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Question Number 7945    Answers: 1   Comments: 4

Question Number 7939    Answers: 1   Comments: 3

f(x, y) = xy^3 + 5xy^2 + 2x + 1 find: f_x , f_y , f_(xx) , f_(yy) , f_(xy) , f_(yx)

$${f}\left({x},\:{y}\right)\:=\:{xy}^{\mathrm{3}} \:+\:\mathrm{5}{xy}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:+\:\mathrm{1} \\ $$$${find}:\:\:{f}_{{x}} \:,\:{f}_{{y}} \:,\:{f}_{{xx}} \:,\:{f}_{{yy}} \:,\:{f}_{{xy}} \:,\:{f}_{{yx}} \\ $$

Question Number 7938    Answers: 0   Comments: 0

if f(x) = xlog(x + r) − r and r^2 = x^2 + y^2 prove that: f_(xx) + f_(yy) = (1/(x + r))

$${if}\:\:{f}\left({x}\right)\:=\:{xlog}\left({x}\:+\:{r}\right)\:−\:{r}\:\:{and}\:\:{r}^{\mathrm{2}} \:=\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \\ $$$${prove}\:{that}:\:\:{f}_{{xx}} \:+\:{f}_{{yy}} \:\:=\:\:\frac{\mathrm{1}}{{x}\:+\:{r}} \\ $$

Question Number 7937    Answers: 0   Comments: 0

f(x, y) = x^2 siny + cos(x − 2y) Obtain f_(xx) , f_(yy) , f_(xy) , is f(x, y) contineous ?

$${f}\left({x},\:{y}\right)\:=\:{x}^{\mathrm{2}} {siny}\:+\:{cos}\left({x}\:−\:\mathrm{2}{y}\right) \\ $$$${Obtain}\:\:{f}_{{xx}} \:,\:\:{f}_{{yy}} \:,\:\:{f}_{{xy}} \:,\:\:{is}\:\:{f}\left({x},\:{y}\right)\:{contineous}\:? \\ $$

Question Number 7935    Answers: 1   Comments: 2

Find U_x , U_(xy ) , U_(yy) Given that : U = x^3 y − siny

$${Find}\:\:{U}_{{x}} \:,\:\:{U}_{{xy}\:} \:,\:\:{U}_{{yy}} \:\: \\ $$$${Given}\:{that}\::\:\: \\ $$$${U}\:=\:{x}^{\mathrm{3}} {y}\:−\:{siny} \\ $$

Question Number 7932    Answers: 1   Comments: 2

Question Number 7912    Answers: 2   Comments: 1

a^3 +b^3 =?

$${a}^{\mathrm{3}} +{b}^{\mathrm{3}} =? \\ $$

Question Number 7911    Answers: 1   Comments: 0

If a>0, b>0, c>0 are respectively the p^(th) , q^(th) , r^(th) terms of a GP, then the value of the determinant determinant (((log a),p,1),((log b),q,1),((log c),r,1)) is

$$\mathrm{If}\:{a}>\mathrm{0},\:{b}>\mathrm{0},\:{c}>\mathrm{0}\:\mathrm{are}\:\mathrm{respectively}\:\mathrm{the} \\ $$$${p}^{\mathrm{th}} ,\:{q}^{\mathrm{th}} ,\:{r}^{\mathrm{th}} \:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{GP},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{determinant}\:\begin{vmatrix}{\mathrm{log}\:{a}}&{{p}}&{\mathrm{1}}\\{\mathrm{log}\:{b}}&{{q}}&{\mathrm{1}}\\{\mathrm{log}\:{c}}&{{r}}&{\mathrm{1}}\end{vmatrix}\:\mathrm{is} \\ $$

Question Number 7903    Answers: 1   Comments: 4

Question Number 7902    Answers: 1   Comments: 0

The diameter of the wheel of a car is 36 cm. how many revolutions correct to 3 significant figure , will it make to cover a distance of 1.05km take π = ((22)/7)

$${The}\:{diameter}\:{of}\:{the}\:{wheel}\:{of}\:{a}\:{car}\:{is}\:\mathrm{36}\:{cm}.\: \\ $$$${how}\:{many}\:{revolutions}\:{correct}\:{to}\:\mathrm{3}\:{significant} \\ $$$${figure}\:,\:{will}\:{it}\:{make}\:{to}\:{cover}\:{a}\:{distance}\:{of}\:\mathrm{1}.\mathrm{05}{km} \\ $$$${take}\:\pi\:=\:\frac{\mathrm{22}}{\mathrm{7}} \\ $$

