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Question Number 39312 Answers: 5 Comments: 0

prove that (tan 4a+tan 2a)(1−tan^2 3a tan^2 a)=2tan 3a sec^2 a

$${prove}\:{that} \\ $$$$\left({tan}\:\mathrm{4}{a}+{tan}\:\mathrm{2}{a}\right)\left(\mathrm{1}−{tan}^{\mathrm{2}} \mathrm{3}{a}\:{tan}^{\mathrm{2}} {a}\right)=\mathrm{2}{tan}\:\mathrm{3}{a}\:{sec}^{\mathrm{2}} {a} \\ $$

Question Number 39303 Answers: 1 Comments: 1

Question Number 39300 Answers: 1 Comments: 0

Question Number 39298 Answers: 0 Comments: 0

Question Number 39292 Answers: 0 Comments: 3

let f(x)= arctan(2x) 1) calculate f^((n)) (x) then f^((n)) (0) 2) developp f at integr serie 3) let F(t)= ∫_0 ^t arctan(2x)dx developp F at integr serie 4) give F(1) at form of serie.

$${let}\:{f}\left({x}\right)=\:{arctan}\left(\mathrm{2}{x}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{then}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{3}\right)\:{let}\:{F}\left({t}\right)=\:\int_{\mathrm{0}} ^{{t}} \:\:{arctan}\left(\mathrm{2}{x}\right){dx} \\ $$$${developp}\:{F}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{4}\right)\:{give}\:{F}\left(\mathrm{1}\right)\:{at}\:{form}\:{of}\:{serie}. \\ $$

Question Number 39289 Answers: 1 Comments: 0

Find the value of x if the matrix (((3x 5x)),((x 3)) ) (((x 1)),((3 x)) ) has no inverse

$${Find}\:{the}\:{value}\:{of}\:{x}\:{if}\: \\ $$$${the}\:{matrix}\: \\ $$$$ \\ $$$$\begin{pmatrix}{\mathrm{3}{x}\:\:\:\:\:\:\:\:\mathrm{5}{x}}\\{{x}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}}\end{pmatrix}\begin{pmatrix}{{x}\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{3}\:\:\:\:\:\:\:\:\:{x}}\end{pmatrix}\: \\ $$$${has}\:{no}\:{inverse} \\ $$

Question Number 39291 Answers: 0 Comments: 2

let f(x)=(e^(−x^2 ) /(1+x^2 )) developp f at integr serie .

$${let}\:{f}\left({x}\right)=\frac{{e}^{−{x}^{\mathrm{2}} } }{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 39280 Answers: 3 Comments: 1

∫_0 ^(π/2) cos^(10) x.sin 12x dx = ? Given reduction formula : ∫ cos^m x sin nx dx I_(m,n) = −((cos^m x . cosnx)/(m+n)) + (m/(m+n)) I_(m−1,n−1)

$$\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\mathrm{cos}\:^{\mathrm{10}} {x}.\mathrm{sin}\:\mathrm{12}{x}\:{dx}\:=\:? \\ $$$$\mathrm{Given} \\ $$$$\mathrm{reduction}\:\mathrm{formula}\:: \\ $$$$\int\:\mathrm{cos}^{\mathrm{m}} {x}\:{sin}\:{nx}\:{dx}\: \\ $$$$\:\mathrm{I}_{\mathrm{m},\mathrm{n}} =\:−\frac{\mathrm{cos}\:^{\mathrm{m}} {x}\:.\:{cosnx}}{{m}+{n}}\:+\:\frac{{m}}{{m}+{n}}\:\mathrm{I}_{\mathrm{m}−\mathrm{1},\mathrm{n}−\mathrm{1}} \\ $$

Question Number 40946 Answers: 1 Comments: 0

Each of two long straight wires 4cm apart carry equal electric currents and experience a force of 2×10^(−4) N/m. What is the magnitude of the electric current in each?

$${Each}\:{of}\:{two}\:{long}\:{straight}\:{wires}\:\mathrm{4}{cm} \\ $$$${apart}\:{carry}\:{equal}\:{electric}\:{currents} \\ $$$${and}\:{experience}\:{a}\:{force}\:{of}\:\mathrm{2}×\mathrm{10}^{−\mathrm{4}} {N}/{m}. \\ $$$${What}\:{is}\:{the}\:{magnitude}\:{of}\:{the} \\ $$$${electric}\:{current}\:{in}\:{each}? \\ $$

Question Number 40142 Answers: 1 Comments: 1

calculate ∫_(−(π/6)) ^(π/6) ((1+tan(x))/(1+sin(2x)))dx

$${calculate}\:\:\:\:\int_{−\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{6}}} \:\:\:\frac{\mathrm{1}+{tan}\left({x}\right)}{\mathrm{1}+{sin}\left(\mathrm{2}{x}\right)}{dx} \\ $$$$ \\ $$

Question Number 39272 Answers: 0 Comments: 1

∫_0 ^( 2π) (((acos α−bcos θ)dθ)/([a^2 +b^2 −2abcos (θ−α)]^(3/2) )) = ?

