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Question Number 179105    Answers: 2   Comments: 0

1. Compare: Ο€^(2022e) and e^(2022𝛑) 2. Compute value of P = Ο€^𝛑^𝛑^(...^𝛑 )

$$\mathrm{1}.\:\mathrm{Compare}:\:\:\:\pi^{\mathrm{2022}\boldsymbol{\mathrm{e}}} \:\:\:\mathrm{and}\:\:\:\mathrm{e}^{\mathrm{2022}\boldsymbol{\pi}} \\ $$$$\mathrm{2}.\:\mathrm{Compute}\:\mathrm{value}\:\mathrm{of}\:\:\:\mathrm{P}\:=\:\pi^{\boldsymbol{\pi}^{\boldsymbol{\pi}^{...^{\boldsymbol{\pi}} } } } \\ $$

Question Number 179100    Answers: 4   Comments: 2

if x^2 +y^2 +xy=5, find the range of x^2 +y^2 βˆ’xy. (x,y ∈R)

$${if}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{xy}=\mathrm{5},\:{find}\:{the}\:{range}\:{of} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} βˆ’{xy}. \\ $$$$\left({x},{y}\:\in\mathbb{R}\right) \\ $$

Question Number 179095    Answers: 2   Comments: 1

Question Number 179094    Answers: 0   Comments: 1

determine 1)L^βˆ’ [((s^3 +3)/(s(s^2 +9)))] 2)L^βˆ’ [(4/((s^2 +2s+5)^2 ))] L^βˆ’ is the inverse laplace transform

$${determine} \\ $$$$\left.\mathrm{1}\right)\mathcal{L}^{βˆ’} \left[\frac{{s}^{\mathrm{3}} +\mathrm{3}}{{s}\left({s}^{\mathrm{2}} +\mathrm{9}\right)}\right] \\ $$$$\left.\mathrm{2}\right)\mathcal{L}^{βˆ’} \left[\frac{\mathrm{4}}{\left({s}^{\mathrm{2}} +\mathrm{2}{s}+\mathrm{5}\right)^{\mathrm{2}} }\right] \\ $$$$\mathcal{L}^{βˆ’} \:{is}\:{the}\:{inverse}\:{laplace}\:{transform} \\ $$

Question Number 179093    Answers: 0   Comments: 0

find the laplace transform of f(t)= t^2 cos(2t) u(t) u(t) is unit step function u(t)= { ((1 tβ‰₯0)),((0 t<0)) :}

$$\:{find}\:{the}\:{laplace}\:{transform}\:{of} \\ $$$${f}\left({t}\right)=\:{t}^{\mathrm{2}} \:{cos}\left(\mathrm{2}{t}\right)\:{u}\left({t}\right) \\ $$$${u}\left({t}\right)\:{is}\:{unit}\:{step}\:{function}\: \\ $$$${u}\left({t}\right)=\begin{cases}{\mathrm{1}\:\:\:\:\:\:\:{t}\geqslant\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:{t}<\mathrm{0}}\end{cases} \\ $$$$ \\ $$

Question Number 179090    Answers: 1   Comments: 1

Given a>0, b>0, c>2, a+b=1. find the minimum value of ((3ac)/b)+(c/(ab))+(6/(cβˆ’2)).

$$\mathrm{Given}\:{a}>\mathrm{0},\:{b}>\mathrm{0},\:{c}>\mathrm{2},\:{a}+{b}=\mathrm{1}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\:\frac{\mathrm{3}{ac}}{{b}}+\frac{{c}}{{ab}}+\frac{\mathrm{6}}{{c}βˆ’\mathrm{2}}. \\ $$

Question Number 179088    Answers: 2   Comments: 0

Question Number 179073    Answers: 3   Comments: 0

Question Number 179107    Answers: 1   Comments: 0

I= ∫ (x^2 /(sin (2arctan (e^x )))) dx , Find I

$${I}=\:\int\:\frac{{x}^{\mathrm{2}} }{\mathrm{sin}\:\left(\mathrm{2arctan}\:\left({e}^{{x}} \right)\right)}\:{dx}\:\:,\:{Find}\:{I} \\ $$

Question Number 179066    Answers: 1   Comments: 0

If f(x)=∫ (x^2 /(x^2 +tan x)) dx then ∫ ((tan x)/(x^2 +tan x)) dx =?

$$\:\:\:\:\:\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\int\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$$$\:\:\:\:\mathrm{then}\:\int\:\frac{\mathrm{tan}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}} +\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\:=? \\ $$

Question Number 179064    Answers: 1   Comments: 3

Question Number 179063    Answers: 1   Comments: 2

why is not a polynomial (√(25x^8 )) ?

