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Question Number 95760 Answers: 1 Comments: 0

(d/(d(x)))(W(x))=? W(x) is lambert W function

$$\frac{{d}}{{d}\left({x}\right)}\left({W}\left({x}\right)\right)=? \\ $$$$\:{W}\left({x}\right)\:{is}\:{lambert}\:{W}\:{function} \\ $$

Question Number 95748 Answers: 2 Comments: 0

y′′ = sin x−cos x

$$\mathrm{y}''\:=\:\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x} \\ $$

Question Number 95742 Answers: 2 Comments: 2

(0/0)=2 ((100−100)/(100−100))=((10^2 −10^2 )/(10^2 −10^2 ))=(((10+10)(10−10))/(10(10−10))) ((20)/(10))=2 where is the mastike

$$\frac{\mathrm{0}}{\mathrm{0}}=\mathrm{2} \\ $$$$\frac{\mathrm{100}−\mathrm{100}}{\mathrm{100}−\mathrm{100}}=\frac{\mathrm{10}^{\mathrm{2}} −\mathrm{10}^{\mathrm{2}} }{\mathrm{10}^{\mathrm{2}} −\mathrm{10}^{\mathrm{2}} }=\frac{\left(\mathrm{10}+\mathrm{10}\right)\left(\mathrm{10}−\mathrm{10}\right)}{\mathrm{10}\left(\mathrm{10}−\mathrm{10}\right)} \\ $$$$\frac{\mathrm{20}}{\mathrm{10}}=\mathrm{2} \\ $$$$\mathrm{where}\:\mathrm{is}\:\mathrm{the}\:\mathrm{mastike} \\ $$

Question Number 95738 Answers: 1 Comments: 2

∫ ((p−tan x)/(p+tan x)) dx

$$\int\:\frac{\mathrm{p}−\mathrm{tan}\:\mathrm{x}}{\mathrm{p}+\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$

Question Number 95846 Answers: 1 Comments: 0

A = { 0, 1, 2, 3, ... , 2020 } how many zero on A ?

$${A}\:=\:\left\{\:\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:...\:,\:\mathrm{2020}\:\right\} \\ $$$${how}\:\:{many}\:\:{zero}\:\:{on}\:\:{A}\:? \\ $$

Question Number 95726 Answers: 0 Comments: 1

th forces F_1 ,F_2 ,F_3 act at points ith position vectors r_1 ,r_2 ,r_3 where F_1 = (4i + j + 2k)N r_1 = (6i + 4j + k) m F_2 = (i−2j + k)N r_2 = (i + 5j −2k) m F_3 = (−5i + j−3k)N r_3 = (i + j + k) m (a) show that this system reduces to a couple and find its magnitude. (b) if F_3 is removed and replaced with F_4 such that the system is now in equilibrium find the force vector F_4 . (c) the equation of the line of action of F_4 (d) the moment of F_4 about the origin.

$$\mathrm{th}\:\mathrm{forces}\:{F}_{\mathrm{1}} \:,{F}_{\mathrm{2}} ,{F}_{\mathrm{3}} \:\mathrm{act}\:\mathrm{at}\:\mathrm{points}\:\mathrm{ith}\:\mathrm{position}\:\mathrm{vectors}\:{r}_{\mathrm{1}} ,{r}_{\mathrm{2}} ,{r}_{\mathrm{3}} \:\:\mathrm{where} \\ $$$${F}_{\mathrm{1}} \:=\:\left(\mathrm{4}{i}\:+\:{j}\:+\:\mathrm{2}{k}\right){N}\:\:\:\:\:\:\:{r}_{\mathrm{1}} \:=\:\left(\mathrm{6}{i}\:+\:\mathrm{4}{j}\:+\:{k}\right)\:\mathrm{m} \\ $$$${F}_{\mathrm{2}} \:=\:\left({i}−\mathrm{2}{j}\:+\:{k}\right){N}\:\:\:\:\:\:\:\:\:\:\:{r}_{\mathrm{2}} \:=\:\left({i}\:+\:\mathrm{5}{j}\:−\mathrm{2}{k}\right)\:\mathrm{m} \\ $$$$\:{F}_{\mathrm{3}} \:=\:\left(−\mathrm{5}{i}\:+\:{j}−\mathrm{3}{k}\right){N}\:\:\:\:{r}_{\mathrm{3}} \:=\:\left({i}\:+\:{j}\:+\:{k}\right)\:\mathrm{m} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{show}\:\mathrm{that}\:\mathrm{this}\:\mathrm{system}\:\mathrm{reduces}\:\mathrm{to}\:\mathrm{a}\:\mathrm{couple}\:\mathrm{and}\:\mathrm{find}\:\mathrm{its}\:\mathrm{magnitude}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{if}\:\mathrm{F}_{\mathrm{3}} \:\mathrm{is}\:\mathrm{removed}\:\mathrm{and}\:\mathrm{replaced}\:\mathrm{with}\:{F}_{\mathrm{4}} \:\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{system}\:\mathrm{is}\: \\ $$$$\mathrm{now}\:\mathrm{in}\:\mathrm{equilibrium}\:\mathrm{find}\:\mathrm{the}\:\mathrm{force}\:\mathrm{vector}\:{F}_{\mathrm{4}} . \\ $$$$\left(\mathrm{c}\right)\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:\mathrm{of}\:\mathrm{action}\:\mathrm{of}\:{F}_{\mathrm{4}} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{the}\:\mathrm{moment}\:\mathrm{of}\:\mathrm{F}_{\mathrm{4}} \:\mathrm{about}\:\mathrm{the}\:\mathrm{origin}. \\ $$

