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Question Number 91508 Answers: 0 Comments: 1

Find the greatest number that divides 59 and 54 leaving remainders 3 and 5 respectively.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{number}\:\mathrm{that}\:\mathrm{divides} \\ $$$$\mathrm{59}\:\mathrm{and}\:\mathrm{54}\:\mathrm{leaving}\:\mathrm{remainders}\:\mathrm{3}\:\mathrm{and} \\ $$$$\mathrm{5}\:\mathrm{respectively}. \\ $$

Question Number 91507 Answers: 0 Comments: 1

(((−a^6 ×b^3 ×c^(21) )/(c^9 ×a^(12) )))^(1/3) =

$$\sqrt[{\mathrm{3}}]{\frac{−{a}^{\mathrm{6}} ×{b}^{\mathrm{3}} ×{c}^{\mathrm{21}} }{{c}^{\mathrm{9}} ×{a}^{\mathrm{12}} }}\:=\: \\ $$

Question Number 91500 Answers: 0 Comments: 1

v=π∫_1 ^4 [((1/4).x^2 )^2 dx

$${v}=\pi\int_{\mathrm{1}} ^{\mathrm{4}} \left[\left(\frac{\mathrm{1}}{\mathrm{4}}.{x}^{\mathrm{2}} \right)^{\mathrm{2}} {dx}\right. \\ $$

Question Number 91497 Answers: 0 Comments: 1

v=π∫_0 ^2 x^2 dx

$${v}=\pi\int_{\mathrm{0}} ^{\mathrm{2}} {x}^{\mathrm{2}} {dx} \\ $$

Question Number 91496 Answers: 0 Comments: 1

The vector a=3i−2j+2k and b=−i−2k are the adjacent sides of a parallelogram. Then angle between its diagonal is

$$\mathrm{The}\:\mathrm{vector}\:\boldsymbol{\mathrm{a}}=\mathrm{3}\boldsymbol{\mathrm{i}}−\mathrm{2}\boldsymbol{\mathrm{j}}+\mathrm{2}\boldsymbol{\mathrm{k}}\:\:\mathrm{and}\:\boldsymbol{\mathrm{b}}=−\boldsymbol{\mathrm{i}}−\mathrm{2}\boldsymbol{\mathrm{k}} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{adjacent}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{parallelogram}. \\ $$$$\mathrm{Then}\:\mathrm{angle}\:\mathrm{between}\:\mathrm{its}\:\mathrm{diagonal}\:\mathrm{is} \\ $$

Question Number 91494 Answers: 1 Comments: 0

The value of the integral ∫_( 1) ^3 (√(3+x^3 )) dx lies in the interval....

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral}\:\underset{\:\mathrm{1}} {\overset{\mathrm{3}} {\int}}\:\sqrt{\mathrm{3}+{x}^{\mathrm{3}} }\:{dx} \\ $$$$\mathrm{lies}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval}.... \\ $$

Question Number 91493 Answers: 1 Comments: 1

∫_( 0) ^(π/2) log (((4+3 sin x)/(4+3 cos x)))dx =

$$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\mathrm{log}\:\left(\frac{\mathrm{4}+\mathrm{3}\:\mathrm{sin}\:{x}}{\mathrm{4}+\mathrm{3}\:\mathrm{cos}\:{x}}\right){dx}\:= \\ $$

Question Number 91484 Answers: 0 Comments: 2

Question Number 91491 Answers: 1 Comments: 0

x^3 +1 = 2 ((2x−1))^(1/(3 )) x =?

$${x}^{\mathrm{3}} +\mathrm{1}\:=\:\mathrm{2}\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{2}{x}−\mathrm{1}} \\ $$$${x}\:=? \\ $$

Question Number 91479 Answers: 1 Comments: 4

∫_(−π/2 ) ^(π/2) (√(cos x−cos^3 x)) dx=...

$$\:\underset{−\pi/\mathrm{2}\:} {\overset{\pi/\mathrm{2}} {\int}}\:\sqrt{\mathrm{cos}\:{x}−\mathrm{cos}^{\mathrm{3}} {x}}\:\mathrm{dx}=... \\ $$

