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Category: Arithmetic

Question-169538

Question Number 169538 by BRR last updated on 02/May/22 Commented by Tinku Tara last updated on 02/May/22 $$\mathrm{fare}\:\mathrm{increase}\:\mathrm{5}{x} \\ $$$$\mathrm{total}\:\mathrm{earning}\:=\left(\mathrm{400}−\mathrm{10}{x}\right)×\left(\mathrm{50}+\mathrm{5}{x}\right) \\ $$$${f}\left({x}\right)=\mathrm{20000}+\mathrm{1500}{x}−\mathrm{50}{x}^{\mathrm{2}} \\ $$$${f}\:'\left({x}\right)=\mathrm{1500}−\mathrm{100}{x} \\…

220-30-35-

Question Number 169429 by Fridunatjan08 last updated on 30/Apr/22 $$\sqrt{\mathrm{220}+\mathrm{30}\sqrt{\mathrm{35}}}= \\ $$ Answered by cortano1 last updated on 30/Apr/22 $$\sqrt{\mathrm{220}+\mathrm{2}\sqrt{\mathrm{225}×\mathrm{35}}}\:=\sqrt{\left(\mathrm{45}+\mathrm{175}\right)+\mathrm{2}\sqrt{\mathrm{45}×\mathrm{175}}} \\ $$$$=\:\sqrt{\mathrm{45}}\:+\sqrt{\mathrm{175}} \\ $$$$=\mathrm{3}\sqrt{\mathrm{5}}\:+\mathrm{5}\sqrt{\mathrm{7}} \\…

n-1-2n-1-2n-1-4n-2-

Question Number 103881 by bemath last updated on 18/Jul/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\frac{\left(\mathrm{2}{n}−\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}{\mathrm{4}{n}^{\mathrm{2}} }\:? \\ $$ Answered by bramlex last updated on 18/Jul/20 $${use}\:{Euler}\:{infinity}\:{product}\: \\ $$$$\frac{\mathrm{sin}\:{x}}{{x}}\:=\:\underset{{n}=\mathrm{1}}…

3-5-2-3-5-2-

Question Number 38332 by ajfour last updated on 24/Jun/18 $$\:\frac{\mathrm{3}+\sqrt{\mathrm{5}}}{\mathrm{2}}\:−\sqrt{\frac{\mathrm{3}+\sqrt{\mathrm{5}}}{\mathrm{2}}}\:=\:?! \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 24/Jun/18 $${x}=\frac{\mathrm{3}+\sqrt{\mathrm{5}\:}}{\mathrm{2}} \\ $$$$=\frac{\mathrm{6}+\mathrm{2}\sqrt{\mathrm{5}}\:}{\mathrm{4}} \\ $$$$=\left(\frac{\sqrt{\mathrm{5}}\:+\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} =\pm\frac{\sqrt{\mathrm{5}}\:+\mathrm{1}}{\mathrm{2}}…

p-x-x-4-ax-3-bx-2-cx-d-if-p-1-10-p-2-20-and-p-3-30-find-p-12-p-8-10-

Question Number 103832 by bemath last updated on 17/Jul/20 $${p}\left({x}\right)\:=\:{x}^{\mathrm{4}} +{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}\:+{d} \\ $$$${if}\:{p}\left(\mathrm{1}\right)=\mathrm{10},{p}\left(\mathrm{2}\right)=\mathrm{20}\:{and} \\ $$$${p}\left(\mathrm{3}\right)=\mathrm{30}\:.\:{find}\:\frac{{p}\left(\mathrm{12}\right)+{p}\left(−\mathrm{8}\right)}{\mathrm{10}} \\ $$ Answered by floor(10²Eta[1]) last updated on…

the-third-sixth-and-seventh-terms-of-a-geometric-progression-whose-common-ratio-is-neither-0-nor-1-are-in-arithmetic-progression-prove-that-the-sum-of-the-first-three-terms-is-equal-to-fourth-

Question Number 103780 by bobhans last updated on 17/Jul/20 $${the}\:{third},\:{sixth}\:{and}\:{seventh}\:{terms}\:{of}\:{a} \\ $$$${geometric}\:{progression}\:\left({whose}\:{common}\right. \\ $$$$\left.{ratio}\:{is}\:{neither}\:\mathrm{0}\:{nor}\:\mathrm{1}\:\right)\:{are}\:{in} \\ $$$${arithmetic}\:{progression}\:.\:{prove}\:{that}\:{the} \\ $$$${sum}\:{of}\:{the}\:{first}\:{three}\:{terms}\:{is}\:{equal}\:{to} \\ $$$${fourth}\:. \\ $$ Answered by bemath…