Question and Answers Forum

AllQuestion and Answers: Page 1249

Question Number 89461 Answers: 2 Comments: 0

Question Number 89456 Answers: 1 Comments: 0

(log_x (6))^2 + (log_(1/6) ((1/x)))^2 + log_(1/(√x)) ((1/6)) + log_(√6) (x) + (3/4) = 0

$$\left(\mathrm{log}_{{x}} \left(\mathrm{6}\right)\right)^{\mathrm{2}} \:+\:\left(\mathrm{log}_{\frac{\mathrm{1}}{\mathrm{6}}} \left(\frac{\mathrm{1}}{{x}}\right)\right)^{\mathrm{2}} +\: \\ $$$$\mathrm{log}_{\frac{\mathrm{1}}{\sqrt{{x}}}} \left(\frac{\mathrm{1}}{\mathrm{6}}\right)\:+\:\mathrm{log}_{\sqrt{\mathrm{6}}} \:\left({x}\right)\:+\:\frac{\mathrm{3}}{\mathrm{4}}\:=\:\mathrm{0} \\ $$

Question Number 89454 Answers: 0 Comments: 1

Question Number 89451 Answers: 1 Comments: 0

log_5 ((3−x)(x^2 +2)) ≥ log_5 (x^2 −7x+12)+log_5 (5−x)

$$\mathrm{log}_{\mathrm{5}} \:\left(\left(\mathrm{3}−{x}\right)\left({x}^{\mathrm{2}} +\mathrm{2}\right)\right)\:\geqslant\:\mathrm{log}_{\mathrm{5}} \left({x}^{\mathrm{2}} −\mathrm{7}{x}+\mathrm{12}\right)+\mathrm{log}_{\mathrm{5}} \left(\mathrm{5}−{x}\right) \\ $$

Question Number 89446 Answers: 0 Comments: 1

$$.. \\ $$

Question Number 89592 Answers: 1 Comments: 2

cos(x)=k {−1≤k<0}

$${cos}\left({x}\right)={k}\: \\ $$$$\left\{−\mathrm{1}\leqslant{k}<\mathrm{0}\right\} \\ $$

Question Number 89596 Answers: 0 Comments: 1

Question Number 89593 Answers: 0 Comments: 5

show that ∫_0 ^(π/2) ln(sec(x)) ln(csc(x)) dx=((π^2 ln^2 (2))/2)−(π^4 /(48))

$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({sec}\left({x}\right)\right)\:{ln}\left({csc}\left({x}\right)\right)\:{dx}=\frac{\pi^{\mathrm{2}} \:{ln}^{\mathrm{2}} \left(\mathrm{2}\right)}{\mathrm{2}}−\frac{\pi^{\mathrm{4}} }{\mathrm{48}} \\ $$

Question Number 89425 Answers: 0 Comments: 0

∫_1 ^4 (√(1+((y^3 /2)−(1/2)y^(−1) )^2 )) dy

$$\int_{\mathrm{1}} ^{\mathrm{4}} \sqrt{\mathrm{1}+\left(\frac{{y}^{\mathrm{3}} }{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}{y}^{−\mathrm{1}} \right)^{\mathrm{2}} }\:{dy} \\ $$$$ \\ $$

Question Number 89422 Answers: 1 Comments: 1

Question Number 89415 Answers: 1 Comments: 4

Question Number 89412 Answers: 0 Comments: 8

Question Number 89399 Answers: 0 Comments: 11

Hi. A ballot box contains 3 red balls, 4 blues balls and 5 white balls. we draw successively 3 balls in ballot box by re−puting the drawn balls. 1)Calculate the number of draws containing one ball of each color.

$$\mathrm{Hi}. \\ $$$$\mathrm{A}\:\mathrm{ballot}\:\mathrm{box}\:\mathrm{contains}\:\mathrm{3}\:\mathrm{red}\:\mathrm{balls},\:\mathrm{4}\:\mathrm{blues} \\ $$$$\mathrm{balls}\:\mathrm{and}\:\mathrm{5}\:\mathrm{white}\:\mathrm{balls}. \\ $$$$\mathrm{we}\:\mathrm{draw}\:\mathrm{successively}\:\mathrm{3}\:\mathrm{balls}\:\mathrm{in}\:\mathrm{ballot}\:\mathrm{box}\: \\ $$$$\mathrm{by}\:\mathrm{re}−\mathrm{puting}\:\mathrm{the}\:\mathrm{drawn}\:\mathrm{balls}. \\ $$$$\left.\mathrm{1}\right)\mathrm{Calculate}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{draws}\: \\ $$$$\mathrm{containing}\:\mathrm{one}\:\mathrm{ball}\:\mathrm{of}\:\mathrm{each}\:\mathrm{color}. \\ $$

