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Category: Algebra

10-20-13-45-

Question Number 143507 by Billy last updated on 15/Jun/21 $$\mathrm{10}\sqrt{\mathrm{20}}+\mathrm{13}\sqrt{\mathrm{45}} \\ $$ Answered by qaz last updated on 15/Jun/21 $$\mathrm{10}\sqrt{\mathrm{20}}+\mathrm{13}\sqrt{\mathrm{45}} \\ $$$$=\mathrm{10}×\mathrm{2}\sqrt{\mathrm{5}}+\mathrm{13}×\mathrm{3}\sqrt{\mathrm{5}} \\ $$$$=\left(\mathrm{20}+\mathrm{39}\right)\sqrt{\mathrm{5}} \\…

does-i-1-p-i-converge-p-i-P-

Question Number 12414 by FilupS last updated on 21/Apr/17 $$\mathrm{does}\:\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}{p}_{{i}} \:\:\:\mathrm{converge},\:\:\:\:{p}_{{i}} \in\mathbb{P} \\ $$ Answered by prakash jain last updated on 22/Apr/17 $$\mathrm{There}\:\mathrm{are}\:\mathrm{infinitely}\:\mathrm{many}\:\mathrm{primes}.…

f-x-x-3-e-x-3-e-f-1-

Question Number 12403 by sin (x) last updated on 21/Apr/17 $${f}\left({x}\right)=\lfloor{x}−\frac{\mathrm{3}}{{e}}\rfloor+\lfloor{x}+\frac{\mathrm{3}}{{e}}\rfloor\Rightarrow{f}\left(\mathrm{1}\right)=? \\ $$ Answered by FilupS last updated on 21/Apr/17 $$\lfloor{x}\rfloor\:=\:\mathrm{floor}\left({x}\right) \\ $$$${f}\left(\mathrm{1}\right)=\lfloor\mathrm{1}−\frac{\mathrm{3}}{{e}}\rfloor+\lfloor\mathrm{1}+\frac{\mathrm{3}}{{e}}\rfloor \\ $$$$\mathrm{2}{e}>\mathrm{3}>{e}\:\:\Rightarrow\:\:\:\mathrm{2}>\frac{\mathrm{3}}{{e}}>\mathrm{1}…

0-2pi-sgn-cosx-dx-

Question Number 12401 by sin (x) last updated on 21/Apr/17 $$\int_{\mathrm{0}} ^{\mathrm{2}\pi} {sgn}\left({cosx}\right){dx}=? \\ $$ Commented by FilupS last updated on 21/Apr/17 $${n}\in\mathbb{Z} \\ $$$$\mathrm{for}\:\mathrm{cos}\left({x}\right)>\mathrm{0},\:\:\:\frac{\pi}{\mathrm{2}}\left(\mathrm{4}{n}−\mathrm{1}\right)<{x}<\frac{\pi}{\mathrm{2}}\left(\mathrm{4}{n}+\mathrm{1}\right)…

12sgn-x-2-x-20-3-0-ss-

Question Number 12402 by sin (x) last updated on 21/Apr/17 $$\mathrm{12}{sgn}\left({x}^{\mathrm{2}} −{x}−\mathrm{20}\right)+\mathrm{3}\geqslant\mathrm{0}\Rightarrow \\ $$$$\left({ss}\right)=? \\ $$ Commented by FilupS last updated on 21/Apr/17 $$\mathrm{sgn}\left({x}\right)=\begin{cases}{\mathrm{1}\:\:\:\mathrm{if}\:\:{x}>\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\mathrm{if}\:\:{x}=\mathrm{0}}\\{−\mathrm{1}\:\:\:\mathrm{if}\:\:{x}<\mathrm{0}}\end{cases} \\…

Question-77902

Question Number 77902 by TawaTawa last updated on 12/Jan/20 Commented by mr W last updated on 12/Jan/20 $${try}\:{to}\:{solve}\:{by}\:{yourself}.\:{i}\:{think}\:{you} \\ $$$${can}\:{solve}. \\ $$$${but}\:{the}\:{question}\:{is}\:{not}\:{a}\:{good}\:{one}.\:{it}\:{says} \\ $$$${only}\:\alpha,\beta,\gamma>\mathrm{0}.\:{but}\:\alpha+\beta−\gamma\:{could}\:{be}\:>\mathrm{0}, \\…

Question-12368

Question Number 12368 by sin (x) last updated on 20/Apr/17 Answered by mrW1 last updated on 22/Apr/17 $${EF}×\mathrm{cot}\:\mathrm{55}+{EF}×\mathrm{cot}\:\mathrm{35}+\mathrm{4}=\mathrm{10} \\ $$$${EF}×\mathrm{tan}\:\:\mathrm{35}+{EF}×\mathrm{tan}\:\:\mathrm{55}=\mathrm{6} \\ $$$${EF}=\frac{\mathrm{6}}{\mathrm{tan}\:\mathrm{35}+\mathrm{tan}\:\mathrm{55}}=\mathrm{2}.\mathrm{819}\approx\mathrm{3} \\ $$$$\Rightarrow{Answer}\:\boldsymbol{{A}} \\…