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Question Number 23138 Answers: 1 Comments: 1

Question Number 23133 Answers: 1 Comments: 0

Find the minimum surface area of a solid circular cylinder , if its volume is 16π cm^3 (leave your answer in terms of π)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{surface}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{solid}\:\mathrm{circular}\:\mathrm{cylinder}\:,\:\:\mathrm{if}\:\mathrm{its}\:\mathrm{volume}\:\mathrm{is} \\ $$$$\mathrm{16}\pi\:\mathrm{cm}^{\mathrm{3}} \:\:\:\left(\mathrm{leave}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\pi\right) \\ $$

Question Number 23131 Answers: 0 Comments: 7

Question Number 23130 Answers: 0 Comments: 1

A baloon filled with helium rises against gravity increasing its potential energy. The speed of the baloon also increases as it rises. How do you reconcile this with the law of conservation of mechanical energy? You can neglect viscous drag of air and assume that density of air is constant.

$$\mathrm{A}\:\mathrm{baloon}\:\mathrm{filled}\:\mathrm{with}\:\mathrm{helium}\:\mathrm{rises}\:\mathrm{against} \\ $$$$\mathrm{gravity}\:\mathrm{increasing}\:\mathrm{its}\:\mathrm{potential}\:\mathrm{energy}. \\ $$$$\mathrm{The}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{baloon}\:\mathrm{also}\:\mathrm{increases} \\ $$$$\mathrm{as}\:\mathrm{it}\:\mathrm{rises}.\:\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{reconcile}\:\mathrm{this} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{law}\:\mathrm{of}\:\mathrm{conservation}\:\mathrm{of} \\ $$$$\mathrm{mechanical}\:\mathrm{energy}?\:\mathrm{You}\:\mathrm{can}\:\mathrm{neglect} \\ $$$$\mathrm{viscous}\:\mathrm{drag}\:\mathrm{of}\:\mathrm{air}\:\mathrm{and}\:\mathrm{assume}\:\mathrm{that} \\ $$$$\mathrm{density}\:\mathrm{of}\:\mathrm{air}\:\mathrm{is}\:\mathrm{constant}. \\ $$

Question Number 23162 Answers: 1 Comments: 1

Question Number 23122 Answers: 0 Comments: 3

Question Number 23110 Answers: 0 Comments: 0

In which apptent give when to 10 grams stop in 800−th apptent add 0.1 gram of copper?

$${In}\:{which}\:{apptent}\:{give}\:{when}\:{to}\:\mathrm{10}\:{grams}\:{stop}\:{in}\:\mathrm{800}−{th}\:{apptent}\:{add}\:\:\mathrm{0}.\mathrm{1}\:{gram}\:{of}\:{copper}? \\ $$

Question Number 23109 Answers: 0 Comments: 1

Concourse started in 24 November and takes 12 days. Which date ends Concourse?

$${Concourse}\:{started}\:{in}\:\mathrm{24}\:{November}\:{and}\:{takes}\:\mathrm{12}\:{days}. \\ $$$${Which}\:{date}\:{ends}\:{Concourse}? \\ $$

Question Number 23108 Answers: 1 Comments: 0

∫e^(−x) sin2x dx

$$\int\mathrm{e}^{−\mathrm{x}} \mathrm{sin2x}\:\mathrm{dx} \\ $$

Question Number 23105 Answers: 0 Comments: 4

(∣m^2 −n^2 ∣,2mn,m^2 +n^2 ) is pythagorean triplet for all m,n∈N. This can be proved easily.Is the vice versa of the statement is also true? I-E If for a,b,c∈N ,a^2 +b^2 =c^2 then there exist m,n∈N such that m^2 +n^2 =c and {a,b}={∣m^2 −n^2 ∣,2mn}

$$\left(\mid\mathrm{m}^{\mathrm{2}} −\mathrm{n}^{\mathrm{2}} \mid,\mathrm{2mn},\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} \right)\:\mathrm{is}\:\mathrm{pythagorean} \\ $$$$\mathrm{triplet}\:\mathrm{for}\:\mathrm{all}\:\mathrm{m},\mathrm{n}\in\mathbb{N}.\:\mathrm{This}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{proved}\:\mathrm{easily}.\mathrm{Is}\:\mathrm{the}\:\mathrm{vice}\:\mathrm{versa}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{statement}\:\mathrm{is}\:\mathrm{also}\:\mathrm{true}? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}-\mathrm{E} \\ $$$$\mathrm{If}\:\:\mathrm{for}\:\mathrm{a},\mathrm{b},\mathrm{c}\in\mathbb{N}\:,\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} =\mathrm{c}^{\mathrm{2}} \:\mathrm{then}\:\mathrm{there}\: \\ $$$$\mathrm{exist}\:\mathrm{m},\mathrm{n}\in\mathbb{N}\:\mathrm{such}\:\mathrm{that}\:\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} =\mathrm{c}\:\mathrm{and} \\ $$$$\left\{\mathrm{a},\mathrm{b}\right\}=\left\{\mid\mathrm{m}^{\mathrm{2}} −\mathrm{n}^{\mathrm{2}} \mid,\mathrm{2mn}\right\} \\ $$

Question Number 23104 Answers: 1 Comments: 0

show tht the curve with parametric equcations x=t^2 ,y=t^3 −9t intersect at the point (9,0).

$${show}\:{tht}\:{the}\:{curve}\:{with}\:{parametric}\:{equcations} \\ $$$${x}={t}^{\mathrm{2}} \:,{y}={t}^{\mathrm{3}} \:−\mathrm{9}{t}\:{intersect}\:{at}\:{the}\:{point}\:\left(\mathrm{9},\mathrm{0}\right). \\ $$

