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Question Number 95563 Answers: 1 Comments: 0

∫((ax^2 +bx+c)/((x−p)(x−q)(x−r)))dx

$$\int\frac{\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}}{\left(\mathrm{x}−\mathrm{p}\right)\left(\mathrm{x}−\mathrm{q}\right)\left(\mathrm{x}−\mathrm{r}\right)}\mathrm{dx} \\ $$

Question Number 95562 Answers: 1 Comments: 0

show that ∫((sin (x−θ))/(sin x))dx=xcos x−sin θlog sin x

$$\mathrm{show}\:\mathrm{that} \\ $$$$\int\frac{\mathrm{sin}\:\left(\mathrm{x}−\theta\right)}{\mathrm{sin}\:\mathrm{x}}\mathrm{dx}=\mathrm{xcos}\:\mathrm{x}−\mathrm{sin}\:\theta\mathrm{log}\:\mathrm{sin}\:\mathrm{x} \\ $$

Question Number 95560 Answers: 1 Comments: 1

Question Number 95557 Answers: 0 Comments: 0

Question Number 95549 Answers: 3 Comments: 0

∫_(−π) ^π ∣cos^3 x∣dx

$$\int_{−\pi} ^{\pi} \mid{cos}^{\mathrm{3}} {x}\mid{dx} \\ $$

Question Number 95548 Answers: 0 Comments: 2

Question Number 95547 Answers: 2 Comments: 0

∫((2x^3 dx)/(2x^2 −4x+3))=?

$$\int\frac{\mathrm{2}{x}^{\mathrm{3}} {dx}}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}}=? \\ $$

Question Number 95546 Answers: 2 Comments: 0

∫x^2 (√(a^2 +x^2 ))dx=?

$$\int{x}^{\mathrm{2}} \sqrt{{a}^{\mathrm{2}} +{x}^{\mathrm{2}} }{dx}=? \\ $$

Question Number 95531 Answers: 0 Comments: 4

((tanx×ctg2x)/(tan^2 x−1))=?

$$\frac{\mathrm{tanx}×\mathrm{ctg2x}}{\mathrm{tan}^{\mathrm{2}} \mathrm{x}−\mathrm{1}}=? \\ $$

Question Number 95524 Answers: 0 Comments: 4

(1/(sin10))−((√3)/(cos10))=?

$$\frac{\mathrm{1}}{\mathrm{sin10}}−\frac{\sqrt{\mathrm{3}}}{\mathrm{cos10}}=? \\ $$

Question Number 95520 Answers: 0 Comments: 0

For 0<x<(π/(6 )), all the values of tan^2 (3x)cos^2 (x)−4tan (3x)sin (2x)+16sin^2 (x) lie in the interval (a). (0,((121)/(36))) (b).(1,((121)/9)) (c). (−1,0) (d). None of these.

$$\mathrm{For}\:\mathrm{0}<\mathrm{x}<\frac{\pi}{\mathrm{6}\:},\:\mathrm{all}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of} \\ $$$$\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{3x}\right)\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{x}\right)−\mathrm{4tan}\:\left(\mathrm{3x}\right)\mathrm{sin}\:\left(\mathrm{2x}\right)+\mathrm{16sin}\:^{\mathrm{2}} \left(\mathrm{x}\right) \\ $$$$\mathrm{lie}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$$$\left(\mathrm{a}\right).\:\left(\mathrm{0},\frac{\mathrm{121}}{\mathrm{36}}\right)\:\left(\mathrm{b}\right).\left(\mathrm{1},\frac{\mathrm{121}}{\mathrm{9}}\right)\:\left(\mathrm{c}\right).\:\left(−\mathrm{1},\mathrm{0}\right)\:\left(\mathrm{d}\right).\:\mathrm{None}\:\mathrm{of}\:\mathrm{these}. \\ $$

Question Number 95518 Answers: 0 Comments: 0

Question Number 95515 Answers: 1 Comments: 0

If A+B+C = π, then sin^2 A+sin^2 B+sin^2 C−2 cos A cos B cos C=

$$\mathrm{If}\:{A}+{B}+{C}\:=\:\pi,\:\mathrm{then} \\ $$$$\mathrm{sin}^{\mathrm{2}} {A}+\mathrm{sin}^{\mathrm{2}} {B}+\mathrm{sin}^{\mathrm{2}} {C}−\mathrm{2}\:\mathrm{cos}\:{A}\:\mathrm{cos}\:{B}\:\mathrm{cos}\:{C}= \\ $$

