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Question-159345

Question Number 159345 by akolade last updated on 15/Nov/21 Answered by Ar Brandon last updated on 15/Nov/21 $$\mathrm{5}^{\frac{\mathrm{y}}{\mathrm{2}}+\mathrm{3}} =\mathrm{125}\left(\mathrm{5}^{\frac{\mathrm{y}}{\mathrm{2}}} \right)=\mathrm{125}\left(\mathrm{5}^{\mathrm{y}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$$=\mathrm{125}\left(\mathrm{36}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} =\mathrm{125}×\mathrm{6}=\mathrm{750} \\…

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Question Number 159330 by bounhome last updated on 15/Nov/21 $${how}\:{to}\:{think}\:{from}\: \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{3}+…+{n}=\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}} \\ $$$$\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +…+{n}^{\mathrm{2}} =\frac{{n}\left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}{\mathrm{6}} \\ $$$$\mathrm{1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} +\mathrm{3}^{\mathrm{3}} +…+{n}^{\mathrm{3}} =\left(\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}}\right)^{\mathrm{2}} \\…

Question-159327

Question Number 159327 by SANOGO last updated on 15/Nov/21 Answered by Derrick last updated on 16/Nov/21 $$\left.\mathrm{1}\right){montrons}\:{que}\:{f}\:{est}\:{lineaire} \\ $$$${soient}\:{X}=\left({x}.{y}.{z}\right)\:{et}\:{Y}=\left({x}'.{y}'.{z}'\right) \\ $$$${on}\:{a}: \\ $$$${f}\left({X}+{Y}\right)=\left[\left({x}+{x}'\right)+\mathrm{2}\left({y}+{y}'\right)+\mathrm{3}\left({z}+{z}'\right);\mathrm{2}\left({x}+{x}'\right)+\left({y}+{y}'\right)+\mathrm{3}\left({z}+{z}'\right);−\left({x}+{x}'\right)−\left({y}+{y}'\right)−\left({z}+{z}'\right)\right] \\ $$$$=\left[{x}+\mathrm{2}{y}+\mathrm{3}{z};\mathrm{2}{x}+{y}+\mathrm{3}{z};−{x}−{y}−{z}\right]+\left[{x}'+\mathrm{2}{y}'+\mathrm{3}{z}';\mathrm{2}{x}'+{y}'+\mathrm{3}{z}';−{x}'−{y}'−{z}'\right]…

Question-28248

Question Number 28248 by mondodotto@gmail.com last updated on 22/Jan/18 Answered by mrW2 last updated on 22/Jan/18 $$\mathrm{3}×\frac{{n}\left({n}−\mathrm{1}\right)\left({n}−\mathrm{2}\right)}{\mathrm{6}}=\mathrm{7}×\frac{{n}\left({n}−\mathrm{1}\right)}{\mathrm{2}} \\ $$$${n}−\mathrm{2}=\mathrm{7} \\ $$$$\Rightarrow{n}=\mathrm{9} \\ $$$$ \\ $$$${check}:…

Question-28202

Question Number 28202 by naka3546 last updated on 21/Jan/18 Commented by naka3546 last updated on 21/Jan/18 $${If}\:\:{area}\:{the}\:{smallest}\:{square}\:{is}\:\mathrm{1}\:{cm}^{\mathrm{2}} \:. \\ $$$${find}\:{the}\:{area}\:{of}\:{red}\:{region}\:.\: \\ $$$$ \\ $$ Answered…