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Question Number 168347 by cortano1 last updated on 08/Apr/22

Commented by mr W last updated on 09/Apr/22

see Q128303  s=(√3)(r_1 +r_2 )+(√(3(r_1 +r_2 )^2 −8r_1 r_2 ))    =(√3)×5+(√(3×5^2 −8×6))=8(√3)  A=(((√3)s^2 )/4)=48(√3)

$${see}\:{Q}\mathrm{128303} \\ $$$${s}=\sqrt{\mathrm{3}}\left({r}_{\mathrm{1}} +{r}_{\mathrm{2}} \right)+\sqrt{\mathrm{3}\left({r}_{\mathrm{1}} +{r}_{\mathrm{2}} \right)^{\mathrm{2}} −\mathrm{8}{r}_{\mathrm{1}} {r}_{\mathrm{2}} } \\ $$$$\:\:=\sqrt{\mathrm{3}}×\mathrm{5}+\sqrt{\mathrm{3}×\mathrm{5}^{\mathrm{2}} −\mathrm{8}×\mathrm{6}}=\mathrm{8}\sqrt{\mathrm{3}} \\ $$$${A}=\frac{\sqrt{\mathrm{3}}{s}^{\mathrm{2}} }{\mathrm{4}}=\mathrm{48}\sqrt{\mathrm{3}} \\ $$

Commented by Tawa11 last updated on 08/Apr/22

Great sir

$$\mathrm{Great}\:\mathrm{sir} \\ $$

Commented by mathman1234 last updated on 09/Apr/22

plz help me and proove if 0<a<b and x>0 that  (2/π)(1−(a/b))≤sup∣((sin(ax))/(ax)) − ((sin(bx))/(bx))∣≤4(1−(a/b))

$$\mathrm{plz}\:\mathrm{help}\:\mathrm{me}\:\mathrm{and}\:\mathrm{proove}\:\mathrm{if}\:\mathrm{0}<\mathrm{a}<\mathrm{b}\:\mathrm{and}\:\mathrm{x}>\mathrm{0}\:\mathrm{that} \\ $$$$\frac{\mathrm{2}}{\pi}\left(\mathrm{1}−\frac{\mathrm{a}}{\mathrm{b}}\right)\leqslant\mathrm{sup}\mid\frac{\mathrm{sin}\left(\mathrm{ax}\right)}{\mathrm{ax}}\:−\:\frac{\mathrm{sin}\left(\mathrm{bx}\right)}{\mathrm{bx}}\mid\leqslant\mathrm{4}\left(\mathrm{1}−\frac{\mathrm{a}}{\mathrm{b}}\right) \\ $$

Commented by mr W last updated on 09/Apr/22

please don′t put your new question in  existing threads of other people′s  questions! please open a new post  for your own question!

$${please}\:{don}'{t}\:{put}\:{your}\:{new}\:{question}\:{in} \\ $$$${existing}\:{threads}\:{of}\:{other}\:{people}'{s} \\ $$$${questions}!\:{please}\:{open}\:{a}\:{new}\:{post} \\ $$$${for}\:{your}\:{own}\:{question}! \\ $$

Answered by infinityaction last updated on 11/Apr/22

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