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Question Number 51494 Answers: 0 Comments: 2

Solve: (t^2 + 1) (dp/dt) = p^t

$$\mathrm{Solve}:\:\:\:\:\:\:\:\:\left(\mathrm{t}^{\mathrm{2}} \:+\:\mathrm{1}\right)\:\frac{\mathrm{dp}}{\mathrm{dt}}\:\:=\:\:\mathrm{p}^{\mathrm{t}} \\ $$

Question Number 51492 Answers: 1 Comments: 0

For ellipse 16x^2 +4y^2 +96x−8y−84=0 find i)centre ii)verteces iii)focus iv)directrix v)length of major and minor axis vi)ecentricity vii)graph the ellipse

$${For}\:{ellipse}\: \\ $$$$\mathrm{16}{x}^{\mathrm{2}} +\mathrm{4}{y}^{\mathrm{2}} +\mathrm{96}{x}−\mathrm{8}{y}−\mathrm{84}=\mathrm{0} \\ $$$${find} \\ $$$$\left.{i}\right){centre} \\ $$$$\left.{ii}\right){verteces} \\ $$$$\left.{iii}\right){focus} \\ $$$$\left.{iv}\right){directrix} \\ $$$$\left.{v}\right){length}\:{of}\:{major}\: \\ $$$${and}\:{minor}\:{axis} \\ $$$$\left.{vi}\right){ecentricity} \\ $$$$\left.{vii}\right){graph}\:{the}\:{ellipse} \\ $$

Question Number 51489 Answers: 1 Comments: 0

Given that y=mx+c is equation of tangent to the ellipse (x^2 /a^(2 ) )+(y^2 /b^2 )=1 find coordinate of point of contact.

$${Given}\:{that}\:{y}={mx}+{c} \\ $$$${is}\:{equation}\:{of}\:\:{tangent} \\ $$$${to}\:{the}\:{ellipse}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}\:} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1} \\ $$$${find}\:{coordinate}\:{of}\: \\ $$$${point}\:{of}\:{contact}. \\ $$

Question Number 51485 Answers: 0 Comments: 1

Question Number 51520 Answers: 1 Comments: 1

Question Number 51448 Answers: 0 Comments: 3

Question Number 51446 Answers: 1 Comments: 0

f(x)=(√((1−x^2 )/(x^2 +1))) f^′ (−2)=...

$${f}\left({x}\right)=\sqrt{\frac{\mathrm{1}−{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{1}}} \\ $$$${f}^{'} \left(−\mathrm{2}\right)=... \\ $$

Question Number 51436 Answers: 1 Comments: 0

If y = (((e^x + e^(−x) ). tanh x)/(e^x − sinh x)) prove that y′ = 2 sech^2 x

$$\mathrm{If}\:\:\:\:\mathrm{y}\:=\:\frac{\left(\mathrm{e}^{\mathrm{x}} \:+\:\mathrm{e}^{−\mathrm{x}} \right).\:\mathrm{tanh}\:\mathrm{x}}{\mathrm{e}^{\mathrm{x}} \:−\:\mathrm{sinh}\:\mathrm{x}} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\:\:\:\:\:\:\mathrm{y}'\:\:=\:\:\mathrm{2}\:\mathrm{sech}^{\mathrm{2}} \:\mathrm{x} \\ $$

Question Number 51431 Answers: 3 Comments: 3

Find x and y x^2 + y^2 = 25 ...... (i) x^3 + y^3 = 91 ....... (ii)

$$\mathrm{Find}\:\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\:\:\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:\:=\:\:\mathrm{25}\:\:\:\:\:......\:\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:\:=\:\:\mathrm{91}\:\:\:.......\:\left(\mathrm{ii}\right) \\ $$

Question Number 51466 Answers: 1 Comments: 5

Question Number 51465 Answers: 2 Comments: 4

Question Number 51456 Answers: 1 Comments: 0

∫ (x^8 /(x^6 + 64)) dx

$$\int\:\:\:\frac{\mathrm{x}^{\mathrm{8}} }{\mathrm{x}^{\mathrm{6}} \:+\:\mathrm{64}}\:\mathrm{dx} \\ $$

