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Question-131595

Question Number 131595 by Algoritm last updated on 06/Feb/21 Commented by Algoritm last updated on 06/Feb/21 $$\mathrm{x}_{\mathrm{1}} =\mathrm{37}/\mathrm{2}\:\:\:\mathrm{x}_{\mathrm{2}} =\mathrm{77}/\mathrm{4}\:\:\:\mathrm{x}_{\mathrm{3}} =\mathrm{65}/\mathrm{4} \\ $$$$\Sigma\boldsymbol{\mathrm{x}}=\mathrm{37}/\mathrm{2}+\mathrm{77}/\mathrm{4}+\mathrm{65}/\mathrm{4}=\mathrm{54}\:\: \\ $$$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}! \\…

Find-the-sum-r-0-n-3r-5-n-r-5-n-0-8-n-1-11-n-2-3n-5-n-n-as-a-simple-function-of-n-

Question Number 519 by Yugi last updated on 25/Jan/15 $${Find}\:{the}\:{sum}\:\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\left(\mathrm{3}{r}+\mathrm{5}\right)\begin{pmatrix}{{n}}\\{{r}}\end{pmatrix}=\mathrm{5}\begin{pmatrix}{{n}}\\{\mathrm{0}}\end{pmatrix}\:+\mathrm{8}\begin{pmatrix}{{n}}\\{\mathrm{1}}\end{pmatrix}\:+\mathrm{11}\begin{pmatrix}{{n}}\\{\mathrm{2}}\end{pmatrix}\:+…\left(\mathrm{3}{n}+\mathrm{5}\right)\begin{pmatrix}{{n}}\\{{n}}\end{pmatrix}\: \\ $$$${as}\:{a}\:{simple}\:{function}\:{of}\:{n}. \\ $$ Commented by prakash jain last updated on 22/Jan/15 $$\underset{{r}=\mathrm{0}}…

Question-66055

Question Number 66055 by ajfour last updated on 08/Aug/19 Commented by ajfour last updated on 08/Aug/19 $${Eq}.\:{of}\:{ellipse}\:\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{\left({y}−{b}\right)^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1} \\ $$$${parabola}\:{touches}\:{the}\:{x}-{axis} \\ $$$${and}\:{the}\:{ellipse}\:{and}\:{passes}…

Give-the-result-of-the-following-computation-as-an-integer-in-the-usual-decimal-form-303-000-000-000-303-3-300-000-033-1-000-100-010-001-

Question Number 518 by Yugi last updated on 25/Jan/15 $${Give}\:{the}\:{result}\:{of}\:{the}\:{following}\:{computation}\:{as}\:{an}\:{integer}\:{in}\:{the}\:{usual}\:{decimal} \\ $$$${form}.\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{303},\mathrm{000},\mathrm{000},\mathrm{000},\mathrm{303}×\mathrm{3},\mathrm{300},\mathrm{000},\mathrm{033}}{\mathrm{1},\mathrm{000},\mathrm{100},\mathrm{010},\mathrm{001}} \\ $$ Answered by prakash jain last updated on 22/Jan/15 $$\frac{\mathrm{303}\left(\mathrm{10}^{\mathrm{12}}…

A-person-is-said-to-be-n-years-old-where-n-is-a-non-negative-integer-if-the-person-has-lived-at-least-n-years-and-has-not-lived-n-1-years-At-some-point-Tom-is-4-years-old-and-John-is-three-times-

Question Number 517 by Yugi last updated on 25/Jan/15 $${A}\:{person}\:{is}\:{said}\:{to}\:{be}\:{n}\:{years}\:{old}\:\left(\:{where}\:{n}\:{is}\:{a}\:{non}−{negative}\:{integer}\right)\:{if}\: \\ $$$${the}\:{person}\:{has}\:{lived}\:{at}\:{least}\:{n}\:{years}\:{and}\:{has}\:{not}\:{lived}\:{n}+\mathrm{1}\:{years}.\:{At}\:{some}\:{point} \\ $$$${Tom}\:{is}\:\mathrm{4}\:{years}\:{old}\:{and}\:{John}\:{is}\:{three}\:{times}\:{as}\:{old}\:{as}\:{Mary}.\:{At}\:{another}\:{time}, \\ $$$${Mary}\:{is}\:{twice}\:{as}\:{old}\:{as}\:{Tom}\:{and}\:{John}\:{is}\:{five}\:{times}\:{as}\:{old}\:{as}\:{Tom}.\:{At}\:{a}\:{third}\: \\ $$$${time},\:{John}\:{is}\:{twice}\:{as}\:{old}\:{as}\:{Mary}\:{and}\:{Tom}\:{is}\:{t}\:{years}\:{old}.\:{What}\:{is}\:{the}\:{largest} \\ $$$${possible}\:{value}\:{of}\:{t}? \\ $$ Commented by prakash…