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Question Number 182441    Answers: 2   Comments: 0

Question Number 182438    Answers: 1   Comments: 0

[Help me!] The rate of change of w = x^3 y^2 z + y^3 z^2 − xz^4 at the point Q(0, 1, 2) in the direction V^→ = 2i + j + 2k is: a) −2 b) −3 c) −4 d) No alternative

$$\: \\ $$$$\:\left[\boldsymbol{\mathrm{Help}}\:\:\boldsymbol{\mathrm{me}}!\right] \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{The}}\:\:\boldsymbol{\mathrm{rate}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{change}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{w}}\:\:=\:\:\boldsymbol{\mathrm{x}}^{\mathrm{3}} \boldsymbol{\mathrm{y}}^{\mathrm{2}} \boldsymbol{\mathrm{z}}\:\:+\:\boldsymbol{\mathrm{y}}^{\mathrm{3}} \boldsymbol{\mathrm{z}}^{\mathrm{2}} \:−\:\boldsymbol{\mathrm{xz}}^{\mathrm{4}} \:\:\boldsymbol{\mathrm{at}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{point}}\:\:\boldsymbol{\mathrm{Q}}\left(\mathrm{0},\:\mathrm{1},\:\mathrm{2}\right) \\ $$$$\:\boldsymbol{\mathrm{in}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{direction}}\:\:\overset{\rightarrow} {\boldsymbol{\mathrm{V}}}\:\:=\:\:\mathrm{2}\boldsymbol{\mathrm{i}}\:\:+\:\:\boldsymbol{\mathrm{j}}\:\:+\:\:\mathrm{2}\boldsymbol{\mathrm{k}}\:\:\boldsymbol{\mathrm{is}}: \\ $$$$\: \\ $$$$\left.\:\boldsymbol{\mathrm{a}}\right)\:−\mathrm{2} \\ $$$$\left.\:\boldsymbol{\mathrm{b}}\right)\:−\mathrm{3} \\ $$$$\left.\:\boldsymbol{\mathrm{c}}\right)\:−\mathrm{4} \\ $$$$\left.\:\boldsymbol{\mathrm{d}}\right)\:\boldsymbol{\mathrm{No}}\:\:\boldsymbol{\mathrm{alternative}} \\ $$$$\: \\ $$

Question Number 182437    Answers: 1   Comments: 0

Question Number 182436    Answers: 1   Comments: 0

Question Number 182435    Answers: 1   Comments: 0

Question Number 182432    Answers: 1   Comments: 0

∫_R (t^2 /((t^2 +a^2 )^(n+1) ))dt =? / a≠o , nεN^∗

$$\int_{{R}} \frac{{t}^{\mathrm{2}} }{\left({t}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{{n}+\mathrm{1}} }{dt}\:=?\:/\:\:{a}\neq{o}\:,\:{n}\epsilon{N}^{\ast} \\ $$

Question Number 182429    Answers: 0   Comments: 1

Question Number 182461    Answers: 2   Comments: 0

Let x be a positive integer multiple of 17 that satisfies the inequality: 0 < ((5(x − 120))/x) < 1 Find the value of x.

$${Let}\:{x}\:{be}\:{a}\:{positive}\:{integer}\:{multiple}\:{of}\:\mathrm{17} \\ $$$${that}\:{satisfies}\:{the}\:{inequality}: \\ $$$$\:\mathrm{0}\:<\:\frac{\mathrm{5}\left({x}\:−\:\mathrm{120}\right)}{{x}}\:<\:\mathrm{1} \\ $$$$\:{Find}\:{the}\:{value}\:{of}\:{x}. \\ $$

Question Number 182459    Answers: 0   Comments: 21

Question Number 182457    Answers: 0   Comments: 0

$$ \\ $$

Question Number 182456    Answers: 0   Comments: 1

Question Number 182423    Answers: 4   Comments: 0

Question Number 182407    Answers: 1   Comments: 0

Question Number 182404    Answers: 0   Comments: 0

Question Number 182405    Answers: 1   Comments: 1

Zombie apocalypse has started. You are at point A (3,2). At point B (−5,4) there is a shelter. A river flows along the X axis. You are running at a constant velocity 1 ms^(−1) with an intention to reach the shelter but before that, you have to reach the river and fill-up your water jar. What is the lowest time it takes to reach B from A? [It takes 1 second time to fill the jar with water.] a) 11.0 s b) 8.24 s c) 10.1 s d) 9 s

