Question Number 124109 by mathocean1 last updated on 30/Nov/20 $$ \\ $$$$ \\ $$$${N}={x}\mathrm{32}{y}\:{in}\:{base}\:\mathrm{5}. \\ $$$${determinate}\:{x}\:{and}\:{y}\:{such}\:{that}\:{N}\:{is} \\ $$$${divisible}\:{by}\:\mathrm{3}\:{and}\:\mathrm{4}. \\ $$ Answered by floor(10²Eta[1]) last updated…
Question Number 124108 by mathocean1 last updated on 30/Nov/20 $${N}={x}\mathrm{43}{y}\:{in}\:{base}\:\mathrm{7}. \\ $$$${determinate}\:{x}\:{and}\:{y}\:{such}\:{that}\:{N}\:{is} \\ $$$${divisible}\:{by}\:\mathrm{6}. \\ $$$$ \\ $$ Answered by floor(10²Eta[1]) last updated on 01/Dec/20…
Question Number 124107 by mathocean1 last updated on 30/Nov/20 $${n}\:\in\:\mathbb{N}\:{and}\:{p}\:{is}\:{a}\:{prime}\:{number}\:\left({p}\geqslant\mathrm{3}\right). \\ $$$${a}\:{and}\:{b}\:{are}\:{defined}\:{by}:\:{a}=\mathrm{2}^{{n}} \:{and} \\ $$$${b}={a}×{b}.\:\:{S}\left({a}\right)\:{is}\:{the}\:{sum}\:{of}\:{divisors}\: \\ $$$${of}\:{a}\:{and}\:{S}\left({b}\right)\:\:{is}\:{the}\:{sum}\:{of}\:{divisors} \\ $$$${of}\:{b}. \\ $$$$\mathrm{1}.{Determinate}\:{the}\:{set}\:{of}\:{divisors}\:{of} \\ $$$${a}\:{and}\:{the}\:{set}\:{of}\:{divisors}\:{of}\:{b}. \\ $$$$\mathrm{2}.{show}\:{that}\:{S}\left({a}\right)+\mathrm{2}^{{n}+\mathrm{1}}…
Question Number 124106 by mathocean1 last updated on 30/Nov/20 $${U}_{{n}\:} {is}\:{a}\:{sequence}\:{of}\:{real}\:{numbers}\: \\ $$$${defined}\:{by}\:{U}_{\mathrm{0}} =\mathrm{0}\:{and}\:{for}\:{n}\:\in\:\mathbb{N},\: \\ $$$${U}_{{n}+\mathrm{1}} =\sqrt{{U}_{{n}} +\mathrm{6}} \\ $$$$\mathrm{1}.\:\mathrm{show}\:\mathrm{that}\:\mathrm{0}\leqslant{U}_{{n}} \leqslant\mathrm{3}. \\ $$$$\mathrm{2}.\:{show}\:{that}\:{U}_{{n}\:} {is}\:{non}−{decreasing}. \\…
Question Number 58568 by olalekan2 last updated on 25/Apr/19 $${factorize} \\ $$$${px}^{\mathrm{2}} −{py}^{\mathrm{2}} +{qy}^{\mathrm{2}} −{px}^{\mathrm{2}} \\ $$ Commented by malwaan last updated on 26/Apr/19 $${I}\:{think}\:{the}\:{last}\:{term}\:{is}\:{qx}^{\mathrm{2}}…
Question Number 189610 by Spillover last updated on 19/Mar/23 $${solve}\:{for}\:{x}\:{if}\:\:\: \\ $$$$\mathrm{log}\:{x}=\frac{{x}^{\mathrm{2}} }{\mathrm{25}} \\ $$ Answered by mr W last updated on 19/Mar/23 $$\mathrm{ln}\:{x}=\frac{{x}^{\mathrm{2}} }{\mathrm{25}}=\frac{{e}^{\mathrm{2ln}\:{x}}…
Question Number 58529 by Tawa1 last updated on 24/Apr/19 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{y}}\:=\:\mathrm{4}\:\:\:\:\:\:\:…….\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{y}}\:+\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{x}}\:\:=\:\:\mathrm{9}\:\:\:\:\:\:…….\:\left(\mathrm{ii}\right) \\ $$ Commented by MJS last updated on 24/Apr/19…
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