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Question Number 224735 Answers: 1 Comments: 0

Let u=((y^2 −x^2 )/(x^2 y^2 )), v=((z^2 −y^2 )/(y^2 z^2 )) for x≠0,y≠0z≠0. Let w=f(u,v), where f is a real valued function defined on R^2 having continuous first order partial derivatives. the value of x^3 (∂w/∂x)+y^3 (∂w/∂y)+z^3 (∂w/∂z) at point (1,2,3) is

$${Let}\:{u}=\frac{{y}^{\mathrm{2}} −{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} {y}^{\mathrm{2}} },\:{v}=\frac{{z}^{\mathrm{2}} −{y}^{\mathrm{2}} }{{y}^{\mathrm{2}} {z}^{\mathrm{2}} }\:{for}\:{x}\neq\mathrm{0},{y}\neq\mathrm{0}{z}\neq\mathrm{0}. \\ $$$${Let}\:{w}={f}\left({u},{v}\right),\:{where}\:{f}\:{is}\:{a}\:{real} \\ $$$${valued}\:{function}\:{defined}\:{on}\:{R}^{\mathrm{2}} \\ $$$${having}\:{continuous}\:{first}\:{order} \\ $$$${partial}\:{derivatives}. \\ $$$${the}\:{value}\:{of} \\ $$$${x}^{\mathrm{3}} \:\frac{\partial{w}}{\partial{x}}+{y}^{\mathrm{3}} \:\frac{\partial{w}}{\partial{y}}+{z}^{\mathrm{3}} \:\frac{\partial{w}}{\partial{z}}\:{at}\:{point}\:\left(\mathrm{1},\mathrm{2},\mathrm{3}\right)\:{is} \\ $$

Question Number 224733 Answers: 1 Comments: 0

Let f be a continuously differentiable function such that ∫_0 ^(2x^2 ) f(t)dt=e^(cos x^2 ) for all x∈(0,∞) the value of f ′(π)=?

$${Let}\:{f}\:{be}\:{a}\:{continuously}\:{differentiable}\:{function} \\ $$$${such}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{2}{x}^{\mathrm{2}} } {f}\left({t}\right){dt}={e}^{\mathrm{cos}\:{x}^{\mathrm{2}} } \:{for}\:{all}\:{x}\in\left(\mathrm{0},\infty\right) \\ $$$${the}\:{value}\:{of}\:{f}\:'\left(\pi\right)=? \\ $$

Question Number 224732 Answers: 0 Comments: 0

The value of n for which the divergence of the function F=(r/ determinant ((r))^n ), r=xi^ +yj^ +zk^ , determinant ((r))≠0, vanishes is a)1 b)−1 c)3 d)−3 p=38

$${The}\:{value}\:{of}\:{n}\:{for}\:{which}\:{the}\:{divergence} \\ $$$${of}\:{the}\:{function} \\ $$$$\mathrm{F}=\frac{\mathrm{r}}{\begin{vmatrix}{\mathrm{r}}\end{vmatrix}^{{n}} },\:\mathrm{r}=\mathrm{x}\hat {\mathrm{i}}+{y}\hat {\mathrm{j}}+{z}\hat {\mathrm{k}},\begin{vmatrix}{\mathrm{r}}\end{vmatrix}\neq\mathrm{0}, \\ $$$${vanishes}\:{is} \\ $$$$\left.{a}\right)\mathrm{1} \\ $$$$\left.{b}\right)−\mathrm{1} \\ $$$$\left.{c}\right)\mathrm{3} \\ $$$$\left.{d}\right)−\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{p}=\mathrm{38} \\ $$

Question Number 224728 Answers: 2 Comments: 2

Question Number 224723 Answers: 0 Comments: 9

So here is what it shows.

$${So}\:{here}\:{is}\:{what}\:{it}\:{shows}. \\ $$

Question Number 224714 Answers: 0 Comments: 1

∫(1/( (√(tan θ)))) dθ

$$\int\frac{\mathrm{1}}{\:\sqrt{\mathrm{tan}\:\theta}}\:{d}\theta \\ $$

Question Number 224713 Answers: 1 Comments: 0

lim_(x→0) (((sin x)/x))^((x−3sin x)/x) .?

$$\:\: \underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}\right)^{\frac{\mathrm{x}−\mathrm{3sin}\:\mathrm{x}}{\mathrm{x}}} .? \\ $$$$\: \\ $$

Question Number 224709 Answers: 1 Comments: 0

Question Number 224702 Answers: 3 Comments: 1

Question Number 224692 Answers: 0 Comments: 10

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Question Number 224691 Answers: 1 Comments: 0