Question Number 7901    Answers: 2   Comments: 0

A dealer sold a car to a man and made a profit of 15% the man then sold it to a woman for #120,175.00 at a loss of 5%. How much did the dealer buy the car.

$${A}\:{dealer}\:{sold}\:{a}\:{car}\:{to}\:{a}\:{man}\:{and}\:{made}\:{a}\:{profit}\:{of}\:\mathrm{15\%} \\ $$$${the}\:{man}\:{then}\:{sold}\:{it}\:{to}\:{a}\:{woman}\:{for}\:#\mathrm{120},\mathrm{175}.\mathrm{00} \\ $$$${at}\:{a}\:{loss}\:{of}\:\mathrm{5\%}.\:{How}\:{much}\:{did}\:{the}\:{dealer}\:{buy}\:{the}\:{car}. \\ $$

Question Number 7900    Answers: 1   Comments: 2

Find an equation of the tangent line to the curve y = tan^2 x at the point ((π/3), 3)

$${Find}\:{an}\:{equation}\:{of}\:{the}\:{tangent}\:{line}\:{to}\:{the}\:{curve}\: \\ $$$${y}\:=\:{tan}^{\mathrm{2}} {x}\:\:\:{at}\:\:{the}\:{point}\:\:\left(\frac{\pi}{\mathrm{3}},\:\mathrm{3}\right) \\ $$

Question Number 7898    Answers: 1   Comments: 2

∫cos^6 x dx

$$\int{cos}^{\mathrm{6}} {x}\:\:{dx} \\ $$

Question Number 7887    Answers: 1   Comments: 0

Find the first four terms of the power series expansion of ((sinx)/(1 − x))

$${Find}\:{the}\:{first}\:{four}\:{terms}\:{of}\:{the}\:{power}\:{series}\: \\ $$$${expansion}\:{of}\:\:\:\:\:\frac{{sinx}}{\mathrm{1}\:−\:{x}}\:\:\: \\ $$

Question Number 7884    Answers: 1   Comments: 0

pls help me solve this chemistry question: Considering a general equilibrium equation: mA_((g)) +nB_((g)) ⇋xC_((g) ) +yD_((g)) where m,n,x and y are the coefficient in the balanced eqn. show that: K_p =K_c (RT)^((x+y)−(m+n)) where; K_c is equilibrium constant and K_p is equilibrium constant when P =[gas conc]RT NB: P=partial pressure T=temperature in kevin and R=gas constant

$${pls}\:{help}\:{me}\:{solve}\:{this}\:{chemistry} \\ $$$${question}: \\ $$$${Considering}\:{a}\:{general}\:{equilibrium} \\ $$$${equation}: \\ $$$${mA}_{\left({g}\right)} +{nB}_{\left({g}\right)} \leftrightharpoons{xC}_{\left({g}\right)\:\:} +{yD}_{\left({g}\right)} \\ $$$${where}\:{m},{n},{x}\:{and}\:{y}\:{are}\:{the}\: \\ $$$${coefficient}\:{in}\:{the}\:{balanced}\:{eqn}. \\ $$$${show}\:{that}:\:{K}_{{p}} ={K}_{{c}} \left({RT}\right)^{\left({x}+{y}\right)−\left({m}+{n}\right)} \\ $$$${where};\:{K}_{{c}} \:{is}\:{equilibrium}\:{constant} \\ $$$${and}\:{K}_{{p}} \:{is}\:{equilibrium}\:{constant} \\ $$$${when}\:{P}\:=\left[{gas}\:{conc}\right]{RT} \\ $$$${NB}:\:{P}={partial}\:{pressure} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{T}={temperature}\:{in}\:{kevin} \\ $$$$\:{and}\:{R}={gas}\:{constant} \\ $$$$ \\ $$

Question Number 7883    Answers: 1   Comments: 3

Let a,b,c be the lengths of the sides of a triangle. Show that abc≥(a+b−c)(b+c−a)(c+a−b).

$${Let}\:{a},{b},{c}\:{be}\:{the}\:{lengths}\:{of}\:{the}\:{sides}\:{of}\:{a}\:{triangle}. \\ $$$${Show}\:{that}\:{abc}\geqslant\left({a}+{b}−{c}\right)\left({b}+{c}−{a}\right)\left({c}+{a}−{b}\right). \\ $$

Question Number 7881    Answers: 1   Comments: 2

A gets 1/5 of some amount, B gets 1/3 of remaining, C gets 1/6 of remaining, D gets 1/7 of remaining and E gets rest of amount. What fraction gets E ?

