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AllQuestion and Answers: Page 1566

Question Number 42673 Answers: 1 Comments: 0

Question Number 42672 Answers: 0 Comments: 0

Simplify: (x + y + z)(x^(−1) + y^(−1) + z^(−1) ) = (x^(−1) y^(−1) z^(−1) )(x + y)(y + z)(z + x)

$$\mathrm{Simplify}:\:\:\:\left(\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\right)\left(\mathrm{x}^{−\mathrm{1}} \:+\:\mathrm{y}^{−\mathrm{1}} \:+\:\mathrm{z}^{−\mathrm{1}} \right)\:=\:\left(\mathrm{x}^{−\mathrm{1}} \:\mathrm{y}^{−\mathrm{1}} \:\mathrm{z}^{−\mathrm{1}} \right)\left(\mathrm{x}\:+\:\mathrm{y}\right)\left(\mathrm{y}\:+\:\mathrm{z}\right)\left(\mathrm{z}\:+\:\mathrm{x}\right) \\ $$

Question Number 42671 Answers: 0 Comments: 0

If pqr = 1 Hence evaluate: (1/(1 + e + f^(−1) )) + (1/(1 + f + g^(−1) )) + (1/(1 + g + e^(−1) ))

$$\mathrm{If}\:\mathrm{pqr}\:=\:\mathrm{1} \\ $$$$\mathrm{Hence}\:\mathrm{evaluate}:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{e}\:+\:\mathrm{f}^{−\mathrm{1}} }\:\:+\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{f}\:+\:\mathrm{g}^{−\mathrm{1}} }\:\:+\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{g}\:+\:\mathrm{e}^{−\mathrm{1}} } \\ $$

Question Number 42670 Answers: 1 Comments: 3

If a, b and c are in a GP. Prove that log_n a , log_n b , log_n c are in AP

$$\mathrm{If}\:\:\mathrm{a},\:\mathrm{b}\:\mathrm{and}\:\mathrm{c}\:\:\mathrm{are}\:\mathrm{in}\:\mathrm{a}\:\mathrm{GP}.\:\:\mathrm{Prove}\:\mathrm{that}\:\:\:\mathrm{log}_{\mathrm{n}} \mathrm{a}\:,\:\:\mathrm{log}_{\mathrm{n}} \mathrm{b}\:\:,\:\:\mathrm{log}_{\mathrm{n}} \mathrm{c}\:\:\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP} \\ $$

Question Number 42698 Answers: 1 Comments: 0

A boy lying flat on level ground sees a bird on a tree and the angle of Elevation from the boy to the birth is 42°,if the boy is 6m from the tree.find the hieght of the tree if the bird is at the top of the tree

$${A}\:{boy}\:{lying}\:{flat}\:{on}\:{level}\:{ground}\:{sees}\:{a}\:{bird}\:\:{on}\:{a}\:{tree}\:{and}\:{the} \\ $$$${angle}\:{of}\:{Elevation}\:{from}\:{the}\:{boy}\:{to}\:{the}\:{birth}\:{is}\:\mathrm{42}°,{if}\:{the}\:{boy} \\ $$$${is}\:\mathrm{6}{m}\:{from}\:{the}\:{tree}.{find}\:{the}\:{hieght}\:{of}\:{the}\:{tree}\:{if}\:{the}\:{bird} \\ $$$${is}\:{at}\:{the}\:{top}\:{of}\:{the}\:{tree} \\ $$

