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AllQuestion and Answers: Page 482

Question Number 171694 Answers: 2 Comments: 0

Question Number 171693 Answers: 2 Comments: 0

Question Number 171688 Answers: 0 Comments: 0

In △ABC AA^′ , BB^′ , CC^′ - cevians AA^′ ∩ BB^′ ∩ CC^′ = {P} Prove that: min([APC^′ ],[BPA^′ ],[CPB^′ ])+min([APB^′ ],[BPC^′ ],[CPA^′ ]) ≤ ((Rr (√3))/2)

$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC} \\ $$$$\mathrm{AA}^{'} \:,\:\mathrm{BB}^{'} \:,\:\mathrm{CC}^{'} \:-\:\mathrm{cevians} \\ $$$$\mathrm{AA}^{'} \:\cap\:\mathrm{BB}^{'} \:\cap\:\mathrm{CC}^{'} \:=\:\left\{\mathrm{P}\right\} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{min}\left(\left[\mathrm{APC}^{'} \right],\left[\mathrm{BPA}^{'} \right],\left[\mathrm{CPB}^{'} \right]\right)+\mathrm{min}\left(\left[\mathrm{APB}^{'} \right],\left[\mathrm{BPC}^{'} \right],\left[\mathrm{CPA}^{'} \right]\right)\:\leqslant\:\frac{\mathrm{Rr}\:\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$

Question Number 171684 Answers: 1 Comments: 0

Question Number 171681 Answers: 1 Comments: 0

Question Number 171677 Answers: 1 Comments: 0

Question Number 171673 Answers: 0 Comments: 0

Question Number 171667 Answers: 1 Comments: 0

Question Number 171666 Answers: 0 Comments: 1

Question Number 171665 Answers: 1 Comments: 0

Ω=∫_0 ^1 Log(((Log^2 (x))/x^(x^5 −x^4 +x^3 −x^2 +x−1) ))dx Anyone?

$$\Omega=\int_{\mathrm{0}} ^{\mathrm{1}} {Log}\left(\frac{{Log}^{\mathrm{2}} \left({x}\right)}{{x}^{{x}^{\mathrm{5}} −{x}^{\mathrm{4}} +{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +{x}−\mathrm{1}} }\right){dx} \\ $$$$ \\ $$$${Anyone}? \\ $$

Question Number 171664 Answers: 1 Comments: 1

Solve ∫(x^2 /(1+x^2 ))tan^(−1) xdx

$${Solve} \\ $$$$\int\frac{{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{2}} }\mathrm{tan}^{−\mathrm{1}} {xdx} \\ $$

Question Number 171649 Answers: 0 Comments: 0

Question Number 171642 Answers: 1 Comments: 5

evaluate ((√(((a−b)^7 + (b−c)^7 + (c−a)^7 )/((a−b)^3 + (b−c)^3 + (c−a)^3 )))/(a^2 +b^2 +c^2 −ab−bc−ca)) = ??

$$\:\:\:\:\:\:\:\:{evaluate}\:\:\: \\ $$$$\:\:\:\:\frac{\sqrt{\frac{\left({a}−{b}\right)^{\mathrm{7}} \:+\:\left({b}−{c}\right)^{\mathrm{7}} \:+\:\left({c}−{a}\right)^{\mathrm{7}} }{\left({a}−{b}\right)^{\mathrm{3}} \:+\:\left({b}−{c}\right)^{\mathrm{3}} \:+\:\left({c}−{a}\right)^{\mathrm{3}} }}}{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} −{ab}−{bc}−{ca}}\:=\:\:?? \\ $$

Question Number 176844 Answers: 0 Comments: 0

If x, y, z are prime digits. What is the remainder of the smallest negative number generated by these digits divided by 11 ?

$$\mathrm{If}\:{x},\:{y},\:{z}\:\mathrm{are}\:\mathrm{prime}\:\mathrm{digits}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{remainder} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{negative}\:\mathrm{number}\:\mathrm{generated} \\ $$$$\mathrm{by}\:\mathrm{these}\:\mathrm{digits}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{11}\:? \\ $$