$${A}\:{gets}\:\mathrm{1}/\mathrm{5}\:\:{of}\:\:{some}\:\:{amount}, \\ $$$${B}\:\:{gets}\:\mathrm{1}/\mathrm{3}\:\:{of}\:\:{remaining},\:{C} \\ $$$${gets}\:\mathrm{1}/\mathrm{6}\:{of}\:{remaining},\:{D}\:{gets} \\ $$$$\mathrm{1}/\mathrm{7}\:\:{of}\:\:{remaining}\:\:{and}\:{E}\:{gets} \\ $$$${rest}\:{of}\:{amount}.\:{What}\:{fraction} \\ $$$${gets}\:{E}\:? \\ $$

Question Number 7880    Answers: 0   Comments: 0

∫((√(1 − x − x^2 ))) dx

$$\int\left(\sqrt{\mathrm{1}\:−\:{x}\:−\:{x}^{\mathrm{2}} }\right)\:{dx} \\ $$

Question Number 7872    Answers: 1   Comments: 4

∫((x − 8)/(x^2 + 4x + 16)) dx

$$\int\frac{{x}\:−\:\mathrm{8}}{{x}^{\mathrm{2}} \:+\:\mathrm{4}{x}\:+\:\mathrm{16}}\:{dx} \\ $$

Question Number 7869    Answers: 0   Comments: 2

How do you find the numerical value for x in: xe^x =1

$$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{find}\:\mathrm{the}\:\mathrm{numerical}\:\mathrm{value} \\ $$$$\mathrm{for}\:{x}\:\mathrm{in}: \\ $$$${xe}^{{x}} =\mathrm{1} \\ $$

Question Number 7861    Answers: 1   Comments: 3

Prove that Σ_(i=0) ^(n+1) (((n+1)),(i) ) i^n (−1)^(i+1) =0 for ∀n∈N.

$${Prove}\:{that}\:\underset{{i}=\mathrm{0}} {\overset{{n}+\mathrm{1}} {\sum}}\begin{pmatrix}{{n}+\mathrm{1}}\\{{i}}\end{pmatrix}\:{i}^{{n}} \left(−\mathrm{1}\right)^{{i}+\mathrm{1}} =\mathrm{0}\: \\ $$$${for}\:\forall{n}\in\mathbb{N}. \\ $$

Question Number 7859    Answers: 1   Comments: 0

Find the remainder if 49^(1296) × 7^(131) is divided by 13

$${Find}\:{the}\:{remainder}\:{if}\:\:\:\mathrm{49}^{\mathrm{1296}} \:×\:\mathrm{7}^{\mathrm{131}} \:\:{is}\:{divided} \\ $$$${by}\:\:\mathrm{13}\:\: \\ $$

Question Number 7858    Answers: 0   Comments: 0

Find the derivative of x^(sin2x) from the first priniple.

$${Find}\:{the}\:{derivative}\:{of}\:\:\:\:{x}^{{sin}\mathrm{2}{x}} \:\:\:{from}\:{the}\: \\ $$$${first}\:{priniple}. \\ $$

Question Number 7855    Answers: 0   Comments: 4

Question Number 7847    Answers: 1   Comments: 2

is there a proof of a relationship between ϕ,π,e where π=3.14,ϕ=1.618 and e=2.718 such that ε is some oporator,ε=−+×÷ ϕεπεe=0 or πεeεϕ=0 or eεϕεπ=0

$${is}\:{there}\:{a}\:{proof}\:{of}\:{a}\:{relationship}\:\: \\ $$$${between}\:\varphi,\pi,{e}\:{where}\:\pi=\mathrm{3}.\mathrm{14},\varphi=\mathrm{1}.\mathrm{618}\: \\ $$$${and}\:{e}=\mathrm{2}.\mathrm{718}\:{such}\:{that}\:\varepsilon\:{is}\:{some} \\ $$$${oporator},\varepsilon=−+×\boldsymbol{\div} \\ $$$$\varphi\varepsilon\pi\varepsilon{e}=\mathrm{0}\:{or}\:\pi\varepsilon{e}\varepsilon\varphi=\mathrm{0}\:{or}\:{e}\varepsilon\varphi\varepsilon\pi=\mathrm{0} \\ $$

