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Question Number 39016 Answers: 0 Comments: 0

calculate ∫_0 ^π ((sin(nx))/(cosx))dx with n from N .

$${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{sin}\left({nx}\right)}{{cosx}}{dx}\:\:{with}\:{n}\:{from}\:{N}\:. \\ $$

Question Number 39015 Answers: 0 Comments: 2

find ∫ (dx/(x(2x+1)(3x+2))) 2) calculate ∫_1 ^2 (dx/(x(2x+1)(3x+2)))

$${find}\:\:\int\:\:\:\:\:\:\frac{{dx}}{{x}\left(\mathrm{2}{x}+\mathrm{1}\right)\left(\mathrm{3}{x}+\mathrm{2}\right)} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\:\:\:\frac{{dx}}{{x}\left(\mathrm{2}{x}+\mathrm{1}\right)\left(\mathrm{3}{x}+\mathrm{2}\right)} \\ $$

Question Number 39013 Answers: 0 Comments: 1

Given the matrices A = ((3,5),(2,4) ) and I = ((1,0),(0,1) ) find matrix B if BA= I find A′ the reflection on the line y = x and A′′ the enlargement with matrix (((2 0)),((0 2)) ).

$${Given}\:{the}\:{matrices} \\ $$$${A}\:=\:\begin{pmatrix}{\mathrm{3}}&{\mathrm{5}}\\{\mathrm{2}}&{\mathrm{4}}\end{pmatrix}\:{and}\:{I}\:=\:\begin{pmatrix}{\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{1}}\end{pmatrix} \\ $$$${find}\:{matrix}\:{B}\:{if}\: \\ $$$${BA}=\:{I} \\ $$$${find}\:{A}'\:{the}\:{reflection}\:{on}\:{the} \\ $$$${line}\:{y}\:=\:{x}\:{and}\:{A}''\:{the}\:{enlargement} \\ $$$${with}\:{matrix}\:\begin{pmatrix}{\mathrm{2}\:\:\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\end{pmatrix}. \\ $$

Question Number 39053 Answers: 1 Comments: 0

Question Number 39003 Answers: 2 Comments: 0

Question Number 38982 Answers: 0 Comments: 9

Question Number 38967 Answers: 1 Comments: 8

Question Number 38996 Answers: 1 Comments: 1

a line with equation y = 2x + 5.the point (1,7) lie on this line.find the distance between this line and the line joining (2,3) and (6,7).

$${a}\:{line}\:{with}\:{equation} \\ $$$$\:{y}\:=\:\mathrm{2}{x}\:+\:\mathrm{5}.{the}\:{point}\:\left(\mathrm{1},\mathrm{7}\right) \\ $$$${lie}\:{on}\:{this}\:{line}.{find}\:{the}\: \\ $$$${distance}\:{between}\:{this}\:{line}\: \\ $$$${and}\:{the}\:{line}\:{joining}\: \\ $$$$\left(\mathrm{2},\mathrm{3}\right)\:{and}\:\left(\mathrm{6},\mathrm{7}\right). \\ $$

Question Number 38960 Answers: 1 Comments: 0

Question Number 38957 Answers: 1 Comments: 1

solve for x e^(2x) + 2e^x + 1 = 0

$${solve}\:{for}\:{x}\: \\ $$$${e}^{\mathrm{2}{x}} \:+\:\mathrm{2}{e}^{{x}} \:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$

Question Number 38946 Answers: 0 Comments: 0

find ∫ arcos(2(√(1−x^2 )))dx .

$${find}\:\int\:{arcos}\left(\mathrm{2}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right){dx}\:. \\ $$

Question Number 38942 Answers: 0 Comments: 1

find Σ_(n=1) ^∞ (((−1)^n )/n)cos(nx) and Σ_(n=1) ^∞ (((−1)^n )/n)sin(nx)

$${find}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}}{cos}\left({nx}\right)\:{and}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}}{sin}\left({nx}\right) \\ $$

Question Number 38939 Answers: 2 Comments: 2

Question Number 38936 Answers: 1 Comments: 1

Question Number 38933 Answers: 0 Comments: 9

[Refreshing an old question] Find the smallest number which is a multiple of 75 and has 75 divisors.

$$\left[{Refreshing}\:{an}\:{old}\:{question}\right] \\ $$$${Find}\:{the}\:{smallest}\:{number}\:{which}\:{is} \\ $$$${a}\:{multiple}\:{of}\:\mathrm{75}\:{and}\:{has}\:\mathrm{75}\:{divisors}. \\ $$

