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For-all-positive-integer-n-f-n-is-defined-as-the-remainder-when-n-is-divided-by-k-where-k-is-an-integer-greater-than-1-f-k-25-3-Quantity-A-k-Quantity-B-5-

Question Number 177621 by aurpeyz last updated on 07/Oct/22 $$\mathrm{For}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{n}.\:\mathrm{f}\left(\mathrm{n}\right)\:\mathrm{is}\:\mathrm{defined} \\ $$$$\mathrm{as}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\mathrm{n}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{k} \\ $$$$\mathrm{where}\:\mathrm{k}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{1}.\: \\ $$$$\mathrm{f}\left(\mathrm{k}+\mathrm{25}\right)=\mathrm{3} \\ $$$$\mathrm{Quantity}\:\mathrm{A}:\:\mathrm{k} \\ $$$$\mathrm{Quantity}\:\mathrm{B}:\:\mathrm{5} \\ $$ Commented by aurpeyz…

Let-r-be-a-positive-integer-List-S-consists-of-integers-from-r-to-r-where-each-integers-occurs-once-List-T-consists-of-the-integers-from-r-to-r-where-each-of-the-two-integers-r-and-r-occurs-twic

Question Number 177619 by aurpeyz last updated on 07/Oct/22 $${Let}\:{r}\:{be}\:{a}\:{positive}\:{integer}.\:{List}\:{S}\:{consists} \\ $$$${of}\:{integers}\:{from}\:−{r}\:{to}\:\:{r}\:{where}\:{each}\:{integers} \\ $$$${occurs}\:{once}.\:{List}\:{T}\:{consists}\:{of}\:{the}\:{integers}\:{from} \\ $$$$−{r}\:{to}\:{r}\:{where}\:{each}\:{of}\:{the}\:{two}\:{integers} \\ $$$$−{r}\:{and}\:{r}\:{occurs}\:{twice}\:{and}\:{each}\:{of}\:{the}\: \\ $$$${other}\:{integers}\:{occur}\:{once}. \\ $$$${Quantity}\:{A}:\:{the}\:{standard}\:{deviation}\:{of}\:{the} \\ $$$${integers}\:{in}\:{S} \\…

Question-112050

Question Number 112050 by naka3546 last updated on 05/Sep/20 Answered by ajfour last updated on 05/Sep/20 $$\frac{{x}}{{y}}={t} \\ $$$$\frac{{t}^{\mathrm{2}} −\mathrm{7}{t}−\mathrm{9}}{{t}^{\mathrm{2}} +\mathrm{5}{t}+\mathrm{11}}=\frac{\mathrm{9}}{\mathrm{5}} \\ $$$${t}^{\mathrm{2}} +\mathrm{20}{t}+\mathrm{36}=\mathrm{0} \\…

Question-177540

Question Number 177540 by yaslm last updated on 06/Oct/22 Answered by aleks041103 last updated on 07/Oct/22 $${its}\:{either}\:{circle}\:{inscribed}\:{in}\:{an}\:{ellipse}\:{or} \\ $$$${the}\:{other}\:{way}\:{around}. \\ $$$$\Rightarrow{Ans}.\:=\:\mid\pi{ab}−\pi{a}^{\mathrm{2}} \mid \\ $$$$\Rightarrow{Ans}.\:=\:\pi{a}\mid{b}−{a}\mid \\…