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Coordinate GeometryQuestion and Answers: Page 1

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The foot of the perpendicular from a point of the circle x^2 +y^2 =1,z=0 to the plan 2x+3y+z=6 lie on curve−−−−−−

$${The}\:{foot}\:{of}\:{the}\:{perpendicular}\:{from}\: \\ $$$${a}\:{point}\:{of}\:{the}\:{circle}\:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1},{z}=\mathrm{0} \\ $$$${to}\:{the}\:{plan}\:\mathrm{2}{x}+\mathrm{3}{y}+{z}=\mathrm{6}\:{lie}\:{on}\:{curve}−−−−−− \\ $$

Question Number 221288    Answers: 1   Comments: 0

Question Number 221271    Answers: 1   Comments: 0

Find the remainder when x^(100) is divided by (x^2 +x+1)

$$\:\:{Find}\:{the}\:{remainder}\:{when}\:{x}^{\mathrm{100}} \: \\ $$$$\:\:{is}\:{divided}\:{by}\:\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right) \\ $$

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Question Number 220257    Answers: 2   Comments: 0

proof that volume of frustum of circular cone is (1/3)h[A1+A2+(√(A1A2)) A_1 and A_2 are areas of base

$${proof}\:{that}\:{volume}\:{of}\:{frustum}\:{of} \\ $$$$\:{circular}\:{cone}\:{is}\:\frac{\mathrm{1}}{\mathrm{3}}{h}\left[{A}\mathrm{1}+{A}\mathrm{2}+\sqrt{{A}\mathrm{1}{A}\mathrm{2}}\right. \\ $$$${A}_{\mathrm{1}} {and}\:{A}_{\mathrm{2}} \:{are}\:\:{areas}\:{of}\:{base} \\ $$

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Question Number 219461    Answers: 1   Comments: 0

I_n = ∫_0 ^( 1) (x/((x + 1)^n ))dx find I_0 and I_1 express I_n interms of n for all n ≥ 2

$${I}_{{n}} \:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{x}}{\left({x}\:+\:\mathrm{1}\right)^{{n}} }{dx} \\ $$$${find}\:{I}_{\mathrm{0}} \:{and}\:{I}_{\mathrm{1}} \\ $$$${express}\:{I}_{{n}} \:{interms}\:{of}\:{n}\:{for}\:{all}\:{n}\:\geqslant\:\mathrm{2} \\ $$

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