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Question Number 33533    Answers: 1   Comments: 0

A mass of 2kg is attached to a spring with constant 8N/m.It is⊛ then displaced to the point x=2. What time does it take for the block to travel to the point x=1? a)40s b)60s c)30s d)20s

$${A}\:{mass}\:{of}\:\mathrm{2}{kg}\:{is}\:{attached}\:{to}\:{a} \\ $$$${spring}\:{with}\:{constant}\:\mathrm{8}{N}/{m}.{It}\:{is}\circledast \\ $$$${then}\:{displaced}\:{to}\:{the}\:{point}\:{x}=\mathrm{2}. \\ $$$${What}\:{time}\:{does}\:{it}\:{take}\:{for}\:{the}\:{block} \\ $$$${to}\:{travel}\:{to}\:{the}\:{point}\:{x}=\mathrm{1}? \\ $$$$\left.{a}\left.\right)\left.\mathrm{4}\left.\mathrm{0}{s}\:{b}\right)\mathrm{60}{s}\:{c}\right)\mathrm{30}{s}\:{d}\right)\mathrm{20}{s} \\ $$

Question Number 33531    Answers: 0   Comments: 16

∫_0 ^∞ (e^(−x^2 ) /(x^2 +1))dx=?

$$\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−{x}^{\mathrm{2}} } }{{x}^{\mathrm{2}} +\mathrm{1}}{dx}=? \\ $$

Question Number 33518    Answers: 0   Comments: 0

α^4 +β^(4 ) solve please

$$\alpha^{\mathrm{4}} +\beta^{\mathrm{4}\:} {solve}\:{please} \\ $$

Question Number 33515    Answers: 0   Comments: 1

expand α^4 +β^(β ) please

$${expand}\:\alpha^{\mathrm{4}} +\beta^{\beta\:\:} {please} \\ $$

Question Number 33513    Answers: 0   Comments: 1

In a recent pool of 500 men and 500 women it was observed that a total of 650 were married. of those married 275 were men and 500 claimed to be happy.out of 750 who claimed to be happy,400 were men of which 200 were married.Represent this information on the venn−diagram and then find (i)the number of married who are unhappy. (ii)the number of married who are happy.

$$\boldsymbol{\mathrm{In}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{recent}}\:\boldsymbol{\mathrm{pool}}\:\boldsymbol{\mathrm{of}}\:\mathrm{500}\:\boldsymbol{\mathrm{men}}\:\boldsymbol{\mathrm{and}}\:\mathrm{500}\:\boldsymbol{\mathrm{women}} \\ $$$$\boldsymbol{\mathrm{it}}\:\boldsymbol{\mathrm{was}}\:\boldsymbol{\mathrm{observed}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{total}}\:\boldsymbol{\mathrm{of}}\:\mathrm{650}\:\boldsymbol{\mathrm{were}}\:\boldsymbol{\mathrm{married}}. \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{those}}\:\boldsymbol{\mathrm{married}}\:\mathrm{275}\:\boldsymbol{\mathrm{were}}\:\boldsymbol{\mathrm{men}}\:\boldsymbol{\mathrm{and}}\:\mathrm{500} \\ $$$$\boldsymbol{\mathrm{claimed}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{happy}}.\boldsymbol{\mathrm{out}}\:\boldsymbol{\mathrm{of}}\:\mathrm{750}\:\boldsymbol{\mathrm{who}}\:\boldsymbol{\mathrm{claimed}} \\ $$$$\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{happy}},\mathrm{400}\:\boldsymbol{\mathrm{were}}\:\boldsymbol{\mathrm{men}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{which}}\:\mathrm{200} \\ $$$$\boldsymbol{\mathrm{were}}\:\boldsymbol{\mathrm{married}}.\boldsymbol{\mathrm{Represent}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{information}} \\ $$$$\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{venn}}−\boldsymbol{\mathrm{diagram}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{find}} \\ $$$$\left(\boldsymbol{\mathrm{i}}\right)\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{married}}\:\boldsymbol{\mathrm{who}}\: \\ $$$$\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{unhappy}}. \\ $$$$\left(\boldsymbol{\mathrm{ii}}\right)\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{married}}\:\boldsymbol{\mathrm{who}} \\ $$$$\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{happy}}. \\ $$$$ \\ $$$$ \\ $$

