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Question Number 75684    Answers: 2   Comments: 2

Question Number 75681    Answers: 1   Comments: 8

Question Number 75669    Answers: 3   Comments: 3

Question Number 75662    Answers: 0   Comments: 0

Question Number 75661    Answers: 1   Comments: 0

Question Number 75660    Answers: 2   Comments: 1

find all solutions (if exist) of x^2 +5y^2 =2016 with x,y ∈ N.

$${find}\:{all}\:{solutions}\:\left({if}\:{exist}\right)\:{of} \\ $$$${x}^{\mathrm{2}} +\mathrm{5}{y}^{\mathrm{2}} =\mathrm{2016} \\ $$$${with}\:{x},{y}\:\in\:\mathbb{N}. \\ $$

Question Number 75656    Answers: 0   Comments: 5

Question Number 75655    Answers: 1   Comments: 0

if z ∈ C is sin^2 z+cos^2 z=1 also valid?

$${if}\:{z}\:\in\:\mathbb{C} \\ $$$${is}\:\mathrm{sin}^{\mathrm{2}} \:{z}+\mathrm{cos}^{\mathrm{2}} \:{z}=\mathrm{1}\:{also}\:{valid}? \\ $$

Question Number 75648    Answers: 0   Comments: 0

A student seals 200g of ice−cold water in a glass vacuum (thermos) flask and finds that it warms up by 3.5 K in one hour SHC of water =2400 Jkg^(−1) K^(−1) a) Calculate the average rate of heat flow in the flask in watts. To check this result over a longer period,the student fills the flask with equal amounts of ice and water all at 0°C, and leaves it for 4 hours. the specific latent heat(enthalpy) of fusion of ice is 0.33MJg^(−1) b) How much ice would you expect to have melted at the end of the four hours?

$$\:{A}\:{student}\:{seals}\:\mathrm{200}{g}\:{of}\:{ice}−{cold}\:{water}\:{in}\:{a}\:{glass}\:{vacuum} \\ $$$$\left({thermos}\right)\:{flask}\:{and}\:{finds}\:{that}\:{it}\:{warms}\:{up}\:{by}\:\mathrm{3}.\mathrm{5}\:{K}\:{in}\:{one}\:{hour} \\ $$$${SHC}\:{of}\:{water}\:=\mathrm{2400}\:{Jkg}^{−\mathrm{1}} {K}^{−\mathrm{1}} \\ $$$$\left.{a}\right)\:{Calculate}\:{the}\:{average}\:{rate}\:{of}\:{heat}\:{flow}\:{in}\:{the}\:{flask}\:{in}\:{watts}. \\ $$$${To}\:{check}\:{this}\:{result}\:{over}\:{a}\:{longer}\:{period},{the}\:{student}\:{fills}\:{the}\:{flask}\:{with} \\ $$$${equal}\:{amounts}\:{of}\:{ice}\:{and}\:{water}\:{all}\:{at}\:\mathrm{0}°{C},\:{and}\:{leaves}\:{it}\:{for}\: \\ $$$$\mathrm{4}\:{hours}.\:{the}\:{specific}\:{latent}\:{heat}\left({enthalpy}\right)\:{of}\:{fusion}\:{of}\:{ice}\:{is}\:\mathrm{0}.\mathrm{33}{MJg}^{−\mathrm{1}} \\ $$$$\left.{b}\right)\:{How}\:{much}\:{ice}\:{would}\:{you}\:{expect}\:{to}\:{have}\:{melted}\:{at}\:{the}\:{end}\:{of}\:{the} \\ $$$${four}\:{hours}? \\ $$

Question Number 75748    Answers: 0   Comments: 0

((4 sin (((2π)/7)) + sec ((π/(14))))/(cot ((π/7)))) = ?

$$\frac{\mathrm{4}\:\mathrm{sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)\:+\:\mathrm{sec}\:\left(\frac{\pi}{\mathrm{14}}\right)}{\mathrm{cot}\:\left(\frac{\pi}{\mathrm{7}}\right)}\:=\:? \\ $$