Question Number 89385 Answers: 1 Comments: 1

Question Number 89384 Answers: 0 Comments: 3

Question Number 141569 Answers: 0 Comments: 0

lim_(n→+∝) (((110^2 )/((11−10)(11^2 −10^2 ))) + ((110^2 )/((11^2 −10^2 )(11^3 −10^3 ))) + ....+ ((110^2 )/((11^n −10^n )(11^(n+1) −10^(n+1) ))))

$$\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\left(\frac{\mathrm{110}^{\mathrm{2}} }{\left(\mathrm{11}−\mathrm{10}\right)\left(\mathrm{11}^{\mathrm{2}} −\mathrm{10}^{\mathrm{2}} \right)}\:+\:\frac{\mathrm{110}^{\mathrm{2}} }{\left(\mathrm{11}^{\mathrm{2}} −\mathrm{10}^{\mathrm{2}} \right)\left(\mathrm{11}^{\mathrm{3}} −\mathrm{10}^{\mathrm{3}} \right)}\:+\:....+\:\frac{\mathrm{110}^{\mathrm{2}} }{\left(\mathrm{11}^{\mathrm{n}} −\mathrm{10}^{\mathrm{n}} \right)\left(\mathrm{11}^{\mathrm{n}+\mathrm{1}} −\mathrm{10}^{\mathrm{n}+\mathrm{1}} \right)}\right) \\ $$

Question Number 89382 Answers: 1 Comments: 2

∫_0 ^∞ e^(−2x) cos(3x) sin(4x)

$$\int_{\mathrm{0}} ^{\infty} {e}^{−\mathrm{2}{x}} \:{cos}\left(\mathrm{3}{x}\right)\:{sin}\left(\mathrm{4}{x}\right) \\ $$

Question Number 89361 Answers: 1 Comments: 0

Question Number 89351 Answers: 0 Comments: 4

prove tan 3^o ×tan 39^o ×tan 89^o = tan 15^o

$${prove}\:\mathrm{tan}\:\mathrm{3}^{{o}} ×\mathrm{tan}\:\mathrm{39}^{{o}} ×\mathrm{tan}\:\mathrm{89}^{{o}} \:=\:\mathrm{tan}\:\mathrm{15}^{{o}} \\ $$

Question Number 89511 Answers: 1 Comments: 6

∫_0 ^(3π) (√(1+sin^4 (θ/3) cos^2 (θ/3))) dθ

$$\int_{\mathrm{0}} ^{\mathrm{3}\pi} \sqrt{\mathrm{1}+{sin}^{\mathrm{4}} \frac{\theta}{\mathrm{3}}\:{cos}^{\mathrm{2}} \frac{\theta}{\mathrm{3}}}\:{d}\theta \\ $$

Question Number 89510 Answers: 0 Comments: 3

Find the expansion of Xe^(1/x)

$${Find}\:{the}\:{expansion}\:{of}\:{Xe}^{\frac{\mathrm{1}}{{x}}} \: \\ $$

Question Number 89344 Answers: 0 Comments: 6

(2x−1)^2 +8(√(2xy)) = 4 4y−(√(8xy−1)) = 1

$$\left(\mathrm{2}{x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{8}\sqrt{\mathrm{2}{xy}}\:=\:\mathrm{4} \\ $$$$\mathrm{4}{y}−\sqrt{\mathrm{8}{xy}−\mathrm{1}}\:=\:\mathrm{1} \\ $$

Question Number 89343 Answers: 0 Comments: 2

Given α and β ∈N such that I(α,β)=∫_ ^1 t^α (1−t)^β dt show that I(α;β)=((α!β!)/((α+β+1)!))

$${Given}\:\alpha\:{and}\:\beta\:\in\mathbb{N}\:{such}\:{that} \\ $$$${I}\left(\alpha,\beta\right)=\int_{} ^{\mathrm{1}} {t}^{\alpha} \left(\mathrm{1}−{t}\right)^{\beta} {dt} \\ $$$${show}\:{that} \\ $$$${I}\left(\alpha;\beta\right)=\frac{\alpha!\beta!}{\left(\alpha+\beta+\mathrm{1}\right)!} \\ $$

Question Number 89341 Answers: 0 Comments: 3

lim_(n→∞) ((Π_(k=1) ^(n−1) sin(((kπ)/(2n)))))^(1/n) =?

$$\underset{{n}\rightarrow\infty} {{lim}}\sqrt[{{n}}]{\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\prod}}{sin}\left(\frac{{k}\pi}{\mathrm{2}{n}}\right)}=? \\ $$

Question Number 89327 Answers: 1 Comments: 2

Question Number 89324 Answers: 0 Comments: 1

Pg 1244 Pg 1245 Pg 1246 Pg 1247 Pg 1248 Pg 1249 Pg 1250 Pg 1251 Pg 1252 Pg 1253

Contact: info@tinkutara.com