Question Number 7846    Answers: 0   Comments: 5

There is new update available. The following enhacements are made in this update • You can now zoom on images posted on the forum. • Preview of the image is available while answering or commenting. You can zoom within the preview as well. • You can now export any post in the forum as an image for offline reference. • A menu option is added which provides you ability to report post with inappropriate content for this forum. Content reported inappropriate will have red title bar until reviewed and removed by us. zoom: keep one finger touched inside the image and move another away or closer to zoom in or out. To scroll inside a zoomed image keep one finger touch outside of the image and use another finger to scroll. For feedback or questions please comment on this post or email us infoattinkutara.com

$$\mathrm{There}\:\mathrm{is}\:\mathrm{new}\:\mathrm{update}\:\mathrm{available}. \\ $$$$\mathrm{The}\:\mathrm{following}\:\mathrm{enhacements}\:\mathrm{are}\:\mathrm{made}\:\mathrm{in} \\ $$$$\mathrm{this}\:\mathrm{update} \\ $$$$\bullet\:\mathrm{You}\:\mathrm{can}\:\mathrm{now}\:\mathrm{zoom}\:\mathrm{on}\:\mathrm{images}\:\mathrm{posted}\:\mathrm{on} \\ $$$$\:\:\:\:\mathrm{the}\:\mathrm{forum}. \\ $$$$\bullet\:\mathrm{Preview}\:\mathrm{of}\:\mathrm{the}\:\mathrm{image}\:\mathrm{is}\:\mathrm{available}\:\mathrm{while} \\ $$$$\:\:\:\:\mathrm{answering}\:\mathrm{or}\:\mathrm{commenting}.\:\mathrm{You}\:\mathrm{can} \\ $$$$\:\:\:\:\mathrm{zoom}\:\mathrm{within}\:\mathrm{the}\:\mathrm{preview}\:\mathrm{as}\:\mathrm{well}. \\ $$$$\bullet\:\mathrm{You}\:\mathrm{can}\:\mathrm{now}\:\mathrm{export}\:\mathrm{any}\:\mathrm{post}\:\mathrm{in}\:\mathrm{the}\:\mathrm{forum} \\ $$$$\:\:\:\:\mathrm{as}\:\mathrm{an}\:\mathrm{image}\:\mathrm{for}\:\mathrm{offline}\:\mathrm{reference}. \\ $$$$\bullet\:\mathrm{A}\:\mathrm{menu}\:\mathrm{option}\:\mathrm{is}\:\mathrm{added}\:\mathrm{which}\:\mathrm{provides} \\ $$$$\:\:\:\:\mathrm{you}\:\mathrm{ability}\:\mathrm{to}\:\mathrm{report}\:\mathrm{post}\:\mathrm{with}\:\mathrm{inappropriate} \\ $$$$\:\:\:\:\mathrm{content}\:\mathrm{for}\:\mathrm{this}\:\mathrm{forum}.\:\mathrm{Content}\:\mathrm{reported} \\ $$$$\:\:\:\:\mathrm{inappropriate}\:\mathrm{will}\:\mathrm{have}\:\mathrm{red}\:\mathrm{title}\:\mathrm{bar} \\ $$$$\:\:\:\:\mathrm{until}\:\mathrm{reviewed}\:\mathrm{and}\:\mathrm{removed}\:\mathrm{by}\:\mathrm{us}. \\ $$$$\mathrm{zoom}:\:\mathrm{keep}\:\mathrm{one}\:\mathrm{finger}\:\mathrm{touched}\:\mathrm{inside}\:\mathrm{the}\:\mathrm{image} \\ $$$$\mathrm{and}\:\mathrm{move}\:\mathrm{another}\:\mathrm{away}\:\mathrm{or}\:\mathrm{closer}\:\mathrm{to}\:\mathrm{zoom}\:\mathrm{in} \\ $$$$\mathrm{or}\:\mathrm{out}. \\ $$$$\mathrm{To}\:\mathrm{scroll}\:\mathrm{inside}\:\mathrm{a}\:\mathrm{zoomed}\:\mathrm{image}\:\mathrm{keep}\:\mathrm{one} \\ $$$$\mathrm{finger}\:\mathrm{touch}\:\mathrm{outside}\:\mathrm{of}\:\mathrm{the}\:\mathrm{image}\:\mathrm{and} \\ $$$$\mathrm{use}\:\mathrm{another}\:\mathrm{finger}\:\mathrm{to}\:\mathrm{scroll}. \\ $$$$\mathrm{For}\:\mathrm{feedback}\:\mathrm{or}\:\mathrm{questions}\:\mathrm{please}\:\mathrm{comment}\:\mathrm{on} \\ $$$$\mathrm{this}\:\mathrm{post}\:\mathrm{or}\:\mathrm{email}\:\mathrm{us}\:\mathrm{infoattinkutara}.\mathrm{com} \\ $$

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