Question Number 42668 Answers: 0 Comments: 0

If ∣a sin^2 θ+b sin θ cos θ+c cos^2 θ−(1/2)(a−c)∣ ≤ (1/2) k, then k^2 is equal to

$$\mathrm{If} \\ $$$$\mid{a}\:\mathrm{sin}^{\mathrm{2}} \theta+{b}\:\mathrm{sin}\:\theta\:\mathrm{cos}\:\theta+{c}\:\mathrm{cos}^{\mathrm{2}} \theta−\frac{\mathrm{1}}{\mathrm{2}}\left({a}−{c}\right)\mid \\ $$$$\:\:\:\leqslant\:\frac{\mathrm{1}}{\mathrm{2}}\:{k},\:\mathrm{then}\:{k}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 42708 Answers: 0 Comments: 1

calculate f(α)=∫_0 ^∞ ((e^(−2x) −e^(−x) )/x^2 ) e^(−αx^2 ) dx with α>0 1) find the value of ∫_0 ^∞ ((e^(−2x) −e^(−x) )/x^2 ) e^(−2x^2 ) dx

$${calculate}\:\:{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{e}^{−\mathrm{2}{x}} −{e}^{−{x}} }{{x}^{\mathrm{2}} }\:{e}^{−\alpha{x}^{\mathrm{2}} } {dx}\:\:{with}\:\alpha>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{e}^{−\mathrm{2}{x}} \:−{e}^{−{x}} }{{x}^{\mathrm{2}} }\:{e}^{−\mathrm{2}{x}^{\mathrm{2}} } {dx} \\ $$

Question Number 42663 Answers: 0 Comments: 0

if 1.225 g of KClO_3 are heated. Calculate the mass of potassium Chloride produced. Detemine the volume of oxygen obtained at r.t.p

$${if}\:\mathrm{1}.\mathrm{225}\:{g}\:{of}\:{KClO}_{\mathrm{3}} \:{are}\:{heated}. \\ $$$${Calculate}\:{the}\:{mass}\:{of}\:{potassium}\:{Chloride}\:{produced}. \\ $$$${Detemine}\:{the}\:{volume}\:{of}\:{oxygen}\:{obtained}\:{at}\:{r}.{t}.{p} \\ $$

Question Number 42657 Answers: 0 Comments: 0

Question Number 42656 Answers: 1 Comments: 0

Question Number 42654 Answers: 2 Comments: 2

Question Number 42650 Answers: 0 Comments: 0

Question Number 42649 Answers: 0 Comments: 0

Question Number 42648 Answers: 0 Comments: 0

Question Number 42639 Answers: 0 Comments: 0

Find LCM [((13)/2),(2/(13)),(4/7)] [((57)),(0) ]×

$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Find}\:\mathrm{LCM}\:\left[\frac{\mathrm{13}}{\mathrm{2}},\frac{\mathrm{2}}{\mathrm{13}},\frac{\mathrm{4}}{\mathrm{7}}\right] \\ $$$$\begin{bmatrix}{\mathrm{57}}\\{\mathrm{0}}\end{bmatrix}× \\ $$

Question Number 42636 Answers: 0 Comments: 1

lim_(n→∞) Σ_(r=1) ^n (r/(n^2 +n+r))

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{{r}}{{n}^{\mathrm{2}} +{n}+{r}} \\ $$$$ \\ $$

Question Number 42631 Answers: 1 Comments: 7

let f(x)=2(√(x−1)) −2x 1) find D_f 2) study the variation of f(x) 3 ) calculate ∫_1 ^3 f(x)dx 4) determine f^(−1) (x) and calculate ∫_1 ^3 f^(−1) (x)dx 5) find the values of A = ∫_1 ^3 ((f(x))/(f^(−1) (x)dx)) and B = ((∫_1 ^3 f(x))/(∫_1 ^3 f^(−1) (x))) dx.

$${let}\:{f}\left({x}\right)=\mathrm{2}\sqrt{{x}−\mathrm{1}}\:−\mathrm{2}{x} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{variation}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\:\right)\:{calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{3}} \:{f}\left({x}\right){dx} \\ $$$$\left.\mathrm{4}\right)\:{determine}\:{f}^{−\mathrm{1}} \left({x}\right)\:{and}\:{calculate}\:\:\:\int_{\mathrm{1}} ^{\mathrm{3}} \:{f}^{−\mathrm{1}} \left({x}\right){dx} \\ $$$$\left.\mathrm{5}\right)\:\:{find}\:{the}\:{values}\:{of}\:\:{A}\:=\:\:\int_{\mathrm{1}} ^{\mathrm{3}} \:\:\:\frac{{f}\left({x}\right)}{{f}^{−\mathrm{1}} \left({x}\right){dx}}\:{and}\: \\ $$$${B}\:=\:\frac{\int_{\mathrm{1}} ^{\mathrm{3}} \:\:{f}\left({x}\right)}{\int_{\mathrm{1}} ^{\mathrm{3}} \:{f}^{−\mathrm{1}} \left({x}\right)}\:{dx}. \\ $$