Question Number 38923 Answers: 1 Comments: 0

A glass prism made from a material of refractive index 1.55 has a refracting angle of 60°.The prism is immersed in water of refractive index 1.33.Determine the angle of minimum deviation for a parallel beam of light passing through the prism.

$${A}\:{glass}\:{prism}\:{made}\:{from}\:{a}\:{material} \\ $$$${of}\:{refractive}\:{index}\:\mathrm{1}.\mathrm{55}\:{has}\:{a} \\ $$$${refracting}\:{angle}\:{of}\:\mathrm{60}°.{The}\:{prism} \\ $$$${is}\:{immersed}\:{in}\:{water}\:{of}\:{refractive} \\ $$$${index}\:\mathrm{1}.\mathrm{33}.{Determine}\:{the}\:{angle}\:{of} \\ $$$${minimum}\:{deviation}\:{for}\:{a}\:{parallel} \\ $$$${beam}\:{of}\:{light}\:{passing}\:{through}\:{the} \\ $$$${prism}. \\ $$

Question Number 38925 Answers: 1 Comments: 0

Calculate the deviation of a ray of light,which is incident on a plane mirror at an angle of 40°.

$${Calculate}\:{the}\:{deviation}\:{of}\:{a}\:{ray}\:{of} \\ $$$${light},{which}\:{is}\:{incident}\:{on}\:{a}\:{plane} \\ $$$${mirror}\:{at}\:{an}\:{angle}\:{of}\:\mathrm{40}°. \\ $$

Question Number 38907 Answers: 1 Comments: 5

(√(c^2 +x^2 )) = 1+(c/x) how many complex roots ?

$$\sqrt{{c}^{\mathrm{2}} +{x}^{\mathrm{2}} }\:=\:\mathrm{1}+\frac{{c}}{{x}} \\ $$$${how}\:{many}\:{complex}\:{roots}\:? \\ $$

Question Number 38905 Answers: 1 Comments: 0

Question Number 38910 Answers: 1 Comments: 0

Given a polynomial f(x) where f(x) = x^3 + ax^2 + 3x + b and ( x− 1) is a factor of f(x) and f ′(x)= 12 at point ( 2,4) find the values of a and b hence factorise f(x) completely

$${Given}\:{a}\:{polynomial}\:{f}\left({x}\right)\:{where} \\ $$$${f}\left({x}\right)\:=\:{x}^{\mathrm{3}} \:+\:{ax}\:^{\mathrm{2}} \:+\:\mathrm{3}{x}\:+\:{b} \\ $$$${and}\:\left(\:{x}−\:\mathrm{1}\right)\:{is}\:{a}\:{factor}\:{of}\:{f}\left({x}\right) \\ $$$${and}\:{f}\:'\left({x}\right)=\:\:\mathrm{12}\:{at}\:{point}\:\left(\:\mathrm{2},\mathrm{4}\right) \\ $$$${find}\:{the}\:{values}\:{of}\:{a}\:{and}\:{b} \\ $$$${hence}\:{factorise}\:{f}\left({x}\right)\:{completely} \\ $$$$ \\ $$

Question Number 38899 Answers: 0 Comments: 4

find ∫_0 ^π ln(2+cost)dt and ∫_0 ^π ln(2−cost)dt

$${find}\:\int_{\mathrm{0}} ^{\pi} {ln}\left(\mathrm{2}+{cost}\right){dt}\:{and}\:\int_{\mathrm{0}} ^{\pi} {ln}\left(\mathrm{2}−{cost}\right){dt} \\ $$

Question Number 38898 Answers: 0 Comments: 1

find nature od the seri Σ_(n=1) ^∞ ((n(−1)^([x]) )/(1+n[x]^3 ))

$${find}\:{nature}\:{od}\:{the}\:{seri}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{n}\left(−\mathrm{1}\right)^{\left[{x}\right]} }{\mathrm{1}+{n}\left[{x}\right]^{\mathrm{3}} } \\ $$

Question Number 38897 Answers: 0 Comments: 0

find ∫ ln((√x) +(√(x+1)) +(√(x+2)))dx

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

Question Number 38896 Answers: 1 Comments: 2

let A_n = ∫_0 ^n ((x[x])/(1+x^2 )) dx 1) calculate A_n 2) find lim_(n→+∞) A_n