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Question Number 154980    Answers: 1   Comments: 0

if a and b are real numbers determine a necessary and sufficient condition so as the equation x^2 + ((a(√b))/x) = a + b to have three real distinct roots.

$$\mathrm{if}\:\:\boldsymbol{\mathrm{a}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{b}}\:\:\mathrm{are}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\mathrm{determine}\:\mathrm{a}\:\mathrm{necessary}\:\mathrm{and}\:\mathrm{sufficient} \\ $$$$\mathrm{condition}\:\mathrm{so}\:\mathrm{as}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\frac{\mathrm{a}\sqrt{\mathrm{b}}}{\mathrm{x}}\:=\:\mathrm{a}\:+\:\mathrm{b} \\ $$$$\mathrm{to}\:\mathrm{have}\:\mathrm{three}\:\mathrm{real}\:\mathrm{distinct}\:\mathrm{roots}. \\ $$

Question Number 154976    Answers: 0   Comments: 0

Question Number 154975    Answers: 0   Comments: 0

Question Number 154973    Answers: 1   Comments: 0

If x + (7/( (√x))) = 50 Find the value of the expression (√x) - (1/( (√x))) = ?

$$\mathrm{If}\:\:\mathrm{x}\:+\:\frac{\mathrm{7}}{\:\sqrt{\mathrm{x}}}\:=\:\mathrm{50} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expression} \\ $$$$\sqrt{\mathrm{x}}\:-\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}}}\:=\:? \\ $$

Question Number 154972    Answers: 0   Comments: 2

if in a triangle ABC, A and B are complementry, then tanC is....?

$${if}\:{in}\:{a}\:{triangle}\:{ABC},\:{A}\:{and}\:{B} \\ $$$${are}\:{complementry},\:{then}\:{tanC}\:{is}....? \\ $$

Question Number 154966    Answers: 0   Comments: 1

we know y=asin(ωt−kx) is equation of wave which velocity will be (ω/k) But what will be the velocity of a wave that is created from superposition of two sine wave of different velocity like bellow y=5sin(6t−x)cos(13t−6x) ?

$$\:\mathrm{we}\:\mathrm{know}\:\:\mathrm{y}=\mathrm{asin}\left(\omega\mathrm{t}−\mathrm{kx}\right)\:\mathrm{is}\: \\ $$$$\mathrm{equation}\:\mathrm{of}\:\mathrm{wave} \\ $$$$\:\mathrm{which}\:\mathrm{velocity}\:\mathrm{will}\:\mathrm{be}\:\frac{\omega}{\mathrm{k}} \\ $$$$\:\:\mathrm{But}\:\mathrm{what}\:\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\: \\ $$$$\:\:\mathrm{a}\:\mathrm{wave}\:\mathrm{that}\:\mathrm{is}\:\mathrm{created}\:\mathrm{from} \\ $$$$\:\mathrm{superposition}\:\mathrm{of}\:\mathrm{two}\:\mathrm{sine}\:\mathrm{wave}\:\mathrm{of}\: \\ $$$$\mathrm{different}\:\mathrm{velocity}\:\mathrm{like}\:\mathrm{bellow} \\ $$$$\:\:\:\mathrm{y}=\mathrm{5sin}\left(\mathrm{6t}−\mathrm{x}\right)\mathrm{cos}\left(\mathrm{13t}−\mathrm{6x}\right)\:?\: \\ $$

Question Number 154959    Answers: 2   Comments: 2

Consider the polynomial P(x)=x^(10) -6x^9 -11x^8 +3x^2 -18x-7 Calculate: P(3+2(√5))

$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{polynomial} \\ $$$$\mathrm{P}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{10}} -\mathrm{6x}^{\mathrm{9}} -\mathrm{11x}^{\mathrm{8}} +\mathrm{3x}^{\mathrm{2}} -\mathrm{18x}-\mathrm{7} \\ $$$$\mathrm{Calculate}:\:\:\mathrm{P}\left(\mathrm{3}+\mathrm{2}\sqrt{\mathrm{5}}\right) \\ $$

Question Number 154958    Answers: 0   Comments: 3

if , sinA+sinB=(1/5) then ((6cosA+13cosB)/(cosA+6cosB))=?

$$\:\: \\ $$$$\:\:\mathrm{if}\:,\:\mathrm{sinA}+\mathrm{sinB}=\frac{\mathrm{1}}{\mathrm{5}}\: \\ $$$$\:\mathrm{then}\:\:\:\frac{\mathrm{6cosA}+\mathrm{13cosB}}{\mathrm{cosA}+\mathrm{6cosB}}=? \\ $$$$\:\: \\ $$

Question Number 154948    Answers: 0   Comments: 3

If a^(→) = (-1;0;-3;4) b^(→) = (1;-4;0;-3) c^(→) = ((∣a^(→) ∣)/(∣b^(→) ∣)) ∙ (2a^(→) + b^(→) ) d^(→) = ((∣b^(→) ∣)/(∣a^(→) ∣)) ∙ (a^(→) + b^(→) ) k^(→) = -3∙(c^(→) ∙ ∣c^(→) ∣ ∙ d^(→) ) Find ∣k^(→) ∣ = ?