Question Number 176841 Answers: 0 Comments: 0

If 3 of 10 elective courses are been delivered at the same time. How many possibilities are there to take 5 courses ?

$$\mathrm{If}\:\mathrm{3}\:\mathrm{of}\:\mathrm{10}\:\mathrm{elective}\:\mathrm{courses}\:\mathrm{are}\:\mathrm{been}\:\mathrm{delivered}\: \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{same}\:\mathrm{time}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{possibilities}\: \\ $$$$\mathrm{are}\:\mathrm{there}\:\mathrm{to}\:\mathrm{take}\:\mathrm{5}\:\mathrm{courses}\:? \\ $$

Question Number 171627 Answers: 0 Comments: 5

A mass 10kg is placed at the foot of an inclined plane 13m long, whose upper end is 5m higher than the foot. The mass is connected by a light inextensible string, passing over a smooth pulley at the top of the plane, to another mass 10kg which hangs level with the top of the plane, 5m above the floor. If the coefficient of friction between the first mass and then plane is ½ and the system is released from rest, find the acceleration and tension In the string. [Take g = 9.8m/s²]

Question Number 171626 Answers: 0 Comments: 0

x=(√(19)) +((91)/( (√(19))+((91)/( (√(19))+((91)/( (√(19))+((91)/( (√(19))+…))))))))

$$\:\:\:{x}=\sqrt{\mathrm{19}}\:+\frac{\mathrm{91}}{\:\sqrt{\mathrm{19}}+\frac{\mathrm{91}}{\:\sqrt{\mathrm{19}}+\frac{\mathrm{91}}{\:\sqrt{\mathrm{19}}+\frac{\mathrm{91}}{\:\sqrt{\mathrm{19}}+\ldots}}}} \\ $$

Question Number 171622 Answers: 0 Comments: 0

Question Number 171620 Answers: 0 Comments: 4

Question Number 171614 Answers: 0 Comments: 11

A particle is moving along a straight line such that it's position from a fixed point is S = ( 12 - 15t² + 5t³ )m where t is in seconds. Determine: A. Total distance travelled by the particle from t = 1sec to t = 3sec B. The average speed of the particle during this time.

Question Number 171613 Answers: 0 Comments: 0

Question Number 171612 Answers: 0 Comments: 4

f(f(x))=(1/(1+x^2 )) f(x)=?

$${f}\left({f}\left({x}\right)\right)=\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\:\:\:\:\:\:\:\:{f}\left({x}\right)=? \\ $$

Question Number 171611 Answers: 1 Comments: 0

∫_0 ^∞ xe^(−x) cos(x)log^n (x)dx how can we do these

$$\int_{\mathrm{0}} ^{\infty} \boldsymbol{\mathrm{xe}}^{−\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{log}}^{\boldsymbol{\mathrm{n}}} \left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{dx}} \\ $$$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{can}}\:\boldsymbol{\mathrm{we}}\:\boldsymbol{\mathrm{do}}\:\boldsymbol{\mathrm{these}} \\ $$

Question Number 171608 Answers: 1 Comments: 0

montrer que ∫_o ^(+oo) ((sin^2 t)/t^2 )e^(−xt) dt est continu sur R^+

$${montrer}\:{que} \\ $$$$\int_{{o}} ^{+{oo}} \frac{{sin}^{\mathrm{2}} {t}}{{t}^{\mathrm{2}} }{e}^{−{xt}} {dt} \\ $$$${est}\:{continu}\:{sur}\:{R}^{+} \\ $$

Question Number 171601 Answers: 0 Comments: 0

Question Number 171599 Answers: 0 Comments: 0

Ω=∫_0 ^1 Log(((Log^2 (x))/x^(x^5 −x^4 +x^3 −x^2 +x−1) ))dx Mastermind

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