Question Number 75641    Answers: 2   Comments: 1

Question Number 75639    Answers: 1   Comments: 0

Question Number 75627    Answers: 1   Comments: 0

Question Number 75623    Answers: 1   Comments: 1

Question Number 75618    Answers: 0   Comments: 3

Question Number 75617    Answers: 0   Comments: 1

Demonstrate that ∀ x ∈]0;(π/2)[ tanx=((1−cos(2x))/(sin(2x)))

$$\left.\mathrm{Demonstrate}\:\mathrm{that}\:\forall\:\mathrm{x}\:\in\right]\mathrm{0};\frac{\pi}{\mathrm{2}}\left[\right. \\ $$$$\mathrm{tanx}=\frac{\mathrm{1}−\mathrm{cos}\left(\mathrm{2x}\right)}{\mathrm{sin}\left(\mathrm{2x}\right)} \\ $$

Question Number 75616    Answers: 1   Comments: 7

A_1 =2 B_1 =1 A_(n+1) =A_n −8B_n B_(n+1) =A_n +7B_n find A_n =?, B_n =?

$${A}_{\mathrm{1}} =\mathrm{2} \\ $$$${B}_{\mathrm{1}} =\mathrm{1} \\ $$$${A}_{{n}+\mathrm{1}} ={A}_{{n}} −\mathrm{8}{B}_{{n}} \\ $$$${B}_{{n}+\mathrm{1}} ={A}_{{n}} +\mathrm{7}{B}_{{n}} \\ $$$${find}\:{A}_{{n}} =?,\:{B}_{{n}} =? \\ $$

Question Number 75615    Answers: 0   Comments: 0

Question Number 75602    Answers: 1   Comments: 0

If 2x^2 −mxy+3y^2 −5y−2 have two rational factor then find m

$${If}\:\mathrm{2}{x}^{\mathrm{2}} −{mxy}+\mathrm{3}{y}^{\mathrm{2}} −\mathrm{5}{y}−\mathrm{2} \\ $$$${have}\:{two}\:{rational}\:{factor}\:{then} \\ $$$${find}\:\:\:{m} \\ $$

Question Number 75598    Answers: 0   Comments: 1

Question Number 75597    Answers: 0   Comments: 1

Question Number 75593    Answers: 1   Comments: 0

u^3 +v^3 =a , s^3 +m^3 =b , uv=(s+m)^2 , sm=(u+v)^2 . Find u,v,s,m in terms of a,b.

$${u}^{\mathrm{3}} +{v}^{\mathrm{3}} ={a}\:,\:\:{s}^{\mathrm{3}} +{m}^{\mathrm{3}} ={b}\:, \\ $$$${uv}=\left({s}+{m}\right)^{\mathrm{2}} \:,\:\:{sm}=\left({u}+{v}\right)^{\mathrm{2}} \:. \\ $$$${Find}\:{u},{v},{s},{m}\:\:{in}\:{terms}\:{of}\:{a},{b}. \\ $$

Question Number 75590    Answers: 0   Comments: 0

Question Number 75580    Answers: 0   Comments: 1

Define the inversion transformation of Z=a + ib where i is imaginary line passing through the circle of inversion.

$$\mathrm{Define}\:\mathrm{the}\:\mathrm{inversion}\:\mathrm{transformation} \\ $$$$\mathrm{of}\:\mathrm{Z}=\mathrm{a}\:+\:\mathrm{ib}\:\mathrm{where}\:\mathrm{i}\:\mathrm{is}\:\mathrm{imaginary}\:\mathrm{line}\: \\ $$$$\mathrm{passing}\:\mathrm{through}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{inversion}. \\ $$

Question Number 75577    Answers: 1   Comments: 0

∫_(−∞) ^∞ xdx is divergent or convergent?

$$\int_{−\infty} ^{\infty} {xdx}\:{is}\:{divergent}\:{or}\:{convergent}? \\ $$

Question Number 75570    Answers: 2   Comments: 1

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