$$\mathrm{If}\:\:\overset{\rightarrow} {\mathrm{a}}\:=\:\left(-\mathrm{1};\mathrm{0};-\mathrm{3};\mathrm{4}\right) \\ $$$$\:\:\:\:\:\:\overset{\rightarrow} {\mathrm{b}}\:=\:\left(\mathrm{1};-\mathrm{4};\mathrm{0};-\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\overset{\rightarrow} {\mathrm{c}}\:=\:\frac{\mid\overset{\rightarrow} {\mathrm{a}}\mid}{\mid\overset{\rightarrow} {\mathrm{b}}\mid}\:\centerdot\:\left(\mathrm{2}\overset{\rightarrow} {\mathrm{a}}\:+\:\overset{\rightarrow} {\mathrm{b}}\right) \\ $$$$\:\:\:\:\:\:\:\overset{\rightarrow} {\mathrm{d}}\:=\:\frac{\mid\overset{\rightarrow} {\mathrm{b}}\mid}{\mid\overset{\rightarrow} {\mathrm{a}}\mid}\:\centerdot\:\left(\overset{\rightarrow} {\mathrm{a}}\:+\:\overset{\rightarrow} {\mathrm{b}}\right) \\ $$$$\:\:\:\:\:\:\:\overset{\rightarrow} {\mathrm{k}}\:=\:-\mathrm{3}\centerdot\left(\overset{\rightarrow} {\mathrm{c}}\:\centerdot\:\mid\overset{\rightarrow} {\mathrm{c}}\mid\:\centerdot\:\overset{\rightarrow} {\mathrm{d}}\right) \\ $$$$\mathrm{Find}\:\:\mid\overset{\rightarrow} {\mathrm{k}}\mid\:=\:? \\ $$

Question Number 154942    Answers: 2   Comments: 0

Question Number 154940    Answers: 1   Comments: 0

Question Number 154931    Answers: 2   Comments: 0

f(x)=(2x^5 +2x^4 −53x^3 −57x+54)^(2011) f((((√(111))−1)/2))=?

$$\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{2x}^{\mathrm{5}} +\mathrm{2x}^{\mathrm{4}} −\mathrm{53x}^{\mathrm{3}} −\mathrm{57x}+\mathrm{54}\right)^{\mathrm{2011}} \\ $$$$\mathrm{f}\left(\frac{\sqrt{\mathrm{111}}−\mathrm{1}}{\mathrm{2}}\right)=? \\ $$

Question Number 154930    Answers: 0   Comments: 1

Question Number 154928    Answers: 0   Comments: 0

Prove:: Σ_(k=0) ^m ((m),(k) )^2 (((n+2m−k)),(( 2m)) )= (((m+n)),(( n)) )^2

$$\mathrm{Prove}::\:\:\:\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{m}} {\sum}}\begin{pmatrix}{\mathrm{m}}\\{\mathrm{k}}\end{pmatrix}^{\mathrm{2}} \begin{pmatrix}{\mathrm{n}+\mathrm{2m}−\mathrm{k}}\\{\:\:\:\:\:\:\mathrm{2m}}\end{pmatrix}=\begin{pmatrix}{\mathrm{m}+\mathrm{n}}\\{\:\:\:\:\mathrm{n}}\end{pmatrix}^{\mathrm{2}} \\ $$

Question Number 154907    Answers: 0   Comments: 2

∫_2 ^( 8) e^(2x) cos^2 x dx=?

$$\int_{\mathrm{2}} ^{\:\mathrm{8}} \:{e}^{\mathrm{2}{x}} \:\mathrm{cos}^{\mathrm{2}} {x}\:{dx}=? \\ $$

Question Number 154902    Answers: 0   Comments: 1

∫_0 ^(3/2) E(x^2 )dx

$$\int_{\mathrm{0}} ^{\frac{\mathrm{3}}{\mathrm{2}}} {E}\left({x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 154896    Answers: 0   Comments: 2

find the following ?please S=Σ_(k=1) ^n (1/(k(k+1)(k+2)))

$${find}\:{the}\:{following}\:?{please} \\ $$$${S}=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}\left({k}+\mathrm{1}\right)\left({k}+\mathrm{2}\right)} \\ $$

Question Number 154893    Answers: 0   Comments: 0

Question Number 154892    Answers: 1   Comments: 2

Find: cos(((3π)/7)) + cos(((3π)/7)) (√(2 - 2cos(((3π)/7)))) = ?

$$\mathrm{Find}: \\ $$$$\mathrm{cos}\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\:+\:\mathrm{cos}\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\:\sqrt{\mathrm{2}\:-\:\mathrm{2cos}\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)}\:=\:? \\ $$

Question Number 154889    Answers: 0   Comments: 0

Question Number 154888    Answers: 1   Comments: 0

Question Number 154926    Answers: 1   Comments: 0

∫_0 ^1 ((2x^2 )/((x^2 +1)^2 ))dx=

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{2}{x}^{\mathrm{2}} }{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx}= \\ $$

Question Number 154927    Answers: 1   Comments: 0

Let I_n =∫x^n e^(−x) dx show that ∫_0 ^∞ x^n e^(−x) dx=n!

$$\mathrm{Let}\:{I}_{{n}} =\int{x}^{{n}} {e}^{−{x}} {dx} \\ $$$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} {x}^{{n}} {e}^{−{x}} {dx}={n}! \\ $$

Question Number 154880    Answers: 6   Comments: 0

Question Number 154877    Answers: 2   Comments: 1

∫_(π/2) ^(π/4) sin^3 (x)cos^2 (x)dx

$$\int_{\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{4}}} {sin}^{\mathrm{3}} \left({x}\right){cos}^{\mathrm{2}} \left({x}\right){dx} \\ $$

Question Number 154876    Answers: 1   Comments: 0

Integrate: ∫_1 ^( 8) (( (√x)−x^2 )/( ^3 (√x))) dx

$$\:\:\boldsymbol{\mathrm{Integrate}}: \\ $$$$\:\:\:\int_{\mathrm{1}} ^{\:\mathrm{8}} \:\:\frac{\:\sqrt{\boldsymbol{\mathrm{x}}}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\overset{\mathrm{3}} {\:}\sqrt{\boldsymbol{\mathrm{x}}}}\:\boldsymbol{\mathrm{dx}} \\ $$

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