Category: Arithmetic

Question Number 207594 by MATHEMATICSAM last updated on 19/May/24 $$\frac{x\cos \theta }{a}+\frac{y\sin \theta }{b}=1$$$$x\sin \theta -y\cos \theta =\sqrt{a^2{\sin }^2\theta +b^2{\cos }^2\theta }$$$$\mathrm{Eliminate}\theta .$$ Answered by Frix last updated…

Question Number 207416 by efronzo1 last updated on 14/May/24 $$$$ Answered by mr W last updated on 14/May/24 $$\frac{{U}_{\mathrm{2}} }{{q}}+{U}_{\mathrm{2}} +{qU}_{\mathrm{2}} =\mathrm{9}\left(\frac{{q}}{{U}_{\mathrm{2}} }+\frac{\mathrm{1}}{{U}_{\mathrm{2}}…

Question Number 207042 by necx122 last updated on 04/May/24 $$Provethatthesumofasquarefunction$$$$is\frac{n(n+1)(2n+1)}{6}$$ Answered by Rasheed.Sindhi last updated on 04/May/24 $$p\left(n\right):$$$$\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}}…

Question Number 206919 by BaliramKumar last updated on 30/Apr/24 Answered by A5T last updated on 30/Apr/24 $$MA=2x;MC=3x\Rightarrow AC=5x$$$$\Rightarrow AB+BC=4+3x+2x=5x+4$$$${(2+3x)}^2+{(2+2x)}^2=25x^2$$$$\Rightarrow\mathrm{3}{x}^{\mathrm{2}}…

Question Number 206805 by BaliramKumar last updated on 26/Apr/24 Answered by A5T last updated on 26/Apr/24 $${\left(225\right)}^{40}={10}^x\Rightarrow x=40log225\approx 94.087<95$$$$\Rightarrow\mathrm{10}^{\mathrm{94}} <\left(\mathrm{225}\right)^{\mathrm{40}} <\mathrm{10}^{\mathrm{95}} \Rightarrow\mathrm{225}^{\mathrm{40}} \:{has}\:\mathrm{95}\:{digits}…