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Question-10190

Question Number 10190 by ketto last updated on 29/Jan/17 Commented by FilupSmith last updated on 29/Jan/17 $$\angle{ADB}=\mathrm{45}°\:\:\mathrm{and}\:\:\:\angle{BAD}=\mathrm{90}° \\ $$$$\therefore\angle{ABD}=\mathrm{45}° \\ $$$$\therefore\:{AB}={y}={AD} \\ $$$$\mathrm{let}\:{BD}={x} \\ $$$${x}^{\mathrm{2}}…

Question-10188

Question Number 10188 by ridwan balatif last updated on 29/Jan/17 Commented by ridwan balatif last updated on 29/Jan/17 $$\int\sqrt{\mathrm{1}−\mathrm{tan}^{\mathrm{2}} \mathrm{2x}+\mathrm{tan}^{\mathrm{4}} \mathrm{2x}−\mathrm{tan}^{\mathrm{6}} \mathrm{2x}+…}\mathrm{dx}=…? \\ $$$$\mathrm{1}−\mathrm{tan}^{\mathrm{2}} \mathrm{2x}+\mathrm{tan}^{\mathrm{4}}…

Prove-ln-1-1-n-n-1-1-2-n-1-1-2-3-n-1-2-1-3-4-n-1-3-

Question Number 10186 by prakash jain last updated on 29/Jan/17 $$\mathrm{Prove} \\ $$$$\mathrm{ln}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}} =\left[\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}\left({n}+\mathrm{1}\right)}+\frac{\mathrm{1}}{\mathrm{2}\centerdot\mathrm{3}\left({n}+\mathrm{1}\right)^{\mathrm{2}} }−\frac{\mathrm{1}}{\mathrm{3}\centerdot\mathrm{4}\left({n}+\mathrm{1}\right)^{\mathrm{3}} }+..\right] \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

if-a-2i-3j-b-19-15j-and-c-5i-7j-find-the-value-of-x-such-that-xa-yc-b-

Question Number 10184 by ketto last updated on 29/Jan/17 $${if}\:\underset{−} {{a}}\:=\mathrm{2}{i}+\mathrm{3}{j}\:.\:\underset{−} {{b}}=\mathrm{19}−\mathrm{15}{j}\:{and}\: \\ $$$$\underset{−} {{c}}\:=\mathrm{5}{i}−\mathrm{7}{j}.\:{find}\:{the}\:{value}\:{of}\:{x}\:{such} \\ $$$${that}\:{x}\underset{−} {{a}}\:+\:{y}\underset{−} {{c}}\:={b} \\ $$$$ \\ $$ Answered by…

Let-A-be-a-subset-of-0-1-1997-containing-more-than-1000-elements-Prove-that-A-contains-either-a-power-of-2-or-two-distinct-integers-whose-sum-is-a-power-of-2-

Question Number 10181 by 0942679167 last updated on 29/Jan/17 $${Let}\:{A}\:{be}\:{a}\:{subset}\:{of}\:\left\{\mathrm{0};\mathrm{1};\centerdot\centerdot\centerdot;\mathrm{1997}\right\}\: \\ $$$${containing}\:{more}\:{than}\:\mathrm{1000}\:{elements}. \\ $$$${Prove}\:{that}\:{A}\:{contains}\:{either}\:{a}\:{power} \\ $$$${of}\:\mathrm{2}\:{or}\:{two}\:{distinct}\:{integers}\:{whose}\: \\ $$$${sum}\:{is}\:{a}\:{power}\:{of}\:\mathrm{2}. \\ $$ Terms of Service Privacy Policy…