$${Zombie}\:{apocalypse}\:{has}\:{started}.\:{You} \\ $$$${are}\:{at}\:{point}\:{A}\:\left(\mathrm{3},\mathrm{2}\right).\:{At}\:{point}\:{B}\:\left(−\mathrm{5},\mathrm{4}\right) \\ $$$${there}\:{is}\:{a}\:{shelter}.\:{A}\:{river}\:{flows}\:{along}\: \\ $$$${the}\:{X}\:{axis}.\:{You}\:{are}\:{running}\:{at}\:{a}\:{constant} \\ $$$${velocity}\:\mathrm{1}\:{ms}^{−\mathrm{1}} \:{with}\:{an}\:{intention}\:{to} \\ $$$${reach}\:{the}\:{shelter}\:{but}\:{before}\:{that},\:{you} \\ $$$${have}\:{to}\:{reach}\:{the}\:{river}\:{and}\:{fill}-{up}\:{your} \\ $$$${water}\:{jar}.\:{What}\:{is}\:{the}\:{lowest}\:{time}\:{it}\: \\ $$$${takes}\:{to}\:{reach}\:{B}\:{from}\:{A}?\:\left[{It}\:{takes}\:\mathrm{1}\:{second}\right. \\ $$$$\left.{time}\:{to}\:{fill}\:{the}\:{jar}\:{with}\:{water}.\right]\: \\ $$$$ \\ $$$$\left.{a}\right)\:\mathrm{11}.\mathrm{0}\:{s} \\ $$$$\left.{b}\right)\:\mathrm{8}.\mathrm{24}\:{s} \\ $$$$\left.{c}\right)\:\mathrm{10}.\mathrm{1}\:{s} \\ $$$$\left.{d}\right)\:\mathrm{9}\:{s} \\ $$

Question Number 182394    Answers: 1   Comments: 1

Question Number 182392    Answers: 2   Comments: 1

Question Number 182390    Answers: 0   Comments: 0

Question Number 182379    Answers: 2   Comments: 1

Can we show a+b<a^2 −ab+b^2 ∀ a,b∈N

$$\mathrm{Can}\:\mathrm{we}\:\mathrm{show}\:\mathrm{a}+\mathrm{b}<\mathrm{a}^{\mathrm{2}} −\mathrm{ab}+\mathrm{b}^{\mathrm{2}} \\ $$$$\forall\:\mathrm{a},\mathrm{b}\in\mathbb{N} \\ $$

Question Number 182370    Answers: 0   Comments: 1

How to find kenetic energy of one mol Helium gas?

$${How}\:{to}\:{find}\:{kenetic}\:{energy}\:{of}\:{one}\:{mol}\:{Helium}\:{gas}? \\ $$

Question Number 182369    Answers: 1   Comments: 2

Find radius and center of (S): (S): { ((x+y+z=4)),((y^2 +yz+z^2 =4(y+z))) :}

$${Find}\:{radius}\:{and}\:{center}\:{of}\:\left({S}\right): \\ $$$$\left({S}\right):\begin{cases}{{x}+{y}+{z}=\mathrm{4}}\\{{y}^{\mathrm{2}} +{yz}+{z}^{\mathrm{2}} =\mathrm{4}\left({y}+{z}\right)}\end{cases} \\ $$

Question Number 182368    Answers: 1   Comments: 0

find volume of region in R^3 given by 3∣x∣ + 4∣y∣ +3∣z∣ ≤12 is

$$\:\:\:\:\mathrm{find}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{region}\:\mathrm{in}\:\:\mathbb{R}^{\mathrm{3}} \:\:\mathrm{given}\:\mathrm{by}\: \\ $$$$\:\:\:\:\mathrm{3}\mid\mathrm{x}\mid\:+\:\mathrm{4}\mid\mathrm{y}\mid\:+\mathrm{3}\mid\mathrm{z}\mid\:\leqslant\mathrm{12}\:\:\mathrm{is} \\ $$

Question Number 182367    Answers: 1   Comments: 0

find volume of region bounded above by z = 1+(√(1−x^2 −y^2 )) and below by z = (√(x^2 +y^2 ))

$$ \\ $$$$\:\:\:\:\mathrm{find}\:\mathrm{volume}\:\mathrm{of}\:\:\mathrm{region}\:\mathrm{bounded}\:\mathrm{above}\: \\ $$$$\:\:\:\mathrm{by}\:\mathrm{z}\:=\:\mathrm{1}+\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \:}\:\:\mathrm{and}\:\mathrm{below} \\ $$$$\:\:\:\:\mathrm{by}\:\:\:\mathrm{z}\:=\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:}\: \\ $$

Question Number 182360    Answers: 1   Comments: 5

In equation ax^2 +bx+c=0, a,b,c are randomly selected from integers; what is the probability that roots will be real?

$$\mathrm{In}\:\mathrm{equation}\:\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}=\mathrm{0},\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{are} \\ $$$$\mathrm{randomly}\:\mathrm{selected}\:\mathrm{from}\:\mathrm{integers}; \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{roots} \\ $$$$\mathrm{will}\:\mathrm{be}\:\mathrm{real}? \\ $$

Question Number 182348    Answers: 1   Comments: 0

∫_0 ^2 ∫_0 ^3 ∫_0 ^4 e^(x+y+z) dx dy dz=?

$$\int_{\mathrm{0}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\mathrm{3}} \int_{\mathrm{0}} ^{\mathrm{4}} {e}^{{x}+{y}+{z}} {dx}\:{dy}\:{dz}=? \\ $$

Question Number 182347    Answers: 1   Comments: 0

s(x)=Σ_(nεN) ^(+oo ) ((n^2 (n+1)^2 )/(n!))x^n =?

$${s}\left({x}\right)=\underset{{n}\epsilon{N}} {\overset{+{oo}\:\:} {\sum}}\:\frac{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{2}} }{{n}!}{x}^{{n}} =? \\ $$

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