Question Number 77605 by lémùst last updated on 08/Jan/20 $$\mathrm{how}\:\mathrm{to}\:\mathrm{solve}\:: \\ $$$$\mathrm{y}''+\mathrm{p}\left(\mathrm{x}\right)\mathrm{y}'+\mathrm{q}\left(\mathrm{x}\right)\mathrm{y}=\mathrm{r}\left(\mathrm{x}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 77603 by kaivan.ahmadi last updated on 08/Jan/20 $$\int\frac{\mathrm{10}{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{1}}{{x}^{\mathrm{4}} −{x}^{\mathrm{3}} −{x}+\mathrm{1}}{dx} \\ $$$$ \\ $$ Commented by mathmax by abdo last updated on…
Question Number 143139 by loveineq last updated on 10/Jun/21 $$\mathrm{Let}\:{a},{b},{c}\:>\:\mathrm{0}\:\mathrm{and}\:{a}+{b}+{c}\:=\:\mathrm{3}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}+{a}^{\mathrm{2}} \right)\left(\mathrm{1}+{b}^{\mathrm{2}} \right)\left(\mathrm{1}+{c}^{\mathrm{2}} \right)\:\leqslant\:\left(\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{{abc}}}\right)^{\mathrm{3}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service Privacy Policy…
Question Number 143138 by loveineq last updated on 10/Jun/21 $$\mathrm{Let}\:{a},{b}\:>\:\mathrm{0}\:\mathrm{and}\:{a}+{b}\:=\:\mathrm{2}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}+{a}^{\mathrm{2}} \right)\left(\mathrm{1}+{b}^{\mathrm{2}} \right)\:\leqslant\:\left(\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{{ab}}}\right)^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 12064 by tawa last updated on 11/Apr/17 $$\mathrm{A}\:\mathrm{heat}\:\mathrm{pump}\:\mathrm{gas}\:\mathrm{C}.\mathrm{P}\:=\:\mathrm{3},\:\mathrm{while}\:\mathrm{the}\:\mathrm{indoor}\:\mathrm{temperature}\:\mathrm{is}\:\mathrm{27}°\mathrm{C}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{outdoor}\:\mathrm{temperature}\:\mathrm{is}\:\mathrm{8}°\mathrm{C}.\:\mathrm{How}\:\mathrm{much}\:\mathrm{work}\:\mathrm{per}\:\mathrm{hour}\:\mathrm{is}\:\mathrm{required}\:\mathrm{to}\:\mathrm{pump} \\ $$$$\mathrm{3}.\mathrm{07}\:\mathrm{J}\:\mathrm{of}\:\mathrm{heat}\:\mathrm{per}\:\mathrm{hour}\:\mathrm{into}\:\mathrm{the}\:\mathrm{individual}\:\mathrm{unit}\:\mathrm{of}\:\mathrm{10}^{\mathrm{5}} \:\mathrm{J}.\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 12063 by tawa last updated on 10/Apr/17 Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 11/Apr/17 $$\mathrm{100}+\mathrm{4}\left(\mathrm{180}−{a}\right)=\mathrm{360}\Rightarrow\mathrm{4}{a}=\mathrm{820}−\mathrm{360} \\ $$$$\mathrm{4}{a}=\mathrm{460}\Rightarrow{a}=\mathrm{115}\:\:\:\:.\blacksquare \\ $$ Terms of Service Privacy…
Question Number 12062 by tawa last updated on 10/Apr/17 $$\underset{{x}\rightarrow\mathrm{y}} {\mathrm{lim}}\:\:\frac{\mathrm{x}^{\mathrm{n}} \:−\:\mathrm{y}^{\mathrm{n}} }{\mathrm{x}\:−\:\mathrm{y}} \\ $$ Answered by ajfour last updated on 11/Apr/17 $$\boldsymbol{{x}}^{\boldsymbol{{n}}} −\boldsymbol{{y}}^{\boldsymbol{{n}}} =\left(\boldsymbol{{x}}−\boldsymbol{{y}}\right)\left(\boldsymbol{{x}}^{\boldsymbol{{n}}−\mathrm{1}}…
Question Number 143134 by help last updated on 10/Jun/21 Answered by liberty last updated on 10/Jun/21 $$\:{y}'=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\left(\left({x}+{h}\right)^{\mathrm{2}} −\mathrm{4}\left({x}+{h}\right)\right)−\mathrm{cos}\:\left({x}^{\mathrm{2}} −\mathrm{4}{x}\right)}{{h}} \\ $$$$=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\left({x}^{\mathrm{2}} +\mathrm{2}{hx}+{h}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{4}{h}\right)−\mathrm{cos}\:\left({x}^{\mathrm{2}}…
Question Number 143131 by mohammad17 last updated on 10/Jun/21 $${find}\:{the}\:{partial}\:{sums}\:{of}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)} \\ $$ Answered by qaz last updated on 10/Jun/21 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}}…
Question Number 143130 by liberty last updated on 10/Jun/21 Commented by liberty last updated on 10/Jun/21 Answered by EDWIN88 last updated on 10/Jun/21 $$\mathrm{let}\:\mathrm{y}=\mathrm{px} \\…