Question Number 51421 Answers: 2 Comments: 3

∫ ((tan^(−1) x)/x^2 ) dx

$$\int\:\:\frac{\mathrm{tan}^{−\mathrm{1}} \mathrm{x}}{\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{dx} \\ $$

Question Number 51420 Answers: 2 Comments: 0

∫ (e^(3x) /(1 + e^x )) dx

$$\int\:\:\frac{\mathrm{e}^{\mathrm{3x}} }{\mathrm{1}\:+\:\mathrm{e}^{\mathrm{x}} }\:\mathrm{dx} \\ $$

Question Number 51419 Answers: 1 Comments: 0

∫ ((√x)/(1 + (x)^(1/3) )) dx

$$\int\:\frac{\sqrt{\mathrm{x}}}{\mathrm{1}\:+\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}}}\:\mathrm{dx} \\ $$

Question Number 51394 Answers: 1 Comments: 0

∫ (1/(1 + (√(tan x)))) dx

$$\int\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\sqrt{\mathrm{tan}\:\mathrm{x}}}\:\:\mathrm{dx} \\ $$

Question Number 51389 Answers: 1 Comments: 2

Question Number 51372 Answers: 1 Comments: 1

Question Number 51368 Answers: 0 Comments: 8

Question Number 51367 Answers: 3 Comments: 0

Evaluate: cot^(−1) [(((√(1−sinx))+(√(1+sinx)))/((√(1−sinx))−(√(1+sinx))))] = ?

$${Evaluate}: \\ $$$$\mathrm{cot}^{−\mathrm{1}} \left[\frac{\sqrt{\mathrm{1}−\mathrm{sin}{x}}+\sqrt{\mathrm{1}+\mathrm{sin}{x}}}{\sqrt{\mathrm{1}−\mathrm{sin}{x}}−\sqrt{\mathrm{1}+\mathrm{sin}{x}}}\right]\:=\:? \\ $$

Question Number 51360 Answers: 0 Comments: 0

Question Number 51364 Answers: 0 Comments: 2

The value of x for which sin(cot^(−1) (1+x))=cos(tan^(−1) x) is ?

$${The}\:{value}\:{of}\:{x}\:{for}\:{which} \\ $$$$\mathrm{sin}\left(\mathrm{cot}^{−\mathrm{1}} \left(\mathrm{1}+{x}\right)\right)=\mathrm{cos}\left(\mathrm{tan}^{−\mathrm{1}} {x}\right)\:{is}\:? \\ $$

Question Number 51356 Answers: 2 Comments: 1

Evaluate : tan {(1/2)cos^(−1) ((√5)/3)} ?

$${Evaluate}\:: \\ $$$$\mathrm{tan}\:\left\{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}^{−\mathrm{1}} \frac{\sqrt{\mathrm{5}}}{\mathrm{3}}\right\}\:? \\ $$

Question Number 51353 Answers: 4 Comments: 1

Question Number 51403 Answers: 0 Comments: 0

Question Number 51325 Answers: 1 Comments: 0

If a number of little droplets all of the same radius r coalesce to form a single drop of radius R.show that the rise in temperature is given by ((3T)/(pJ))((1/r)−(1/R)) where T is surface tension of water and J is mechanical equivalent of heat

$${If}\:{a}\:{number}\:{of}\:{little}\: \\ $$$${droplets}\:{all}\:{of}\:{the}\:{same}\: \\ $$$${radius}\:{r}\:{coalesce}\:{to} \\ $$$${form}\:\:{a}\:{single} \\ $$$${drop}\:{of}\:{radius}\:{R}.{show} \\ $$$${that}\:{the}\:{rise}\:{in}\:{temperature} \\ $$$${is}\:{given}\:{by} \\ $$$$\frac{\mathrm{3}{T}}{{pJ}}\left(\frac{\mathrm{1}}{{r}}−\frac{\mathrm{1}}{{R}}\right) \\ $$$${where}\:\:{T}\:{is}\:{surface}\:{tension} \\ $$$${of}\:{water}\:{and}\:{J}\:{is}\:{mechanical} \\ $$$${equivalent}\:{of}\:{heat} \\ $$

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