Question Number 23103 Answers: 0 Comments: 1

Can anyone please solve question number 23057

$${Can}\:{anyone}\:{please}\:{solve}\:{question} \\ $$$${number}\:\mathrm{23057} \\ $$

Question Number 23096 Answers: 0 Comments: 1

Solve: 3^(x ) = ((27)/x) + 18

$$\mathrm{Solve}:\:\:\mathrm{3}^{\mathrm{x}\:} =\:\frac{\mathrm{27}}{\mathrm{x}}\:+\:\mathrm{18} \\ $$

Question Number 23073 Answers: 1 Comments: 1

Question Number 23069 Answers: 0 Comments: 0

Why ionic radii of^(35) Cl <^(37) Cl^− ?

$$\mathrm{Why}\:\mathrm{ionic}\:\mathrm{radii}\:\mathrm{of}\:^{\mathrm{35}} \mathrm{Cl}\:<\:^{\mathrm{37}} \mathrm{Cl}^{−} ? \\ $$

Question Number 23066 Answers: 1 Comments: 7

A rocket accelerates straight up by ejecting gas downwards. In a small time interval Δt, it ejects a gas of mass Δm at a relative speed u. Calculate KE of the entire system at t + Δt and t and show that the device that ejects gas does work = ((1/2))Δmu^2 in this time interval (neglect gravity).

$$\mathrm{A}\:\mathrm{rocket}\:\mathrm{accelerates}\:\mathrm{straight}\:\mathrm{up}\:\mathrm{by} \\ $$$$\mathrm{ejecting}\:\mathrm{gas}\:\mathrm{downwards}.\:\mathrm{In}\:\mathrm{a}\:\mathrm{small} \\ $$$$\mathrm{time}\:\mathrm{interval}\:\Delta{t},\:\mathrm{it}\:\mathrm{ejects}\:\mathrm{a}\:\mathrm{gas}\:\mathrm{of}\:\mathrm{mass} \\ $$$$\Delta{m}\:\mathrm{at}\:\mathrm{a}\:\mathrm{relative}\:\mathrm{speed}\:{u}.\:\mathrm{Calculate}\:\mathrm{KE} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{entire}\:\mathrm{system}\:\mathrm{at}\:{t}\:+\:\Delta{t}\:\mathrm{and}\:{t}\:\mathrm{and} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{device}\:\mathrm{that}\:\mathrm{ejects}\:\mathrm{gas} \\ $$$$\mathrm{does}\:\mathrm{work}\:=\:\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\Delta{mu}^{\mathrm{2}} \:\mathrm{in}\:\mathrm{this}\:\mathrm{time} \\ $$$$\mathrm{interval}\:\left(\mathrm{neglect}\:\mathrm{gravity}\right). \\ $$

Question Number 23061 Answers: 0 Comments: 0

∫_0 ^∞ j_4 (x)dx=?

$$\int_{\mathrm{0}} ^{\infty} \mathrm{j}_{\mathrm{4}} \left(\mathrm{x}\right)\mathrm{dx}=? \\ $$

Question Number 23059 Answers: 0 Comments: 3

Question Number 23057 Answers: 0 Comments: 1

Question Number 23050 Answers: 1 Comments: 0

how can demonstred that ∀a,b,c∈N a^2 +b^2 =c^2 ⇒ abc≡0[60]

$${how}\:{can}\:{demonstred}\:{that}\: \\ $$$$\:\:\:\forall{a},{b},{c}\in\mathbb{N}\: \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={c}^{\mathrm{2}} \:\:\Rightarrow \\ $$$${abc}\equiv\mathrm{0}\left[\mathrm{60}\right]\:\: \\ $$

Question Number 23049 Answers: 1 Comments: 0

A particle of mass m strikes on ground with angle of incidence 45°. If coefficient of restitution, e = (1/(√2)) , find the velocity after impact and angle of reflection.

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{strikes}\:\mathrm{on}\:\mathrm{ground} \\ $$$$\mathrm{with}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{incidence}\:\mathrm{45}°.\:\mathrm{If}\:\mathrm{coefficient} \\ $$$$\mathrm{of}\:\mathrm{restitution},\:{e}\:=\:\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}\:,\:\mathrm{find}\:\mathrm{the}\:\mathrm{velocity} \\ $$$$\mathrm{after}\:\mathrm{impact}\:\mathrm{and}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{reflection}. \\ $$

Question Number 23036 Answers: 1 Comments: 16

Question Number 23034 Answers: 0 Comments: 1

Question Number 23022 Answers: 1 Comments: 5

what are the conditions necessary for a body of mass mkg on an incline plane at angle θ to the horizontal to remain at rest?

$${what}\:{are}\:{the}\:{conditions}\:{necessary} \\ $$$${for}\:{a}\:{body}\:{of}\:{mass}\:{mkg}\:{on}\:{an}\:{incline}\:{plane} \\ $$$${at}\:{angle}\:\theta\:{to}\:{the}\:{horizontal}\:{to} \\ $$$${remain}\:{at}\:{rest}? \\ $$

Question Number 23020 Answers: 1 Comments: 3

∫_1 ^3 ((4x+1)/(2x^2 +x−2))dx=?

$$\underset{\mathrm{1}} {\overset{\mathrm{3}} {\int}}\frac{\mathrm{4}\boldsymbol{\mathrm{x}}+\mathrm{1}}{\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}−\mathrm{2}}\boldsymbol{\mathrm{dx}}=? \\ $$

Question Number 23012 Answers: 2 Comments: 2

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