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M-is-the-midpoint-of-segment-AB-Prove-that-for-every-point-P-in-space-PM-PA-PB-2-

Question Number 64203 by Prithwish sen last updated on 15/Jul/19 $$\mathrm{M}\:\mathrm{is}\:\mathrm{the}\:\mathrm{midpoint}\:\mathrm{of}\:\mathrm{segment}\:\mathrm{AB}.\:\mathrm{Prove} \\ $$$$\mathrm{that},\mathrm{for}\:\mathrm{every}\:\mathrm{point}\:\mathrm{P}\:\mathrm{in}\:\mathrm{space}, \\ $$$$\mid\mathrm{PM}\mid\:\leqslant\:\frac{\mid\mathrm{PA}\mid\:+\mid\mathrm{PB}\mid}{\mathrm{2}} \\ $$ Commented by Prithwish sen last updated on 16/Jul/19…

Find-all-positive-solutions-x-y-z-1-x-3-y-3-z-3-xyz-x-4-y-4-z-4-1-

Question Number 64201 by Prithwish sen last updated on 15/Jul/19 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{solutions}\: \\ $$$$\mathrm{x}+\mathrm{y}+\mathrm{z}\:=\:\mathrm{1} \\ $$$$\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} +\:\mathrm{z}^{\mathrm{3}} \:+\:\mathrm{xyz}\:=\:\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \:+\:\mathrm{z}^{\mathrm{4}} \:+\mathrm{1} \\ $$ Answered by…

find-dy-dx-if-x-2-y-2-4-

Question Number 129727 by abdurehime last updated on 18/Jan/21 $$\mathrm{find}\:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\mathrm{if}\:\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{4} \\ $$ Answered by Ar Brandon last updated on 18/Jan/21 $$\mathrm{y}=\pm\sqrt{\mathrm{4}−\mathrm{x}^{\mathrm{2}} } \\…

I-0-pi-2-2304cosx-cos4x-8cos2x-15-2-dx-

Question Number 129710 by SOMEDAVONG last updated on 18/Jan/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{2304cosx}}{\left(\mathrm{cos4x}−\mathrm{8cos2x}+\mathrm{15}\right)^{\mathrm{2}} }\mathrm{dx}\: \\ $$ Answered by MJS_new last updated on 18/Jan/21 $$\mathrm{2304}\int\frac{\mathrm{cos}\:{x}}{\left(\mathrm{cos}\:\mathrm{4}{x}\:−\mathrm{8cos}\:\mathrm{2}{x}\:+\mathrm{15}\right)^{\mathrm{2}} }{dx}= \\…

m-3-4m-

Question Number 64175 by harish kumar last updated on 15/Jul/19 $${m}^{\mathrm{3}} \:−\mathrm{4}{m}\: \\ $$ Commented by Prithwish sen last updated on 15/Jul/19 $$\mathrm{m}\left(\mathrm{m}^{\mathrm{2}} −\mathrm{4}\right)\:=\:\mathrm{m}\left(\mathrm{m}−\mathrm{2}\right)\left(\mathrm{m}+\mathrm{2}\right) \\…

show-that-C-n-k-C-n-1-k-1-C-n-2-k-1-C-k-k-1-C-k-1-k-1-

Question Number 129642 by SOMEDAVONG last updated on 17/Jan/21 $$\mathrm{show}\:\mathrm{that}\:\mathrm{C}_{\mathrm{n}} ^{\mathrm{k}} =\mathrm{C}_{\mathrm{n}−\mathrm{1}} ^{\mathrm{k}−\mathrm{1}} +\mathrm{C}_{\mathrm{n}−\mathrm{2}} ^{\mathrm{k}−\mathrm{1}} +….+\mathrm{C}_{\mathrm{k}} ^{\mathrm{k}−\mathrm{1}} +\mathrm{C}_{\mathrm{k}−\mathrm{1}} ^{\mathrm{k}−\mathrm{1}} . \\ $$ Terms of Service…