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Question Number 42500 Answers: 0 Comments: 2

calculate I = ∫_0 ^(2π) ((cos(2x))/(cosx +sinx))dx and J =∫_0 ^(2π) ((sin(2x))/(cosx +sinx))dx

$${calculate}\:\:\:{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{{cosx}\:+{sinx}}{dx}\:{and}\:{J}\:=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{{cosx}\:+{sinx}}{dx} \\ $$

Question Number 42497 Answers: 0 Comments: 1

A body cools from 90°C to 40°C in 2 minutes at a temperature,20°C of the surrounding.Calculate the temperature of the body after another 5 minutes.

$${A}\:{body}\:{cools}\:{from}\:\mathrm{90}°{C}\:{to}\:\mathrm{40}°{C}\:{in} \\ $$$$\mathrm{2}\:{minutes}\:{at}\:{a}\:{temperature},\mathrm{20}°{C} \\ $$$${of}\:{the}\:{surrounding}.{Calculate}\:{the} \\ $$$${temperature}\:{of}\:{the}\:{body}\:{after} \\ $$$${another}\:\mathrm{5}\:{minutes}. \\ $$

Question Number 42495 Answers: 0 Comments: 0

In the sequence 1, 22, 333, ... 10101010101010101010, 1111111111111111111111, ... The sum of the digits in the 200th term is ??

$$\mathrm{In}\:\mathrm{the}\:\mathrm{sequence}\:\:\mathrm{1},\:\mathrm{22},\:\mathrm{333},\:...\:\mathrm{10101010101010101010},\:\mathrm{1111111111111111111111},\:... \\ $$$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{in}\:\mathrm{the}\:\mathrm{200th}\:\mathrm{term}\:\mathrm{is}\:?? \\ $$

Question Number 42494 Answers: 1 Comments: 1

In the sequence of numbers 1, 2, 11, 22, 111, 222, ... the sum of the digits in 999th terms is ??

$$\mathrm{In}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{of}\:\mathrm{numbers}\:\:\mathrm{1},\:\mathrm{2},\:\mathrm{11},\:\mathrm{22},\:\mathrm{111},\:\mathrm{222},\:...\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits} \\ $$$$\mathrm{in}\:\mathrm{999th}\:\mathrm{terms}\:\mathrm{is}\:?? \\ $$

Question Number 42493 Answers: 0 Comments: 1

calculate lim_(n→+∞) Σ_(1≤i<j≤n) (1/(i^x j^x )) with x>1 for that consider ξ(x) =Σ_(n=1) ^∞ (1/n^x ) 2) calculate lim_(n→+∞) Σ_(1≤i<j≤n) (1/((ij)^2 )) .

$$\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\sum_{\mathrm{1}\leqslant{i}<{j}\leqslant{n}} \:\:\:\:\:\frac{\mathrm{1}}{{i}^{{x}} {j}^{{x}} }\:\:\:{with}\:\:{x}>\mathrm{1}\:\:{for}\:{that}\:{consider} \\ $$$$\xi\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{{x}} } \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:\sum_{\mathrm{1}\leqslant{i}<{j}\leqslant{n}} \:\:\:\:\:\:\frac{\mathrm{1}}{\left({ij}\right)^{\mathrm{2}} }\:. \\ $$

Question Number 42492 Answers: 2 Comments: 0

let x>0 ,y>0,z>0 prove that (x^2 /(yz)) +(y^2 /(xz)) +(z^2 /(xy)) ≥3 .

$${let}\:{x}>\mathrm{0}\:,{y}>\mathrm{0},{z}>\mathrm{0}\:\:\:{prove}\:{that}\:\:\frac{{x}^{\mathrm{2}} }{{yz}}\:+\frac{{y}^{\mathrm{2}} }{{xz}}\:+\frac{{z}^{\mathrm{2}} }{{xy}}\:\geqslant\mathrm{3}\:. \\ $$

Question Number 42490 Answers: 0 Comments: 0

find L(arctanx) .L means laplace transform .

$${find}\:{L}\left({arctanx}\right)\:\:.{L}\:{means}\:{laplace}\:{transform}\:. \\ $$

Question Number 42489 Answers: 0 Comments: 1

calculate L (sinxe^(−ax) ) with a>0 L means laplace transform .

$${calculate}\:{L}\:\left({sinxe}^{−{ax}} \right)\:\:\:{with}\:{a}>\mathrm{0}\:\:{L}\:{means}\:{laplace}\:{transform}\:. \\ $$

Question Number 42488 Answers: 1 Comments: 1

find ∫ (1+(1/t^2 ))arctan(t−(1/t))dt .

$${find}\:\:\int\:\:\:\left(\mathrm{1}+\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\right){arctan}\left({t}−\frac{\mathrm{1}}{{t}}\right){dt}\:. \\ $$

