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Author: Tinku Tara

Question-17884

Question Number 17884 by b.e.h.i.8.3.417@gmail.com last updated on 11/Jul/17 Commented by b.e.h.i.8.3.417@gmail.com last updated on 11/Jul/17 $${diagonals}\:{of}\:{trapezoid}:\:{ABCD},{create} \\ $$$$\mathrm{4}\:{triangles}.{area}\:{of}\:{two}\:{this}\:{triangles} \\ $$$${are}\:{equail}\:{to}:\:{a}^{\mathrm{2}} \:,{and}\:,\:{b}^{\mathrm{2}} . \\ $$$${find}\:{area}\:{of}\:{trapezoid}\:{in}\:{terms}\:{of}:\:{a},{b}.…

Let-complex-number-z-a-cos-2a-sin-i-If-z-2-for-any-R-then-the-range-of-real-number-a-is-

Question Number 148951 by EDWIN88 last updated on 01/Aug/21 $${Let}\:{complex}\:{number}\:{z}=\left({a}+\mathrm{cos}\:\theta\right)+\left(\mathrm{2}{a}−\mathrm{sin}\:\theta\right){i}\:. \\ $$$${If}\:\mid{z}\mid\:\leqslant\mathrm{2}\:{for}\:{any}\:\theta\in{R}\:{then}\:{the} \\ $$$${range}\:{of}\:{real}\:{number}\:{a}\:{is}\:\_\_\_ \\ $$ Answered by iloveisrael last updated on 01/Aug/21 Answered by…

Question-83411

Question Number 83411 by ajfour last updated on 02/Mar/20 Commented by ajfour last updated on 02/Mar/20 $${Given}\:{a}\:{regular}\:{triangular} \\ $$$${pyramid}\:{with}\:{base}\:{sides}\:\boldsymbol{{a}}\:{and} \\ $$$${lateral}\:{edges}\:\boldsymbol{{a}}\sqrt{\mathrm{2}}.\:{A}\:{sphere} \\ $$$${passes}\:{through}\:{A}\:{and}\:{is}\:{tangent} \\ $$$${to}\:{the}\:{lateral}\:{edges}\:{SB}\:{and}\:{SC}…

615-x-2-2-y-x-y-N-x-y-

Question Number 148947 by mathdanisur last updated on 01/Aug/21 $$\mathrm{615}\:+\:{x}^{\mathrm{2}} \:=\:\mathrm{2}^{\boldsymbol{{y}}} \:\:\:;\:\:\:{x};{y}\in\mathbb{N} \\ $$$$\Rightarrow\:{x};{y}\:=\:? \\ $$ Answered by dumitrel last updated on 02/Aug/21 $${if}\:{y}=\mathrm{2}{k}+\mathrm{1}\Rightarrow{u}\left(\mathrm{2}^{{y}} \right)\in\left\{\mathrm{2},\mathrm{8}\right\}\Rightarrow…

Sum-to-n-term-1-1-2-3-1-4-5-6-1-7-8-9-to-n-

Question Number 148946 by Tawa11 last updated on 01/Aug/21 $$\mathrm{Sum}\:\mathrm{to}\:\:\mathrm{n}\:\:\mathrm{term}:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{2}.\mathrm{3}}\:\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}.\mathrm{5}.\mathrm{6}}\:\:\:+\:\:\:\frac{\mathrm{1}}{\mathrm{7}.\mathrm{8}.\mathrm{9}}\:\:+\:\:…\:\:\:\mathrm{to}\:\:\mathrm{n}. \\ $$ Answered by Olaf_Thorendsen last updated on 02/Aug/21 $$\mathrm{S}\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}{n}+\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{2}\right)\left(\mathrm{3}{n}+\mathrm{3}\right)} \\ $$$$\mathrm{S}\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty}…