Question Number 95723 Answers: 3 Comments: 1

Question Number 95722 Answers: 2 Comments: 0

use cylinder ring method y = 2x−1 y = −2x + 3 x = 2 y−axis

$${use}\:{cylinder}\:{ring}\:{method} \\ $$$$ \\ $$$${y}\:=\:\mathrm{2}{x}−\mathrm{1} \\ $$$${y}\:=\:−\mathrm{2}{x}\:+\:\mathrm{3} \\ $$$${x}\:=\:\mathrm{2}\: \\ $$$$ \\ $$$${y}−{axis}\: \\ $$$$ \\ $$$$ \\ $$

Question Number 95707 Answers: 1 Comments: 3

Question Number 95703 Answers: 1 Comments: 1

(1/(cos^2 10^o )) +(1/(sin^2 20^o )) + (1/(sin^2 40^o )) =?

$$\frac{\mathrm{1}}{\mathrm{cos}\:^{\mathrm{2}} \mathrm{10}^{\mathrm{o}} }\:+\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{20}^{\mathrm{o}} }\:+\:\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{40}^{\mathrm{o}} }\:=? \\ $$

Question Number 95699 Answers: 1 Comments: 4

many digits of number 5^8 ×4^5 ×7

$$\mathrm{many}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{number}\: \\ $$$$\mathrm{5}^{\mathrm{8}} ×\mathrm{4}^{\mathrm{5}} ×\mathrm{7}\: \\ $$

Question Number 95697 Answers: 2 Comments: 0

Question Number 95695 Answers: 1 Comments: 0

solve (x+1)y^′ −x^3 y = arctan(2x)

$$\mathrm{solve}\:\left(\mathrm{x}+\mathrm{1}\right)\mathrm{y}^{'} −\mathrm{x}^{\mathrm{3}} \mathrm{y}\:=\:\mathrm{arctan}\left(\mathrm{2x}\right) \\ $$

Question Number 95694 Answers: 1 Comments: 0

solve by laplace transform y^(′′) +3y^′ +2y =e^(−x) withy(0)=1 and y^′ (0) =2

$$\mathrm{solve}\:\mathrm{by}\:\mathrm{laplace}\:\mathrm{transform}\:\:\mathrm{y}^{''} \:+\mathrm{3y}^{'} +\mathrm{2y}\:=\mathrm{e}^{−\mathrm{x}} \:\:\mathrm{withy}\left(\mathrm{0}\right)=\mathrm{1}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=\mathrm{2} \\ $$

Question Number 95693 Answers: 1 Comments: 0

solve y^(′′) −2y^′ +1 =(x−1)shx

$$\mathrm{solve}\:\mathrm{y}^{''} −\mathrm{2y}^{'} \:+\mathrm{1}\:=\left(\mathrm{x}−\mathrm{1}\right)\mathrm{shx} \\ $$

Question Number 95692 Answers: 1 Comments: 0

calculate ∫_(−∞) ^∞ ((xsin(2x))/((x^2 +x+1)^2 ))dx

$$\mathrm{calculate}\:\:\int_{−\infty} ^{\infty} \:\:\frac{\mathrm{xsin}\left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 95691 Answers: 0 Comments: 1

calculate ∫ ((x+1)/(√((x+3)(2−x))))dx

$$\mathrm{calculate}\:\int\:\:\frac{\mathrm{x}+\mathrm{1}}{\sqrt{\left(\mathrm{x}+\mathrm{3}\right)\left(\mathrm{2}−\mathrm{x}\right)}}\mathrm{dx} \\ $$

Question Number 95690 Answers: 0 Comments: 0

calculate I =∫_0 ^(π/2) cos^3 (x)sh^2 (x)dx and J =∫_0 ^(π/3) sin^3 x ch^2 x

$$\mathrm{calculate}\:\mathrm{I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\mathrm{cos}^{\mathrm{3}} \left(\mathrm{x}\right)\mathrm{sh}^{\mathrm{2}} \left(\mathrm{x}\right)\mathrm{dx}\:\mathrm{and}\:\mathrm{J}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{3}}} \:\mathrm{sin}^{\mathrm{3}} \mathrm{x}\:\mathrm{ch}^{\mathrm{2}} \mathrm{x} \\ $$