Question Number 33511    Answers: 1   Comments: 0

find the value of ′k′ such that k(x^2 +y^2 )+(y−2x+1)(y+2x+3)=0 is a circle.Hence obtain the centre and radius of the resulting circle.

$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:'\boldsymbol{\mathrm{k}}'\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}} \\ $$$$\boldsymbol{\mathrm{k}}\left(\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} \right)+\left(\boldsymbol{{y}}−\mathrm{2}\boldsymbol{{x}}+\mathrm{1}\right)\left(\boldsymbol{{y}}+\mathrm{2}\boldsymbol{{x}}+\mathrm{3}\right)=\mathrm{0} \\ $$$$\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{circle}}.\boldsymbol{\mathrm{Hence}}\:\boldsymbol{\mathrm{obtain}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{centre}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{resulting}}\:\boldsymbol{\mathrm{circle}}. \\ $$

Question Number 33508    Answers: 0   Comments: 2

((3^x ×8^x )/(12^(x+1) ))

$$\frac{\mathrm{3}^{{x}} ×\mathrm{8}^{{x}} }{\mathrm{12}^{{x}+\mathrm{1}} } \\ $$

Question Number 33507    Answers: 1   Comments: 0

∫((2cos x)/(3−cos 2x))dx=?

$$\int\frac{\mathrm{2cos}\:{x}}{\mathrm{3}−\mathrm{cos}\:\mathrm{2}{x}}{dx}=? \\ $$

Question Number 33496    Answers: 1   Comments: 0

prove that e^(iπ) +1=0

$$\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{e}^{\mathrm{i}\pi} +\mathrm{1}=\mathrm{0} \\ $$

Question Number 33494    Answers: 0   Comments: 2

∫(e^x /(sin^2 x ))dx

$$\:\int\frac{\boldsymbol{\mathrm{e}}^{\boldsymbol{{x}}} }{\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{{x}}\:\:\:\:}\boldsymbol{{dx}} \\ $$

Question Number 33473    Answers: 1   Comments: 3

e^(iπ ) = −1 squaring both sides e^(2πi) = 1 = e^0 comparing powers 2πi = 0 π = 0 or i = 0 ???

$$\:{e}^{{i}\pi\:} =\:−\mathrm{1} \\ $$$${squaring}\:{both}\:{sides} \\ $$$${e}^{\mathrm{2}\pi{i}} \:=\:\mathrm{1}\:=\:{e}^{\mathrm{0}} \\ $$$${comparing}\:{powers} \\ $$$$\mathrm{2}\pi{i}\:=\:\mathrm{0} \\ $$$$\:\pi\:=\:\mathrm{0}\:{or}\:{i}\:=\:\mathrm{0}\:??? \\ $$

Question Number 33479    Answers: 2   Comments: 2

A man takes 15days to dig 6 hectres.how long would 10 boys take to dig 81 hectres if 2 boys do the same amount of work as one man?

$$\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{man}}\:\boldsymbol{\mathrm{takes}}\:\mathrm{15}\boldsymbol{\mathrm{days}}\:\boldsymbol{\mathrm{to}} \\ $$$$\boldsymbol{\mathrm{dig}}\:\mathrm{6}\:\boldsymbol{\mathrm{hectres}}.\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{long}}\:\boldsymbol{\mathrm{would}} \\ $$$$\mathrm{10}\:\boldsymbol{\mathrm{boys}}\:\boldsymbol{\mathrm{take}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{dig}}\:\mathrm{81}\:\boldsymbol{\mathrm{hectres}} \\ $$$$\boldsymbol{\mathrm{if}}\:\mathrm{2}\:\boldsymbol{\mathrm{boys}}\:\boldsymbol{\mathrm{do}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{same}}\:\boldsymbol{\mathrm{amount}}\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{work}}\:\boldsymbol{\mathrm{as}}\:\boldsymbol{\mathrm{one}}\:\boldsymbol{\mathrm{man}}? \\ $$