Question Number 95512 Answers: 0 Comments: 3

If in a △ABC, 8R^2 = a^2 +b^2 +c^2 , then the △ABC is

$$\mathrm{If}\:\:\mathrm{in}\:\mathrm{a}\:\bigtriangleup{ABC},\:\mathrm{8}{R}^{\mathrm{2}} =\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} ,\:\mathrm{then} \\ $$$$\mathrm{the}\:\bigtriangleup{ABC}\:\mathrm{is} \\ $$

Question Number 95509 Answers: 2 Comments: 0

find the angle of plane 2x−y+2z=1 and x+3y−2z = 2

$$\mathrm{find}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{plane} \\ $$$$\mathrm{2x}−\mathrm{y}+\mathrm{2z}=\mathrm{1}\:\mathrm{and}\:\mathrm{x}+\mathrm{3y}−\mathrm{2z}\:=\:\mathrm{2} \\ $$

Question Number 95502 Answers: 1 Comments: 3

6 man + 8 woman ⇒working a job in 10 days 26 man + 48 woman ⇒ in 2 days if 15 man + 20 woman ⇒ ?? days

$$\mathrm{6}\:\mathrm{man}\:+\:\mathrm{8}\:\mathrm{woman}\:\Rightarrow\mathrm{working}\:\mathrm{a}\:\mathrm{job}\:\mathrm{in}\:\mathrm{10}\:\mathrm{days} \\ $$$$\mathrm{26}\:\mathrm{man}\:+\:\mathrm{48}\:\mathrm{woman}\:\Rightarrow\:\mathrm{in}\:\mathrm{2}\:\mathrm{days} \\ $$$$\mathrm{if}\:\mathrm{15}\:\mathrm{man}\:+\:\mathrm{20}\:\mathrm{woman}\:\Rightarrow\:??\:\mathrm{days} \\ $$

Question Number 95495 Answers: 2 Comments: 0

3cos^2 x − 3cos x sin x + 2sin x = 1 x ∈ [ 0, 2π ]

$$\mathrm{3cos}\:^{\mathrm{2}} {x}\:−\:\mathrm{3cos}\:{x}\:\mathrm{sin}\:{x}\:+\:\mathrm{2sin}\:{x}\:=\:\mathrm{1} \\ $$$${x}\:\in\:\left[\:\mathrm{0},\:\mathrm{2}\pi\:\right]\: \\ $$

Question Number 95494 Answers: 0 Comments: 0

Question Number 95485 Answers: 0 Comments: 2

Question Number 95592 Answers: 0 Comments: 1

∫ ((sin 2x)/(sin^4 x + cos^4 x)) dx

$$\int\:\frac{\mathrm{sin}\:\mathrm{2x}}{\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}\:+\:\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}}\:\mathrm{dx} \\ $$

Question Number 95473 Answers: 1 Comments: 0

Question Number 95471 Answers: 0 Comments: 1

(y^2 −6y) how factorise this one?

$$\left(\mathrm{y}^{\mathrm{2}} −\mathrm{6y}\right) \\ $$$$\mathrm{how}\:\mathrm{factorise}\:\mathrm{this}\:\mathrm{one}? \\ $$

Question Number 95469 Answers: 0 Comments: 1

(9b^2 −25) why is this inside the bracket as it is a diffetence of two squares?

$$\left(\mathrm{9b}^{\mathrm{2}} −\mathrm{25}\right) \\ $$$$\mathrm{why}\:\mathrm{is}\:\mathrm{this}\:\mathrm{inside}\:\mathrm{the}\:\mathrm{bracket}\:\mathrm{as}\:\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{diffetence}\:\mathrm{of}\:\mathrm{two}\:\mathrm{squares}? \\ $$

Question Number 95465 Answers: 1 Comments: 0

solve y^(′′) −y^′ +2 =x^2 e^(−x) with y(0) =1 and y^′ (0) =−1

$$\mathrm{solve}\:\mathrm{y}^{''} \:−\mathrm{y}^{'} \:+\mathrm{2}\:\:\:=\mathrm{x}^{\mathrm{2}} \:\mathrm{e}^{−\mathrm{x}} \:\mathrm{with}\:\mathrm{y}\left(\mathrm{0}\right)\:=\mathrm{1}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=−\mathrm{1} \\ $$

Question Number 95464 Answers: 0 Comments: 8

Question Number 95456 Answers: 0 Comments: 0

solve on R y′+xy=y^2 +1 y(0)=a ∈R

$${solve}\:{on}\:\mathbb{R}\: \\ $$$$\:\:{y}'+{xy}={y}^{\mathrm{2}} +\mathrm{1}\:\:\:\:\:\:\:\:{y}\left(\mathrm{0}\right)={a}\:\in\mathbb{R} \\ $$

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