Question Number 42487 Answers: 0 Comments: 3

let f(x) = ∫_0 ^1 (dt/(x +ch(t))) 1) find a explicite form of f(x) 2) calculate ∫_0 ^1 (dt/((x+ch(t))^2 )) 3) find the value of ∫_0 ^1 (dt/(1+ch(t))) and ∫_0 ^1 (dt/(2+ch(t))) 4) find the value of ∫_0 ^1 (dt/((1+cht)^2 )) and ∫_0 ^1 (dt/((2+cht)^2 ))

$${let}\:\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\:\:\frac{{dt}}{{x}\:+{ch}\left({t}\right)} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicite}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:\:{calculate}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\left({x}+{ch}\left({t}\right)\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\:\frac{{dt}}{\mathrm{1}+{ch}\left({t}\right)}\:{and}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\mathrm{2}+{ch}\left({t}\right)} \\ $$$$\left.\mathrm{4}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{\left(\mathrm{1}+{cht}\right)^{\mathrm{2}} }\:\:{and}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{\left(\mathrm{2}+{cht}\right)^{\mathrm{2}} } \\ $$

Question Number 42479 Answers: 1 Comments: 0

two digit number is seven times the sum of its digits.if 27 is substracted from the number its digits get interchanged. find the number

Question Number 42481 Answers: 0 Comments: 0

find f(x)= ∫_0 ^(π/4) ln(1+xtant)dt .

$${find}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}+{xtant}\right){dt}\:. \\ $$

Question Number 42482 Answers: 0 Comments: 3

let f(x)=e^(−2x) arctan(x) 1) calculate f^((n)) (x) 2) calculate f^((n)) (0) 3) developp f at integr serie .

$${let}\:{f}\left({x}\right)={e}^{−\mathrm{2}{x}} \:{arctan}\left({x}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 42475 Answers: 0 Comments: 1

A signpost 4.5cm high is 30cm away⊛ from Mrs Rahup.What is the height of the image formed in her retina?(Take the eye lens-retina distance as 1.5cm).

$${A}\:{signpost}\:\mathrm{4}.\mathrm{5}{cm}\:{high}\:{is}\:\mathrm{30}{cm}\:{away}\circledast \\ $$$${from}\:{Mrs}\:{Rahup}.{What}\:{is}\:{the} \\ $$$${height}\:{of}\:{the}\:{image}\:{formed}\:{in}\:{her} \\ $$$${retina}?\left({Take}\:{the}\:{eye}\:{lens}-{retina}\right. \\ $$$$\left.{distance}\:{as}\:\mathrm{1}.\mathrm{5}{cm}\right). \\ $$

Question Number 42474 Answers: 0 Comments: 0

Question Number 42473 Answers: 0 Comments: 0

Question Number 42472 Answers: 0 Comments: 0

Question Number 42471 Answers: 0 Comments: 0

Question Number 42470 Answers: 0 Comments: 0

Question Number 42469 Answers: 0 Comments: 0

Question Number 42468 Answers: 0 Comments: 0

Question Number 42463 Answers: 1 Comments: 1

let y =(√(x+(√(x+(√(x+2)))))) calculate (dy/dx)

$${let}\:{y}\:\:=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\mathrm{2}}}} \\ $$$${calculate}\:\:\frac{{dy}}{{dx}} \\ $$

Question Number 42458 Answers: 0 Comments: 0

a boy is in front of a wall.The distance between boy and wall is 12ft.the boy is moving towards the wall in such a way that half the distance between the wall and him is crossed in one minutes.So find the time the boy reach to the wall

$${a}\:{boy}\:{is}\:{in}\:{front}\:{of}\:{a}\:{wall}.{The}\:{distance}\:{between} \\ $$$${boy}\:{and}\:{wall}\:{is}\:\mathrm{12}{ft}.{the}\:{boy}\:{is}\:{moving}\:{towards} \\ $$$${the}\:{wall}\:{in}\:{such}\:{a}\:{way}\:{that}\:\boldsymbol{{half}}\:\boldsymbol{{the}}\:\boldsymbol{{distance}} \\ $$$$\boldsymbol{{between}}\:\boldsymbol{{the}}\:\boldsymbol{{wall}}\:\boldsymbol{{and}}\:\boldsymbol{{him}}\:\boldsymbol{{is}}\:\boldsymbol{{crossed}}\:\boldsymbol{{in}}\:\boldsymbol{{one}} \\ $$$$\boldsymbol{{minutes}}.\boldsymbol{{S}}{o}\:{find}\:{the}\:{time}\:{the}\:{boy}\:{reach}\:{to}\:{the}\:{wall} \\ $$

Question Number 42448 Answers: 3 Comments: 0

Question Number 42446 Answers: 2 Comments: 1

Question Number 42445 Answers: 0 Comments: 0

find A_n = ∫_0 ^(π/4) tan^n t dt with n integer natural .

$${find}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:{tan}^{{n}} {t}\:{dt}\:\:\:{with}\:{n}\:{integer}\:{natural}\:. \\ $$

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