathrm{all}\:\mathrm{x}>\mathrm{0}\:,\:\int_{\mathrm{0}} ^{\infty} \mathrm{f}_{\mathrm{0}} \left(\mathrm{t}\right)\mathrm{e}^{−\mathrm{xt}} \mathrm{dt}=\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\mathrm{Prove}\:\mathrm{that}\:\left(\mathrm{E},\ast\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{semigroup}…
Question Number 143932 by Ar Brandon last updated on 19/Jun/21 Answered by mathmax by abdo last updated on 19/Jun/21 $$\left.\mathrm{1}\right)\:\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{t}^{\mathrm{2}} } \mathrm{dt}\:\:\:\:\:\:\Rightarrow\mathrm{I}=\int_{\mathrm{0}} ^{\mathrm{a}}…
Question Number 78399 by john santu last updated on 17/Jan/20 $${dear}\:{sir}\:{W},\:{Mjs}\: \\ $$$${the}\:{set}\:\left\{\mathrm{1},\mathrm{4},{n}\right\}\:{have}\:{the}\:{condition}\:{that}\: \\ $$$${if}\:{two}\:{different}\:{elements}\:{are} \\ $$$${selected}\:{and}\:\mathrm{2112}\:{is}\:{added}\:{to} \\ $$$${the}\:{result}\:,\:{then}\:{the}\:{result}\: \\ $$$${is}\:{a}\:{perfect}\:{square}\:{if}\:{n}\:{is}\:{a}\: \\ $$$${positif}\:{number}\:.\:{then}\:{the}\:{number}\: \\ $$$${of}\:{possible}\:{values}\:{of}\:{n}\:{is}\:…