Question Number 91476 Answers: 0 Comments: 2

Find the slope of the tangent line to the graph of: y^4 +3y−4x^3 =5x+1 at the point P (1, −2)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tangent}\: \\ $$$$\mathrm{line}\:\mathrm{to}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of}: \\ $$$$\mathrm{y}^{\mathrm{4}} +\mathrm{3y}−\mathrm{4x}^{\mathrm{3}} =\mathrm{5x}+\mathrm{1}\:\:\mathrm{at}\:\mathrm{the}\:\mathrm{point} \\ $$$$\mathrm{P}\:\left(\mathrm{1},\:−\mathrm{2}\right) \\ $$

Question Number 91474 Answers: 0 Comments: 0

f(x)=(√(4−x^2 )) and g(x)=3x+1 find the sum , different, and product f(x) and g(x).

$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{4}−\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{3x}+\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:,\:\mathrm{different},\:\mathrm{and}\:\mathrm{product} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right). \\ $$

Question Number 91473 Answers: 1 Comments: 0

Question Number 91471 Answers: 1 Comments: 0

∣2x−7∣>3

$$\mid\mathrm{2x}−\mathrm{7}\mid>\mathrm{3} \\ $$

Question Number 91470 Answers: 0 Comments: 2

∣x−3∣<0.1

$$\mid\mathrm{x}−\mathrm{3}\mid<\mathrm{0}.\mathrm{1} \\ $$

Question Number 91469 Answers: 0 Comments: 3

−5<((4−3x)/2)<l

$$−\mathrm{5}<\frac{\mathrm{4}−\mathrm{3x}}{\mathrm{2}}<\mathrm{l} \\ $$

Question Number 91468 Answers: 0 Comments: 0

Question Number 91464 Answers: 0 Comments: 12

Find the greatest coefficient in the expansion of (3 − 2x)^(−7)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\:\:\:\:\:\:\:\left(\mathrm{3}\:\:−\:\:\mathrm{2x}\right)^{−\mathrm{7}} \\ $$

Question Number 91465 Answers: 1 Comments: 1

Question Number 91460 Answers: 1 Comments: 0

one of the conditions of the inflection point is inflection tangent. what is inflection tangent?

$${one}\:{of}\:{the}\:{conditions}\:{of}\:{the}\:{inflection} \\ $$$${point}\:{is}\:{inflection}\:{tangent}. \\ $$$${what}\:{is}\:{inflection}\:{tangent}? \\ $$

Question Number 91452 Answers: 2 Comments: 1

((−1))^(1/4) =?

$$\:\:\:\sqrt[{\mathrm{4}}]{−\mathrm{1}}\:=? \\ $$

Question Number 91448 Answers: 0 Comments: 3

prove that 1+x^(111) +x^(222) +x^(333) +x^(444) divides 1+ x^(111) +x^(222) +x^(333) +.......+x^(999)

$${prove}\:{that}\:\mathrm{1}+{x}^{\mathrm{111}} +{x}^{\mathrm{222}} +{x}^{\mathrm{333}} +{x}^{\mathrm{444}} \:\:{divides}\:\mathrm{1}+\:{x}^{\mathrm{111}} +{x}^{\mathrm{222}} +{x}^{\mathrm{333}} +.......+{x}^{\mathrm{999}} \\ $$

Question Number 91446 Answers: 0 Comments: 1

Question Number 91439 Answers: 1 Comments: 2

solve 2x^(99) +3x^(98) +2x^(97) +3x^(96) +.....2x+3=0 in R

$${solve}\:\mathrm{2}{x}^{\mathrm{99}} +\mathrm{3}{x}^{\mathrm{98}} +\mathrm{2}{x}^{\mathrm{97}} +\mathrm{3}{x}^{\mathrm{96}} +.....\mathrm{2}{x}+\mathrm{3}=\mathrm{0}\:{in}\:\mathbb{R} \\ $$

Question Number 91671 Answers: 0 Comments: 2

show that (x)^(1/(ln(x))) =e

$${show}\:{that} \\ $$$$\sqrt[{{ln}\left({x}\right)}]{{x}}={e} \\ $$

Question Number 91419 Answers: 0 Comments: 1

lim_(x→0) (1/(sin^4 x))(sin ((x/(1+x)))−((sin x)/(1+sin x)))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{4}} {x}}\left(\mathrm{sin}\:\left(\frac{{x}}{\mathrm{1}+{x}}\right)−\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{sin}\:{x}}\right) \\ $$

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