3k+4=n^2 . k,n ∈N Find all n numbers .

$$\mathrm{3}{k}+\mathrm{4}={n}^{\mathrm{2}} .\:{k},{n}\:\in\mathbb{N} \\ $$$${Find}\:{all}\:{n}\:{numbers}\:. \\ $$

Question Number 224688 Answers: 2 Comments: 0

A gun, kept on a straight horizontal road, is used to hit a car travelling along the same road away from it with a uniform speed of 72 km/h. The car is at a distance of 500 m from the gun, when the gun is fired at an angle of 45° with the horizontal. Find the distance of the car from the gun, when the shell hits it. g = 10m/s²

Question Number 224678 Answers: 1 Comments: 8

Guys I just turned 15 today :)

$$\left.\mathrm{Guys}\:\mathrm{I}\:\mathrm{just}\:\mathrm{turned}\:\mathrm{15}\:\mathrm{today}\::\right) \\ $$

Question Number 224672 Answers: 1 Comments: 0

Question Number 224665 Answers: 0 Comments: 5

Question Number 224642 Answers: 1 Comments: 0

Question Number 224641 Answers: 1 Comments: 0

Question Number 224637 Answers: 0 Comments: 0

Question Number 224635 Answers: 1 Comments: 0

Prove that: sin(54°) = (((√5) + 1)/4)

$$\mathrm{Prove}\:\mathrm{that}:\:\:\:\mathrm{sin}\left(\mathrm{54}°\right)\:=\:\:\frac{\sqrt{\mathrm{5}}\:+\:\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 224634 Answers: 1 Comments: 0

$$\: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 224633 Answers: 0 Comments: 0

x+y=2,4 x=2 y=4

$${x}+{y}=\mathrm{2},\mathrm{4} \\ $$$${x}=\mathrm{2} \\ $$$${y}=\mathrm{4} \\ $$

Question Number 224629 Answers: 4 Comments: 0

Question Number 224632 Answers: 0 Comments: 0

Question Number 224623 Answers: 2 Comments: 2

$$\:\: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 224615 Answers: 0 Comments: 1

The vectors OP, OQ and OR represented by a,b and c respectively: where a=10i+j, b=−2i+7j, c=a+3b, and O is the origin. OR and PR intersects at M where OM=kOR and PM=lPQ and k, l are constants. Find: (i) The equation of the lines of PQ and OR (ii) The coordinayes of the point M (iii)The values of the constants k and l

$${The}\:{vectors}\:{OP},\:{OQ}\:{and}\:{OR}\:{represented} \\ $$$${by}\:{a},{b}\:{and}\:{c}\:{respectively}:\:{where}\:{a}=\mathrm{10}{i}+{j}, \\ $$$${b}=−\mathrm{2}{i}+\mathrm{7}{j},\:{c}={a}+\mathrm{3}{b},\:{and}\:{O}\:{is}\:{the}\:{origin}. \\ $$$${OR}\:{and}\:{PR}\:{intersects}\:{at}\:{M}\:{where} \\ $$$${OM}={kOR}\:{and}\:{PM}={lPQ}\:{and}\:{k},\:{l}\:{are} \\ $$$${constants}.\:{Find}: \\ $$$$\left({i}\right)\:{The}\:{equation}\:{of}\:{the}\:{lines}\:{of}\:{PQ}\:{and} \\ $$$${OR} \\ $$$$\left({ii}\right)\:{The}\:{coordinayes}\:{of}\:{the}\:{point}\:{M} \\ $$$$\left({iii}\right){The}\:{values}\:{of}\:{the}\:{constants}\:{k}\:{and}\:{l} \\ $$$$ \\ $$

Question Number 224614 Answers: 1 Comments: 0

A binary operation ∗ is defined on a set real numbers, R by x∗y = 2x + 2y −((xy)/3) . find: (i) The inverse of x under the operation ∗ (ii) Truth set when m∗7=−2∗m

$${A}\:{binary}\:{operation}\:\ast\:{is}\:{defined}\:{on}\:{a}\:{set} \\ $$$${real}\:{numbers},\:{R}\:{by} \\ $$$${x}\ast{y}\:=\:\mathrm{2}{x}\:+\:\mathrm{2}{y}\:−\frac{{xy}}{\mathrm{3}}\:. \\ $$$${find}: \\ $$$$\left({i}\right)\:{The}\:{inverse}\:{of}\:{x}\:{under}\:{the}\:{operation}\:\ast \\ $$$$\left({ii}\right)\:{Truth}\:{set}\:{when}\:{m}\ast\mathrm{7}=−\mathrm{2}\ast{m} \\ $$

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