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AllQuestion and Answers: Page 308

Question Number 191442 Answers: 0 Comments: 0

Question Number 191440 Answers: 0 Comments: 0

Question Number 191439 Answers: 0 Comments: 0

Question Number 191436 Answers: 1 Comments: 0

Factorize x^2 + (1/a) (bx + c)

$$\mathrm{Factorize} \\ $$$$\boldsymbol{{x}}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{\boldsymbol{{a}}}\:\left(\boldsymbol{{bx}}\:+\:\boldsymbol{{c}}\right) \\ $$

Question Number 191435 Answers: 0 Comments: 0

It is given that I_1 =∫xg[x(1−x)]dx , I_2 = ∫g[x(1−x)]dx. Find (I_2 /I_1 ). Thanks.

$$\:{It}\:{is}\:{given}\:{that}\:{I}_{\mathrm{1}} =\int{xg}\left[{x}\left(\mathrm{1}−{x}\right)\right]{dx}\:,\: \\ $$$${I}_{\mathrm{2}} =\:\int{g}\left[{x}\left(\mathrm{1}−{x}\right)\right]{dx}.\:{Find}\:\frac{{I}_{\mathrm{2}} }{{I}_{\mathrm{1}} }.\:{Thanks}. \\ $$

Question Number 191410 Answers: 1 Comments: 0

Three villages A, B and C are on a straight road and B is the mid-way between A and C. A motor cyclist moving with a uniform acceleration passes A, B and C. The speeds with which the motorcyclist passes A and C are 20ms^(−1) and 40ms^− respectively. find the speed with which the motor cyclist passes B.

$$\:{Three}\:{villages}\:{A},\:{B}\:{and}\:{C}\:{are}\:{on}\:{a}\: \\ $$$$\:{straight}\:{road}\:{and}\:{B}\:{is}\:{the}\:{mid}-{way} \\ $$$${between}\:{A}\:{and}\:{C}.\:{A}\:{motor}\:{cyclist} \\ $$$${moving}\:{with}\:{a}\:{uniform}\:{acceleration} \\ $$$${passes}\:{A},\:{B}\:{and}\:{C}.\:{The}\:{speeds}\:{with}\: \\ $$$${which}\:{the}\:{motorcyclist}\:{passes}\:{A}\:{and}\: \\ $$$${C}\:{are}\:\mathrm{20}{ms}^{−\mathrm{1}} \:{and}\:\mathrm{40}{ms}^{−} \:{respectively}. \\ $$$${find}\:{the}\:{speed}\:{with}\:{which}\:{the}\:{motor} \\ $$$${cyclist}\:{passes}\:{B}. \\ $$

Question Number 191409 Answers: 1 Comments: 0

Question Number 191405 Answers: 0 Comments: 3

Question Number 191404 Answers: 1 Comments: 0

Question Number 191403 Answers: 1 Comments: 0

Question Number 191399 Answers: 1 Comments: 1

Question Number 191397 Answers: 1 Comments: 1

Question Number 191395 Answers: 1 Comments: 0

Question Number 191394 Answers: 1 Comments: 0

Question Number 191393 Answers: 0 Comments: 0

Question Number 191396 Answers: 0 Comments: 0

Question Number 191389 Answers: 1 Comments: 0

Factorize: x^3 +(1/x^3 )+((11)/8)

$$\mathrm{Factorize}: \\ $$$${x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }+\frac{\mathrm{11}}{\mathrm{8}} \\ $$

Question Number 191392 Answers: 2 Comments: 0

Question Number 191369 Answers: 1 Comments: 0

calculate 𝛗= Σ_(n=1) ^∞ (( sin(((nπ)/3) ))/((2n + 1 )^( 2) ))= ?

$$ \\ $$$$\:\:\:{calculate} \\ $$$$ \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\:{sin}\left(\frac{{n}\pi}{\mathrm{3}}\:\right)}{\left(\mathrm{2}{n}\:+\:\mathrm{1}\:\right)^{\:\mathrm{2}} }=\:? \\ $$$$ \\ $$

Question Number 191364 Answers: 2 Comments: 2

Question Number 191359 Answers: 0 Comments: 0

Find lim_(x→0) (𝚪(x)𝛙^((0)) (x)+π^2 ((cot(πx))/(sin(πx))))=?

$$\boldsymbol{\mathrm{Find}}\:\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\boldsymbol{\Gamma}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\psi}^{\left(\mathrm{0}\right)} \left(\boldsymbol{\mathrm{x}}\right)+\pi^{\mathrm{2}} \frac{\boldsymbol{\mathrm{cot}}\left(\pi\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{sin}}\left(\pi\boldsymbol{\mathrm{x}}\right)}\right)=? \\ $$$$ \\ $$

Question Number 191344 Answers: 3 Comments: 0

if sin(x) + (√3) cos (x) = (1/2) ⇒(√3) sin(4x ) − cos (4x )= ?

$$ \\ $$$$\:\:\:\:\:\:\mathrm{if}\:\:\:{sin}\left({x}\right)\:+\:\sqrt{\mathrm{3}}\:{cos}\:\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\Rightarrow\sqrt{\mathrm{3}}\:\:{sin}\left(\mathrm{4}{x}\:\right)\:−\:\:{cos}\:\left(\mathrm{4}{x}\:\right)=\:? \\ $$$$ \\ $$

Question Number 191343 Answers: 1 Comments: 0

solve in R ⌊ (1/x) ⌋ + ⌊ (2/x) ⌋ + ⌊ (3/x) ⌋ = 1

$$ \\ $$$$\:\:\:\:\:\:\mathrm{solve}\:\:{in}\:\:\mathbb{R} \\ $$$$ \\ $$$$\:\:\:\:\:\:\lfloor\:\frac{\mathrm{1}}{{x}}\:\rfloor\:+\:\lfloor\:\frac{\mathrm{2}}{{x}}\:\rfloor\:+\:\lfloor\:\frac{\mathrm{3}}{{x}}\:\rfloor\:=\:\mathrm{1} \\ $$$$ \\ $$

Question Number 191342 Answers: 1 Comments: 0

calculate... Ω ={ ∫_0 ^( (π/4)) ( 1 + (√3) sin(x) + cos(x) )^( n) dx}^(1/n) = ?

$$ \\ $$$$\:\:\:\:{calculate}... \\ $$$$\:\Omega\:=\left\{\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \left(\:\:\mathrm{1}\:+\:\sqrt{\mathrm{3}}\:{sin}\left({x}\right)\:+\:{cos}\left({x}\right)\:\right)^{\:{n}} {dx}\right\}^{\frac{\mathrm{1}}{{n}}} =\:? \\ $$$$ \\ $$$$ \\ $$

Question Number 191310 Answers: 1 Comments: 0

Question Number 191307 Answers: 1 Comments: 0

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