Question Number 33468    Answers: 1   Comments: 0

The set of integers that satisfies 5>∣n−2∣≥∣n+1∣ is

$${The}\:{set}\:{of}\:{integers}\:{that}\:{satisfies} \\ $$$$\mathrm{5}>\mid{n}−\mathrm{2}\mid\geqslant\mid{n}+\mathrm{1}\mid\:{is} \\ $$

Question Number 33466    Answers: 1   Comments: 2

if tan𝛃=(r/(√s)) and sin𝛃=((√s)/r) show that cos𝛃=(√(r^2 +s))

$$\:\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{tan}\beta}=\frac{\boldsymbol{\mathrm{r}}}{\sqrt{\boldsymbol{\mathrm{s}}}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{sin}\beta}=\frac{\sqrt{\boldsymbol{\mathrm{s}}}}{\boldsymbol{\mathrm{r}}} \\ $$$$\:\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{cos}\beta}=\sqrt{\boldsymbol{\mathrm{r}}^{\mathrm{2}} +\boldsymbol{\mathrm{s}}} \\ $$

Question Number 33463    Answers: 0   Comments: 1

Find the pricipal and ordinary argument of z=(i/(−2−2i))

$${Find}\:{the}\:{pricipal}\:{and}\:{ordinary} \\ $$$${argument}\:{of}\:{z}=\frac{{i}}{−\mathrm{2}−\mathrm{2}{i}} \\ $$

Question Number 33462    Answers: 1   Comments: 0

using PMI show that ∀ n≥2 the number 5^n ends with the digits 25

$${using}\:{PMI}\:{show}\:{that}\:\forall\:{n}\geqslant\mathrm{2}\:{the} \\ $$$${number}\:\mathrm{5}^{{n}} \:{ends}\:{with}\:{the}\:{digits}\:\mathrm{25} \\ $$

Question Number 33460    Answers: 1   Comments: 0

why do we use greek letters like α,β,θ,π,Ω,ρ in mathematics

$$\:\:{why}\:{do}\:{we}\:{use}\:{greek}\:{letters}\:{like}\: \\ $$$$\alpha,\beta,\theta,\pi,\Omega,\rho\:\:\:{in}\:{mathematics} \\ $$

Question Number 33455    Answers: 1   Comments: 2

Please can someone help with a simplier method of solving this question Q1; Given that the expression x^3 +x^2 −4x +5 and x^3 +3x−7 leave same remainder when divided by (x−a) find the possible values of a

$$\:\:\:\:\:{Please}\:{can}\:{someone}\:{help}\:{with}\:{a} \\ $$$${simplier}\:{method}\:{of}\:{solving}\:{this}\:{question} \\ $$$${Q}\mathrm{1};\:\:\: \\ $$$$\:\:\:{Given}\:{that}\:{the}\:{expression}\:{x}^{\mathrm{3}} +{x}^{\mathrm{2}} −\mathrm{4}{x}\:+\mathrm{5} \\ $$$${and}\:{x}^{\mathrm{3}} +\mathrm{3}{x}−\mathrm{7}\:{leave}\:{same}\:{remainder} \\ $$$${when}\:{divided}\:{by}\:\left({x}−{a}\right)\:{find}\:{the}\:{possible} \\ $$$${values}\:{of}\:{a} \\ $$

Question Number 33452    Answers: 1   Comments: 2

Question Number 33435    Answers: 1   Comments: 0

In a region an electric field exist in a given direction and it passes through a circle of radius R normally. The magnitude of electric field is given as : E = E_0 (1− (r/R)). where r is the distance from centre of circle .Find electric flux through plane of circle within it.