Question Number 95679 Answers: 0 Comments: 2

The equation of motion for a particle moving in a straight line along the OX axes is given by (d^2 x/dt^2 ) + (√7) (dt/dx) + 4x = 0. show that the motion is an oscilatory motion hence find its period.

$$\mathrm{The}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{motion}\:\mathrm{for}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{moving}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line} \\ $$$$\mathrm{along}\:\mathrm{the}\:\mathrm{O}{X}\:\mathrm{axes}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\frac{{d}^{\mathrm{2}} {x}}{{dt}^{\mathrm{2}} }\:+\:\sqrt{\mathrm{7}}\:\frac{{dt}}{{dx}}\:+\:\mathrm{4}{x}\:=\:\mathrm{0}. \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{motion}\:\mathrm{is}\:\mathrm{an}\:\mathrm{oscilatory}\:\mathrm{motion}\:\mathrm{hence}\:\mathrm{find} \\ $$$$\mathrm{its}\:\mathrm{period}. \\ $$

Question Number 95677 Answers: 1 Comments: 0

Given f(x) = ((ln x)/(x−1)) (a) find the domain of f. (b) find the limts of f at the boundary of its domain hence state the asymptote of y = f(x).

$$\:\mathrm{Given}\:{f}\left({x}\right)\:=\:\frac{\mathrm{ln}\:{x}}{{x}−\mathrm{1}} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:{f}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{limts}\:\mathrm{of}\:{f}\:\mathrm{at}\:\mathrm{the}\:\mathrm{boundary}\:\mathrm{of}\:\mathrm{its}\:\mathrm{domain} \\ $$$$\mathrm{hence}\:\mathrm{state}\:\mathrm{the}\:\mathrm{asymptote}\:\mathrm{of}\:{y}\:=\:{f}\left({x}\right). \\ $$

Question Number 95676 Answers: 0 Comments: 0

determine the null space of the matrix ((1,(−7)),((−3),(21)) ) please any question number having the definition of linear dependent and linearly independent vectors?

$$\mathrm{determine}\:\mathrm{the}\:\mathrm{null}\:\mathrm{space}\:\mathrm{of}\:\mathrm{the}\:\mathrm{matrix}\:\begin{pmatrix}{\mathrm{1}}&{−\mathrm{7}}\\{−\mathrm{3}}&{\mathrm{21}}\end{pmatrix} \\ $$$$\mathrm{please}\:\mathrm{any}\:\mathrm{question}\:\mathrm{number}\:\mathrm{having}\:\mathrm{the}\:\mathrm{definition}\:\mathrm{of} \\ $$$$\mathrm{linear}\:\mathrm{dependent}\:\mathrm{and}\:\mathrm{linearly}\:\mathrm{independent}\:\mathrm{vectors}? \\ $$

Question Number 95673 Answers: 0 Comments: 2

∫_0 ^1 (1/((√(3 + 4x−4x^2 )) )) dx = ?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\sqrt{\mathrm{3}\:+\:\mathrm{4}{x}−\mathrm{4}{x}^{\mathrm{2}} }\:}\:{dx}\:=\:? \\ $$

Question Number 95670 Answers: 0 Comments: 0

Question Number 95668 Answers: 1 Comments: 2

Prove that: 2^(1/4) .4^(1/8) .8^(1/16) .16^(1/32) . ... ∞ = 2

$$\mathrm{Prove}\:\mathrm{that}:\:\:\:\mathrm{2}^{\mathrm{1}/\mathrm{4}} .\mathrm{4}^{\mathrm{1}/\mathrm{8}} .\mathrm{8}^{\mathrm{1}/\mathrm{16}} .\mathrm{16}^{\mathrm{1}/\mathrm{32}} .\:\:...\:\:\infty\:\:\:=\:\:\:\mathrm{2} \\ $$

Question Number 95662 Answers: 1 Comments: 5

f(x+p) + f(x−p) = 6x−4 f(20) = 29p ((f(p))/(2p)) = ?

$$\mathrm{f}\left(\mathrm{x}+\mathrm{p}\right)\:+\:\mathrm{f}\left(\mathrm{x}−\mathrm{p}\right)\:=\:\mathrm{6x}−\mathrm{4} \\ $$$$\mathrm{f}\left(\mathrm{20}\right)\:=\:\mathrm{29p} \\ $$$$\frac{\mathrm{f}\left(\mathrm{p}\right)}{\mathrm{2p}}\:=\:? \\ $$

Question Number 95653 Answers: 2 Comments: 0

arc length 3x^(3/2) −1 from x=0 and x=1 help please sir

$${arc}\:{length}\:\mathrm{3}{x}^{\frac{\mathrm{3}}{\mathrm{2}}} −\mathrm{1}\: \\ $$$${from}\:{x}=\mathrm{0}\:{and}\:{x}=\mathrm{1}\: \\ $$$${help}\:{please}\:{sir} \\ $$

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