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Question Number 72389 Answers: 1 Comments: 0

find Σ_(k=1) ^n k(C_n ^k )^2 interms of n

$${find}\:\sum_{{k}=\mathrm{1}} ^{{n}} {k}\left({C}_{{n}} ^{{k}} \right)^{\mathrm{2}} \:{interms}\:{of}\:{n} \\ $$

Question Number 72161 Answers: 1 Comments: 4

Question Number 72178 Answers: 0 Comments: 3

Question Number 72153 Answers: 1 Comments: 3

∫((sin^3 x)/(√(cos x)))dx ∫sin(lnx)dx

$$\int\frac{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}}{\sqrt{\mathrm{cos}\:\mathrm{x}}}\mathrm{dx} \\ $$$$\int\mathrm{sin}\left(\mathrm{lnx}\right)\mathrm{dx} \\ $$

Question Number 72150 Answers: 0 Comments: 1

Question Number 72148 Answers: 0 Comments: 1

Question Number 72145 Answers: 0 Comments: 4

prove that: cos α×cos 2α×cos 2^2 α...cos 2^n α =((sin 2^(n+1) α)/(2^(n+1) sin α))

$${prove}\:{that}: \\ $$$$\mathrm{cos}\:\alpha×\mathrm{cos}\:\mathrm{2}\alpha×{cos}\:\mathrm{2}^{\mathrm{2}} \alpha...{cos}\:\mathrm{2}^{{n}} \alpha \\ $$$$=\frac{\mathrm{sin}\:\mathrm{2}^{{n}+\mathrm{1}} \alpha}{\mathrm{2}^{{n}+\mathrm{1}} \mathrm{sin}\:\alpha} \\ $$$$ \\ $$

Question Number 72124 Answers: 0 Comments: 0

Question Number 72118 Answers: 0 Comments: 1

Question Number 72117 Answers: 0 Comments: 1

Please help with the proof of cauchy inequality.

$${Please}\:{help}\:{with}\:{the}\:{proof}\:{of}\:{cauchy}\:{inequality}. \\ $$

Question Number 72122 Answers: 0 Comments: 0

If p is the probability that a man x will die in a year, then the probability that out of n men A_1 , A_2 , ..., A_n each aged x, A_1 will die in a year and be first to die, is

$$\mathrm{If}\:\:{p}\:\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{a}\:\mathrm{man}\:{x}\:\mathrm{will} \\ $$$$\mathrm{die}\:\mathrm{in}\:\mathrm{a}\:\mathrm{year},\:\mathrm{then}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{out}\:\mathrm{of}\:{n}\:\mathrm{men}\:{A}_{\mathrm{1}} ,\:{A}_{\mathrm{2}} ,\:...,\:{A}_{{n}} \:\:\mathrm{each}\:\mathrm{aged}\:{x}, \\ $$$${A}_{\mathrm{1}} \:\mathrm{will}\:\mathrm{die}\:\mathrm{in}\:\mathrm{a}\:\mathrm{year}\:\mathrm{and}\:\mathrm{be}\:\mathrm{first}\:\mathrm{to}\:\mathrm{die}, \\ $$$$\mathrm{is} \\ $$

Question Number 72112 Answers: 1 Comments: 0

Question Number 72111 Answers: 0 Comments: 1

Question Number 72108 Answers: 1 Comments: 0

Question Number 72175 Answers: 1 Comments: 3

(x^2 +y^2 −1)^3 =x^2 y^3 how large (area) is your heart ♥ ?

$$\left(\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{3}} =\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{y}}^{\mathrm{3}} \\ $$$$ \\ $$$${how}\:{large}\:\left({area}\right)\:{is}\:{your}\:{heart}\:\heartsuit\:? \\ $$

Question Number 72093 Answers: 1 Comments: 2

a, b, c, d, e, f, g, h, i, j are different nonnegative integers . Find all numbers that satisfy a × bc × def = ghij

$${a},\:{b},\:{c},\:{d},\:{e},\:{f},\:{g},\:{h},\:{i},\:{j}\:\:\:{are}\:\:\:{different}\:\:{nonnegative}\:\:{integers}\:. \\ $$$${Find}\:\:{all}\:\:{numbers}\:\:{that}\:\:{satisfy} \\ $$$$\:\:\:\:\:{a}\:×\:{bc}\:×\:{def}\:\:=\:\:{ghij} \\ $$

Question Number 72086 Answers: 0 Comments: 0

(sin^(−1) (x))^v +(cos^(−1) (x)^v ) for any value v what is it in terms of pi

$$\left(\mathrm{sin}^{−\mathrm{1}} \left({x}\right)\right)^{{v}} +\left(\mathrm{cos}^{−\mathrm{1}} \left({x}\right)^{{v}} \right) \\ $$$${for}\:{any}\:{value}\:{v}\:{what}\:{is}\:{it}\: \\ $$$${in}\:{terms}\:{of}\:{pi} \\ $$$$ \\ $$

Question Number 72071 Answers: 2 Comments: 1

a) lim_(x→0) ((3x−sin(2x))/(2x−sin(3x)))

$$\left.{a}\right)\underset{{x}\rightarrow\mathrm{0}} {\:{lim}}\frac{\mathrm{3}{x}−{sin}\left(\mathrm{2}{x}\right)}{\mathrm{2}{x}−{sin}\left(\mathrm{3}{x}\right)} \\ $$$$ \\ $$$$ \\ $$

Question Number 72060 Answers: 0 Comments: 2

∫((sin x)/(1+sin x+sin 2x))dx=?

$$\int\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{sin}\:{x}+\mathrm{sin}\:\mathrm{2}{x}}{dx}=? \\ $$

Question Number 72048 Answers: 1 Comments: 0

Question Number 72047 Answers: 0 Comments: 1

Question Number 72046 Answers: 0 Comments: 2

Question Number 72044 Answers: 1 Comments: 3

y=ln(3x^2 +x) solve y^((6)) (x)

$$\mathrm{y}=\mathrm{ln}\left(\mathrm{3x}^{\mathrm{2}} +\mathrm{x}\right)\:\:\:\mathrm{solve}\:\mathrm{y}^{\left(\mathrm{6}\right)} \left(\mathrm{x}\right) \\ $$

Question Number 72036 Answers: 2 Comments: 3

Question Number 72027 Answers: 1 Comments: 1

if a+b+c =3 and a^3 +b^3 +c^3 =27 find a^2 +b^2 +c^2

$${if}\:{a}+{b}+{c}\:=\mathrm{3}\:\:{and}\:{a}^{\mathrm{3}} \:+{b}^{\mathrm{3}} \:+{c}^{\mathrm{3}} =\mathrm{27}\:{find}\:{a}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \:+{c}^{\mathrm{2}} \\ $$

Question Number 72026 Answers: 1 Comments: 1

prove that x^4 divide (1+x^2 )^n −nx^2 −1 without use binomial formula.

$${prove}\:{that}\:{x}^{\mathrm{4}} \:{divide}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} −{nx}^{\mathrm{2}} −\mathrm{1}\:\:{without}\:{use}\:\:{binomial} \\ $$$${formula}. \\ $$

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