$$\int_{\mathrm{0}} ^{\:\:\mathrm{2}\pi} \frac{\left({a}\mathrm{cos}\:\alpha−{b}\mathrm{cos}\:\theta\right){d}\theta}{\left[{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −\mathrm{2}{ab}\mathrm{cos}\:\left(\theta−\alpha\right)\right]^{\mathrm{3}/\mathrm{2}} }\:=\:? \\ $$

Question Number 39267 Answers: 1 Comments: 1

Question Number 39257 Answers: 0 Comments: 0

Question Number 39256 Answers: 0 Comments: 0

Question Number 39255 Answers: 0 Comments: 0

Question Number 39253 Answers: 0 Comments: 2

Question Number 39258 Answers: 0 Comments: 0

Question Number 39237 Answers: 0 Comments: 1

Calculate the triple point for an electrical resistance thermometer, assuming the ratio of resistance at the triple point to that at initial point is 2.0.

$${Calculate}\:{the}\:{triple}\:{point}\:{for}\:{an} \\ $$$${electrical}\:{resistance}\:{thermometer}, \\ $$$${assuming}\:{the}\:{ratio}\:{of}\:{resistance} \\ $$$${at}\:{the}\:{triple}\:{point}\:{to}\:{that}\:{at}\:{initial} \\ $$$${point}\:{is}\:\mathrm{2}.\mathrm{0}. \\ $$

Question Number 39236 Answers: 0 Comments: 3

If a petrol tank costs $2000.00 to fill it up at 10°C ,how much extra dollar must I pay to fill up the tank at 50°C,if the petrol costs $50.00 per litre and its cubic expansivity is 9.5×10^(−4) K^(−1) ?

$${If}\:{a}\:{petrol}\:{tank}\:{costs}\:\$\mathrm{2000}.\mathrm{00}\:{to} \\ $$$${fill}\:{it}\:{up}\:{at}\:\mathrm{10}°{C}\:,{how}\:{much}\:{extra} \\ $$$${dollar}\:{must}\:{I}\:{pay}\:{to}\:{fill}\:{up}\:{the}\:{tank} \\ $$$${at}\:\mathrm{50}°{C},{if}\:{the}\:{petrol}\:{costs}\:\$\mathrm{50}.\mathrm{00} \\ $$$${per}\:{litre}\:{and}\:{its}\:{cubic}\:{expansivity} \\ $$$${is}\:\mathrm{9}.\mathrm{5}×\mathrm{10}^{−\mathrm{4}} {K}^{−\mathrm{1}} ? \\ $$$$ \\ $$

Question Number 39235 Answers: 0 Comments: 1

The length of a mercury column in a mercury in glass thermometer is 4cm at triple point.What is the length of the column when the scale indicates temperature of 560K.

$${The}\:{length}\:{of}\:{a}\:{mercury}\:{column} \\ $$$${in}\:{a}\:{mercury}\:{in}\:{glass}\:{thermometer} \\ $$$${is}\:\mathrm{4}{cm}\:{at}\:{triple}\:{point}.{What}\:{is}\:{the} \\ $$$${length}\:{of}\:{the}\:{column}\:{when}\:{the} \\ $$$${scale}\:{indicates}\:{temperature}\:{of}\:\mathrm{560}{K}. \\ $$

Question Number 39231 Answers: 1 Comments: 0

(sin^(−1) x)^2 + (sin^(−1) y)^2 + 2(sin^(−1) x) (sin^(−1) y)= π^2 ,then x^2 +y^2 is equal to?

$$\left({sin}^{−\mathrm{1}} {x}\right)^{\mathrm{2}} +\:\:\left({sin}^{−\mathrm{1}} {y}\right)^{\mathrm{2}} +\:\:\mathrm{2}\left({sin}^{−\mathrm{1}} {x}\right) \\ $$$$\left({sin}^{−\mathrm{1}} {y}\right)=\:\pi^{\mathrm{2}} ,{then}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:{is}\:{equal}\:{to}? \\ $$

Question Number 39230 Answers: 2 Comments: 0

∫(dα/(sin 2α +sin 3α +sin 5α))=?

$$\int\frac{{d}\alpha}{\mathrm{sin}\:\mathrm{2}\alpha\:+\mathrm{sin}\:\mathrm{3}\alpha\:+\mathrm{sin}\:\mathrm{5}\alpha}=? \\ $$

Question Number 39222 Answers: 1 Comments: 5

Question Number 39218 Answers: 1 Comments: 0

Question Number 39214 Answers: 0 Comments: 1

let f(x)= (e^(−3x) /(x^2 +4)) developp f at integr serie.

$${let}\:{f}\left({x}\right)=\:\frac{{e}^{−\mathrm{3}{x}} }{{x}^{\mathrm{2}} \:+\mathrm{4}} \\ $$$${developp}\:{f}\:\:{at}\:{integr}\:{serie}. \\ $$

Question Number 39204 Answers: 0 Comments: 0

study tbe variation of f(x) =(2x+1)ln(1+e^(−x) ) and give its graph 2) calculate ∫_0 ^4 f(x)dx .

$${study}\:{tbe}\:{variation}\:{of}\:{f}\left({x}\right)\:=\left(\mathrm{2}{x}+\mathrm{1}\right){ln}\left(\mathrm{1}+{e}^{−{x}} \right) \\ $$$${and}\:{give}\:{its}\:{graph} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{4}} \:{f}\left({x}\right){dx}\:. \\ $$

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