Question Number 42630 Answers: 0 Comments: 0

let f(x) = e^x −2(√(x−3)) 1) find f^(−1) (x) 2) find ∫ f^(−1) (t)dt

$${let}\:{f}\left({x}\right)\:=\:{e}^{{x}} −\mathrm{2}\sqrt{{x}−\mathrm{3}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}^{−\mathrm{1}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int\:\:{f}^{−\mathrm{1}} \left({t}\right){dt}\: \\ $$

Question Number 42629 Answers: 0 Comments: 0

find A_n =∫_0 ^∞ ((sin(nx))/(sh(2nx)))dx with n natural integr not 0.

$${find}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({nx}\right)}{{sh}\left(\mathrm{2}{nx}\right)}{dx}\:\:{with}\:{n}\:{natural}\:{integr} \\ $$$${not}\:\mathrm{0}. \\ $$

Question Number 42628 Answers: 0 Comments: 2

calculate I = ∫_(π/3) ^(π/2) ((cos(2x))/(sin(x)+cosx))dx and J =∫_(π/3) ^(π/2) ((sin(2x))/(sin(x) +cos(x)))dx

$${calculate}\:\:{I}\:\:=\:\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{{sin}\left({x}\right)+{cosx}}{dx}\:{and} \\ $$$${J}\:=\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{{sin}\left({x}\right)\:+{cos}\left({x}\right)}{dx} \\ $$

Question Number 42627 Answers: 2 Comments: 0

solve for x (1/3)log(x−3)+log5−log(x−2)^2 =0

$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{{x}} \\ $$$$\frac{\mathrm{1}}{\mathrm{3}}\boldsymbol{\mathrm{log}}\left(\boldsymbol{{x}}−\mathrm{3}\right)+\boldsymbol{\mathrm{log}}\mathrm{5}−\boldsymbol{\mathrm{log}}\left(\boldsymbol{{x}}−\mathrm{2}\right)^{\mathrm{2}} =\mathrm{0} \\ $$

Question Number 42624 Answers: 1 Comments: 2

Question Number 42622 Answers: 0 Comments: 1

find ∫ th(2x+1)dx

$${find}\:\int\:\:{th}\left(\mathrm{2}{x}+\mathrm{1}\right){dx}\: \\ $$

Question Number 42621 Answers: 0 Comments: 1

find ∫ th(x)dx

$${find}\:\int\:{th}\left({x}\right){dx}\: \\ $$

Question Number 42605 Answers: 0 Comments: 3

let f(x) = ∫_(−∞) ^(+∞) ((arctan (xt^2 ))/(1+2t^2 ))dt 1) find a explicite form of f(x) 2) calculate ∫_0 ^∞ ((arctan(t^2 ))/(1+2t^2 ))dt and ∫_0 ^∞ ((arctan(2t^2 ))/(1+2t^2 ))dt

$${let}\:{f}\left({x}\right)\:=\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{arctan}\:\left({xt}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{2}{t}^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicite}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{arctan}\left({t}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{2}{t}^{\mathrm{2}} }{dt}\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{arctan}\left(\mathrm{2}{t}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{2}{t}^{\mathrm{2}} }{dt} \\ $$$$ \\ $$

Question Number 42603 Answers: 0 Comments: 2

let f(x) =∫_0 ^1 ln(1+ixt)dt calculate f^, (x) (x from R).

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{ixt}\right){dt}\:\:{calculate}\:{f}^{,} \left({x}\right)\:\:\:\:\left({x}\:{from}\:{R}\right). \\ $$

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