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Question Number 23488    Answers: 0   Comments: 0

area of a(1−cos θ)

$${area}\:{of}\:{a}\left(\mathrm{1}−\mathrm{cos}\:\theta\right) \\ $$

Question Number 23485    Answers: 0   Comments: 0

(1/(cos (x−a)cos (x−b)))

$$\frac{\mathrm{1}}{\mathrm{cos}\:\left({x}−{a}\right)\mathrm{cos}\:\left({x}−{b}\right)} \\ $$

Question Number 23481    Answers: 0   Comments: 5

Which of the diagrams represents variation of total mechanical energy of a pendulum oscillating in air as function of time?

$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{diagrams}\:\mathrm{represents} \\ $$$$\mathrm{variation}\:\mathrm{of}\:\mathrm{total}\:\mathrm{mechanical}\:\mathrm{energy}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{pendulum}\:\mathrm{oscillating}\:\mathrm{in}\:\mathrm{air}\:\mathrm{as}\:\mathrm{function} \\ $$$$\mathrm{of}\:\mathrm{time}? \\ $$

Question Number 23479    Answers: 0   Comments: 0

Common solution. (d/dy)(u_x +u)+2x^2 y(u_x +u)=0.

$$\boldsymbol{\mathrm{Common}}\:\:\boldsymbol{\mathrm{solution}}. \\ $$$$\frac{\boldsymbol{\mathfrak{d}}}{\boldsymbol{\mathfrak{d}\mathrm{y}}}\left(\boldsymbol{\mathrm{u}}_{\boldsymbol{\mathrm{x}}} +\boldsymbol{\mathrm{u}}\right)+\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}\left(\boldsymbol{\mathrm{u}}_{\boldsymbol{\mathrm{x}}} +\boldsymbol{\mathrm{u}}\right)=\mathrm{0}. \\ $$

Question Number 23477    Answers: 0   Comments: 0

Find the value of x, ∫_(−∞) ^x dx = ∫∣± sinh cot ln (15−(√(33+x)))∣ dx

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}, \\ $$$$\:\:\:\:\:\:\:\int_{−\infty} ^{{x}} {d}\mathrm{x}\:=\:\int\mid\pm\:\mathrm{sinh}\:\mathrm{cot}\:\mathrm{ln}\:\left(\mathrm{15}−\sqrt{\mathrm{33}+{x}}\right)\mid\:\mathrm{dx} \\ $$

Question Number 23476    Answers: 0   Comments: 0

Question Number 23472    Answers: 1   Comments: 1

Question Number 23471    Answers: 1   Comments: 0

Prove that ΣΣ_(0≤i<j≤n) ((1/(^n C_i )) + (1/(^n C_j ))) = Σ_(r=0) ^(n−1) ((n − r)/(^n C_r )) + Σ_(r=1) ^n (r/(^n C_r ))

$${Prove}\:{that} \\ $$$$\underset{\mathrm{0}\leqslant{i}<{j}\leqslant{n}} {\Sigma\Sigma}\left(\frac{\mathrm{1}}{\:^{{n}} {C}_{{i}} }\:+\:\frac{\mathrm{1}}{\:^{{n}} {C}_{{j}} }\right)\:=\:\underset{{r}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\frac{{n}\:−\:{r}}{\:^{{n}} {C}_{{r}} }\:+\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{r}}{\:^{{n}} {C}_{{r}} } \\ $$

Question Number 23458    Answers: 0   Comments: 1

Question Number 23445    Answers: 1   Comments: 0

Solve the equation: (∂^2 u/(∂x∂y)) = sin(x)cos(y), subjected to the boundary conditions at y = (π/2), (∂u/∂x) = 2x and x = π, u = 2sin(y)

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}:\:\:\:\frac{\partial^{\mathrm{2}} \mathrm{u}}{\partial\mathrm{x}\partial\mathrm{y}}\:=\:\mathrm{sin}\left(\mathrm{x}\right)\mathrm{cos}\left(\mathrm{y}\right),\:\:\:\mathrm{subjected}\:\mathrm{to}\:\mathrm{the}\:\mathrm{boundary} \\ $$$$\mathrm{conditions}\:\mathrm{at}\:\:\:\mathrm{y}\:=\:\frac{\pi}{\mathrm{2}},\:\:\:\:\frac{\partial\mathrm{u}}{\partial\mathrm{x}}\:=\:\mathrm{2x}\:\:\:\:\mathrm{and}\:\:\:\:\:\mathrm{x}\:=\:\pi,\:\:\:\:\mathrm{u}\:=\:\mathrm{2sin}\left(\mathrm{y}\right) \\ $$

Question Number 23444    Answers: 0   Comments: 0

Question Number 23442    Answers: 1   Comments: 2

Find a unit vector which is perpendicula to a vector A(3coma5coma1) Sorry for writing coma cuz i dnt see a key for it

$$\mathrm{Find}\:\mathrm{a}\:\mathrm{unit}\:\mathrm{vector}\:\mathrm{which}\:\mathrm{is}\:\mathrm{perpendicula} \\ $$$$\mathrm{to}\:\mathrm{a}\:\mathrm{vector}\:\mathrm{A}\left(\mathrm{3coma5coma1}\right) \\ $$$$ \\ $$$$\mathrm{Sorry}\:\mathrm{for}\:\mathrm{writing}\:\mathrm{coma}\:\mathrm{cuz}\:\mathrm{i}\:\mathrm{dnt}\:\mathrm{see}\:\mathrm{a}\:\mathrm{key}\:\mathrm{for}\:\mathrm{it} \\ $$