$${why}\:{is}\:{not}\:{a}\:{polynomial}\:\sqrt{\mathrm{25}{x}^{\mathrm{8}} }\:\:? \\ $$

Question Number 179062    Answers: 1   Comments: 1

why is not it a polynomial ∣10βˆ’2y∣?

$${why}\:{is}\:{not}\:{it}\:{a}\:{polynomial}\:\mid\mathrm{10}βˆ’\mathrm{2}{y}\mid? \\ $$

Question Number 179058    Answers: 1   Comments: 0

f(x)=(((xβˆ’2)/(x+1)))^(1/3) Dom_(f(x)) =?

$${f}\left({x}\right)=\sqrt[{\mathrm{3}}]{\frac{{x}βˆ’\mathrm{2}}{{x}+\mathrm{1}}}\:\:\:\:\:\:\:{Dom}_{{f}\left({x}\right)} =? \\ $$

Question Number 179054    Answers: 0   Comments: 0

find the sum of the following vectors (a)AB, βˆ’CD, BC and CE (b) PR, βˆ’SR, ST and βˆ’QT (c) AC,3BC,CD,3CD and DA (d) PQRS is a quadilateral with M &N as the midβˆ’points of SP and RQ respectively. Show that PS^(β†’) +SR^(β†’) =2MN^(β†’)

$${find}\:{the}\:{sum}\:{of}\:{the}\:{following}\:{vectors} \\ $$$$\left({a}\right){AB},\:βˆ’{CD},\:{BC}\:{and}\:{CE} \\ $$$$\left({b}\right)\:{PR},\:βˆ’{SR},\:{ST}\:{and}\:βˆ’{QT}\:\: \\ $$$$\left({c}\right)\:{AC},\mathrm{3}{BC},{CD},\mathrm{3}{CD}\:{and}\:{DA} \\ $$$$\left({d}\right)\:{PQRS}\:{is}\:{a}\:{quadilateral}\:{with}\:{M}\:\&{N}\:{as}\:{the} \\ $$$${mid}βˆ’{points}\:{of}\:{SP}\:{and}\:{RQ}\:{respectively}. \\ $$$${Show}\:{that}\:\overset{\rightarrow} {{PS}}+\overset{\rightarrow} {{SR}}=\mathrm{2}\overset{\rightarrow} {{MN}} \\ $$

Question Number 179053    Answers: 1   Comments: 0

Question Number 179052    Answers: 0   Comments: 3

Question Number 179044    Answers: 0   Comments: 0

Three interior angles of a polygon are 160 each. If the other interior angles are 120 each.find the number of sides.

$$\mathrm{Three}\:\mathrm{interior}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{a}\:\mathrm{polygon}\:\mathrm{are} \\ $$$$\:\mathrm{160}\:\mathrm{each}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{other}\:\mathrm{interior}\:\mathrm{angles} \\ $$$$\:\mathrm{are}\:\mathrm{120}\:\mathrm{each}.\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{sides}. \\ $$

Question Number 179042    Answers: 2   Comments: 0

Question Number 179031    Answers: 0   Comments: 1

prove that sgn(0)=0

$${prove}\:{that}\:{sgn}\left(\mathrm{0}\right)=\mathrm{0} \\ $$

Question Number 179025    Answers: 0   Comments: 3

2^(10x) βˆ’x^5 βˆ’4=0

$$\mathrm{2}^{\mathrm{10}{x}} βˆ’{x}^{\mathrm{5}} βˆ’\mathrm{4}=\mathrm{0} \\ $$

Question Number 179023    Answers: 0   Comments: 0

Draw an electrical network (a) p∧(q∨r) (b)(∼p∧∼q)∨(∼p∧q)∨(p∧∼q) (c) p↔q

$$\mathrm{Draw}\:\mathrm{an}\:\mathrm{electrical}\:\mathrm{network} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{p}\wedge\left(\mathrm{q}\vee\mathrm{r}\right) \\ $$$$\left(\mathrm{b}\right)\left(\sim\mathrm{p}\wedge\sim\mathrm{q}\right)\vee\left(\sim\mathrm{p}\wedge\mathrm{q}\right)\vee\left(\mathrm{p}\wedge\sim\mathrm{q}\right) \\ $$$$\left(\mathrm{c}\right)\:\mathrm{p}\leftrightarrow\mathrm{q} \\ $$

Question Number 179018    Answers: 3   Comments: 0

Question Number 178996    Answers: 2   Comments: 0

Question Number 178994    Answers: 4   Comments: 1

Question Number 178993    Answers: 0   Comments: 0

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