$$\boldsymbol{{I}}{n}\:{a}\:{region}\:{an}\:{electric}\:{field}\:{exist}\:{in}\:{a}\:{given} \\ $$$${direction}\:{and}\:{it}\:{passes}\:{through}\:{a}\:{circle} \\ $$$${of}\:{radius}\:{R}\:{normally}.\:{The}\:{magnitude} \\ $$$${of}\:{electric}\:{field}\:{is}\:{given}\:{as}\:: \\ $$$$\boldsymbol{{E}}\:=\:{E}_{\mathrm{0}} \:\left(\mathrm{1}−\:\frac{{r}}{\boldsymbol{{R}}}\right).\:{where}\:{r}\:{is}\:{the}\:{distance} \\ $$$${from}\:{centre}\:{of}\:{circle}\:.{Find}\:{electric}\: \\ $$$${flux}\:{through}\:{plane}\:{of}\:{circle}\:{within}\:{it}. \\ $$

Question Number 33430    Answers: 0   Comments: 3

Question Number 33425    Answers: 1   Comments: 3

find k if the deteminant of (((3 k)),((2 3)) ) is 2 can someone please teach me how to find the deteminant of a 3×3 matrix ?

$${find}\:{k}\:{if}\:{the}\:{deteminant}\:{of}\: \\ $$$$\:\:\:\begin{pmatrix}{\mathrm{3}\:\:\:\:\:\:\:\:\:{k}}\\{\mathrm{2}\:\:\:\:\:\:\:\:\:\:\mathrm{3}}\end{pmatrix}\:\:\:{is}\:\mathrm{2}\: \\ $$$${can}\:{someone}\:{please}\:{teach}\:{me}\:{how} \\ $$$${to}\:{find}\:{the}\:{deteminant}\:{of}\:{a}\:\mathrm{3}×\mathrm{3} \\ $$$${matrix}\:? \\ $$$$\: \\ $$$$\:\: \\ $$

Question Number 33413    Answers: 0   Comments: 2

the value of θ,in the range 0° ≤ θ≤90° for which sinθ = cos θ is...?

$$ \\ $$$${the}\:{value}\:{of}\:\theta,{in}\:{the}\:{range}\:\mathrm{0}°\:\leqslant\:\:\theta\leqslant\mathrm{90}° \\ $$$${for}\:{which}\:{sin}\theta\:=\:{cos}\:\theta\:{is}...? \\ $$

Question Number 33411    Answers: 0   Comments: 1

Given that u and v are real valued functions in x ,then (d/dx)((u/v)) is equal to?

$$\:\mathrm{Given}\:\mathrm{that}\:{u}\:\mathrm{and}\:{v}\:\mathrm{are}\:\mathrm{real}\:\mathrm{valued} \\ $$$$\mathrm{functions}\:\mathrm{in}\:{x}\:,\mathrm{then}\:\frac{{d}}{{dx}}\left(\frac{{u}}{{v}}\right)\:{is}\:{equal}\:{to}? \\ $$

Question Number 33410    Answers: 1   Comments: 1

please is there any general way for calculating the error or uncertainty in g when m=((4π^2 )/g) where m=slope and g=acceleration due to gravity please help

$${please}\:{is}\:{there}\:{any}\:{general}\:{way}\:{for} \\ $$$${calculating}\:{the}\:{error}\:{or}\:{uncertainty} \\ $$$${in}\:{g}\:{when} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:{m}=\frac{\mathrm{4}\pi^{\mathrm{2}} }{{g}}\:{where}\:{m}={slope}\:{and} \\ $$$${g}={acceleration}\:{due}\:{to}\:{gravity} \\ $$$$ \\ $$$$ \\ $$$${please}\:{help} \\ $$

Question Number 33407    Answers: 1   Comments: 0

if y=x! find dy/dx

$${if}\:{y}={x}!\:{find}\:{dy}/{dx} \\ $$

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