Question Number 23433    Answers: 0   Comments: 0

∫_0 ^∞ X^6 e^(−x/2) dx=

$$\int_{\mathrm{0}} ^{\infty} {X}^{\mathrm{6}} {e}^{−{x}/\mathrm{2}} {dx}= \\ $$

Question Number 23432    Answers: 1   Comments: 0

∫_0 ^a f(x)dx=

$$\int_{\mathrm{0}} ^{{a}} {f}\left({x}\right){dx}= \\ $$

Question Number 23431    Answers: 0   Comments: 0

If X is a discrete random variable then p(X≥a)=

$${If}\:{X}\:{is}\:{a}\:{discrete}\:{random}\:{variable}\:{then}\:{p}\left({X}\geqslant{a}\right)= \\ $$

Question Number 23429    Answers: 0   Comments: 1

An asymptote to the curve y^2 (1+x)=x^2 (1−x) is

$${An}\:{asymptote}\:{to}\:{the}\:{curve}\:{y}^{\mathrm{2}} \left(\mathrm{1}+{x}\right)={x}^{\mathrm{2}} \left(\mathrm{1}−{x}\right)\:{is} \\ $$

Question Number 23428    Answers: 2   Comments: 0

the curve ay^2 =x^2 (3a−x) cuts the y-axis at

$${the}\:{curve}\:{ay}^{\mathrm{2}} ={x}^{\mathrm{2}} \left(\mathrm{3}{a}−{x}\right)\:{cuts}\:{the}\:{y}-{axis}\:{at} \\ $$

Question Number 23426    Answers: 1   Comments: 0

just a silly question: write a correct maths equation using only symbols below. Each must be used and only once. 2, 3, 4, 5, =, +

$${just}\:{a}\:{silly}\:{question}: \\ $$$${write}\:{a}\:{correct}\:{maths}\:{equation} \\ $$$${using}\:{only}\:{symbols}\:{below}.\:{Each} \\ $$$${must}\:{be}\:{used}\:{and}\:{only}\:{once}. \\ $$$$\:\:\:\:\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\mathrm{5},\:=,\:+ \\ $$

Question Number 23425    Answers: 0   Comments: 0

a,b,c>0 ⇒((a^3 +b^3 +c^3 )/((a+b)(b+c)(c+a)))≥(3/8) ?

$$\boldsymbol{{a}},\boldsymbol{{b}},\boldsymbol{{c}}>\mathrm{0}\:\Rightarrow\frac{\boldsymbol{{a}}^{\mathrm{3}} +\boldsymbol{{b}}^{\mathrm{3}} +\boldsymbol{{c}}^{\mathrm{3}} }{\left(\boldsymbol{{a}}+\boldsymbol{{b}}\right)\left(\boldsymbol{{b}}+\boldsymbol{{c}}\right)\left(\boldsymbol{{c}}+\boldsymbol{{a}}\right)}\geqslant\frac{\mathrm{3}}{\mathrm{8}}\:? \\ $$

Question Number 23419    Answers: 2   Comments: 0

Question Number 23418    Answers: 1   Comments: 0

∫sec^2 (√x) /(√x) dx

$$\int\mathrm{sec}\:^{\mathrm{2}} \sqrt{\mathrm{x}}\:/\sqrt{\mathrm{x}}\:\mathrm{dx} \\ $$

Question Number 23411    Answers: 2   Comments: 1

Question Number 23409    Answers: 1   Comments: 0

Hybridisation of N in HNO_3 is

$$\mathrm{Hybridisation}\:\mathrm{of}\:\mathrm{N}\:\mathrm{in}\:\mathrm{HNO}_{\mathrm{3}} \:\mathrm{is} \\ $$

Question Number 23408    Answers: 1   Comments: 0

Question Number 23402    Answers: 0   Comments: 2

Question Number 23394    Answers: 1   Comments: 0

Which is correct statement? (1) The entropy of the universe increases and tends towards the maximum value (2) All natural processes are irreversible (3) For reversible isolated processes, change of entropy is zero (4) For irreversible expansion of isolated processes, entropy change < 0

$$\mathrm{Which}\:\mathrm{is}\:\mathrm{correct}\:\mathrm{statement}? \\ $$$$\left(\mathrm{1}\right)\:\mathrm{The}\:\mathrm{entropy}\:\mathrm{of}\:\mathrm{the}\:\mathrm{universe}\:\mathrm{increases} \\ $$$$\mathrm{and}\:\mathrm{tends}\:\mathrm{towards}\:\mathrm{the}\:\mathrm{maximum} \\ $$$$\mathrm{value} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{All}\:\mathrm{natural}\:\mathrm{processes}\:\mathrm{are}\:\mathrm{irreversible} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{For}\:\mathrm{reversible}\:\mathrm{isolated}\:\mathrm{processes}, \\ $$$$\mathrm{change}\:\mathrm{of}\:\mathrm{entropy}\:\mathrm{is}\:\mathrm{zero} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{For}\:\mathrm{irreversible}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\mathrm{isolated}\:\mathrm{processes},\:\mathrm{entropy}\:\mathrm{change}\:<\:\mathrm{0} \\ $$

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