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AllQuestion and Answers: Page 1290

Question Number 85490 Answers: 0 Comments: 3

Given that the expression 2x^3 +px^2 −8x+9 is exactly divisable by x^2 −6x+5, find the value of p and q. Hence factorise the expression fully

$${Given}\:{that}\:{the}\:{expression}\:\mathrm{2}{x}^{\mathrm{3}} +{px}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{9}\:{is}\:{exactly}\:{divisable}\:{by}\:{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{5},\:{find}\:{the}\:{value}\:{of}\:\boldsymbol{\mathrm{p}}\:{and}\:\boldsymbol{\mathrm{q}}.\:{Hence}\:{factorise}\:{the}\:{expression}\:{fully} \\ $$

Question Number 85489 Answers: 0 Comments: 2

Find all angles between 0° and 360°, for which 8sinθ=3cos^2 θ

$${Find}\:{all}\:{angles}\:{between}\:\mathrm{0}°\:{and}\:\mathrm{360}°,\:{for}\:{which}\:\mathrm{8}{sin}\theta=\mathrm{3}{cos}^{\mathrm{2}} \theta \\ $$

Question Number 85488 Answers: 1 Comments: 0

∫ (dx/((x^4 +x^2 +1)^(3/4) ))

$$\int\:\frac{{dx}}{\left({x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} } \\ $$

Question Number 85484 Answers: 1 Comments: 0

show that (1/(secθ+1))+(1/(secθ−1))≡2cosecθcotθ

$${show}\:{that}\:\frac{\mathrm{1}}{{sec}\theta+\mathrm{1}}+\frac{\mathrm{1}}{{sec}\theta−\mathrm{1}}\equiv\mathrm{2}{cosec}\theta{cot}\theta \\ $$

Question Number 85480 Answers: 1 Comments: 0

∫((csc(x))/(cos(x)+cos^3 (x)+...+cos^(2n+1) (x)))dx ∀x∈n

$$\int\frac{{csc}\left({x}\right)}{{cos}\left({x}\right)+{cos}^{\mathrm{3}} \left({x}\right)+...+{cos}^{\mathrm{2}{n}+\mathrm{1}} \left({x}\right)}{dx} \\ $$$$\forall{x}\in{n} \\ $$

Question Number 85472 Answers: 1 Comments: 4

Question Number 85513 Answers: 1 Comments: 0

Solve the following equation: ((dy/dx))^2 +2y cot x (dy/dx) = y^2

$$\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\left(\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\right)^{\mathrm{2}} +\mathrm{2}\boldsymbol{\mathrm{y}}\:\boldsymbol{\mathrm{cot}}\:\boldsymbol{\mathrm{x}}\:\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:=\:\boldsymbol{\mathrm{y}}^{\mathrm{2}} \\ $$

Question Number 85468 Answers: 1 Comments: 0

∫ln(1−e^x ) dx

$$\int{ln}\left(\mathrm{1}−{e}^{{x}} \right)\:{dx} \\ $$

Question Number 85462 Answers: 0 Comments: 0

Question Number 85456 Answers: 0 Comments: 7

∫ (√(csc x )) dx?

$$\int\:\sqrt{\mathrm{csc}\:\mathrm{x}\:}\:\mathrm{dx}? \\ $$

Question Number 85447 Answers: 1 Comments: 5

Question Number 85442 Answers: 1 Comments: 1

Question Number 85441 Answers: 1 Comments: 0

∫ ((6x^4 −4)/(√(x^4 −2))) dx = ?

$$\int\:\frac{\mathrm{6x}^{\mathrm{4}} −\mathrm{4}}{\sqrt{\mathrm{x}^{\mathrm{4}} −\mathrm{2}}}\:\mathrm{dx}\:=\:? \\ $$

Question Number 85433 Answers: 1 Comments: 0

−log_(((x/6))) (((log_(10) (√(6−x)))/(log_(10) x))) > log_(10) (((∣x∣)/x))

$$−\mathrm{log}_{\left(\frac{\mathrm{x}}{\mathrm{6}}\right)} \left(\frac{\mathrm{log}_{\mathrm{10}} \sqrt{\mathrm{6}−\mathrm{x}}}{\mathrm{log}_{\mathrm{10}} \mathrm{x}}\right)\:>\:\mathrm{log}_{\mathrm{10}} \left(\frac{\mid\mathrm{x}\mid}{\mathrm{x}}\right) \\ $$

Question Number 85426 Answers: 1 Comments: 4

∫ _(π/4)^0 ((sin x+cos x)/(9+16sin 2x)) dx

$$\int\:_{\frac{\pi}{\mathrm{4}}} ^{\mathrm{0}} \:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{9}+\mathrm{16sin}\:\mathrm{2}{x}}\:{dx} \\ $$

Question Number 85418 Answers: 0 Comments: 1

Find the term indepent of x in the expression of (2x−(1/(2x)))^9

$${Find}\:{the}\:{term}\:{indepent}\:{of}\:{x}\:{in}\:{the}\:{expression}\:{of}\:\left(\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}{x}}\right)^{\mathrm{9}} \\ $$

Question Number 85414 Answers: 1 Comments: 1

∫(1/(1+(√(cos(x))) )) dx

$$\int\frac{\mathrm{1}}{\mathrm{1}+\sqrt{{cos}\left({x}\right)}\:}\:{dx} \\ $$

Question Number 85413 Answers: 0 Comments: 0

Question Number 85412 Answers: 0 Comments: 1

Question Number 85395 Answers: 1 Comments: 1

Question Number 85813 Answers: 2 Comments: 1

∫ x^2 (√(1+x^2 )) dx ?

$$\int\:\mathrm{x}^{\mathrm{2}} \:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:? \\ $$

Question Number 85391 Answers: 1 Comments: 5

Question Number 85386 Answers: 1 Comments: 0

If cot x−cos x = n and m^2 −n^(2 ) = 4(√(mn)) prove that m = cot x + cos x

$$\mathrm{If}\:\mathrm{cot}\:{x}−\mathrm{cos}\:{x}\:=\:{n}\:{and}\: \\ $$$${m}^{\mathrm{2}} −{n}^{\mathrm{2}\:} =\:\mathrm{4}\sqrt{{mn}} \\ $$$${prove}\:{that}\:{m}\:=\:\mathrm{cot}\:{x}\:+\:\mathrm{cos}\:{x}\: \\ $$

Question Number 85384 Answers: 1 Comments: 1

Question Number 85383 Answers: 1 Comments: 0

∫(((sin(x))/(cos^(11) (x))))^(1/5) dx

$$\int\sqrt[{\mathrm{5}}]{\frac{{sin}\left({x}\right)}{{cos}^{\mathrm{11}} \left({x}\right)}}\:{dx} \\ $$

Question Number 85461 Answers: 0 Comments: 4

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