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f(x,y,z)= x(p+z)+y(p−z) +((4x^3 )/(p+z))+((4y^3 )/(p−z))+4(x+y)^2 (y−x) ∀ p(x,y)=c+(x−y)(√(1+(x+y)^2 )) +(x^2 −y^2 ) Determine x,y,z such that f is maximum. (c is a constant). Assume y≥x.

$${f}\left({x},{y},{z}\right)=\:{x}\left({p}+{z}\right)+{y}\left({p}−{z}\right) \\ $$$$\:\:\:\:+\frac{\mathrm{4}{x}^{\mathrm{3}} }{{p}+{z}}+\frac{\mathrm{4}{y}^{\mathrm{3}} }{{p}−{z}}+\mathrm{4}\left({x}+{y}\right)^{\mathrm{2}} \left({y}−{x}\right) \\ $$$$\forall\:\:{p}\left({x},{y}\right)={c}+\left({x}−{y}\right)\sqrt{\mathrm{1}+\left({x}+{y}\right)^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right) \\ $$$${Determine}\:{x},{y},{z}\:{such}\:{that}\:{f}\:{is} \\ $$$${maximum}.\:\left({c}\:{is}\:{a}\:{constant}\right). \\ $$$${Assume}\:{y}\geqslant{x}. \\ $$

Question Number 62998 Answers: 0 Comments: 12

Solve for x: 5^x +6x=7

$${Solve}\:{for}\:{x}:\:\:\mathrm{5}^{\boldsymbol{{x}}} +\mathrm{6}\boldsymbol{{x}}=\mathrm{7} \\ $$

Question Number 62997 Answers: 0 Comments: 1

∫((ln(1+xsin^2 (x)))/(sin^2 (x))) dx

$$\int\frac{{ln}\left(\mathrm{1}+{xsin}^{\mathrm{2}} \left({x}\right)\right)}{{sin}^{\mathrm{2}} \left({x}\right)}\:{dx} \\ $$

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If tan 2θ tan θ = 1, then θ =

$$\mathrm{If}\:\:\:\mathrm{tan}\:\mathrm{2}\theta\:\mathrm{tan}\:\theta\:=\:\mathrm{1},\:\mathrm{then}\:\theta\:= \\ $$

Question Number 62982 Answers: 1 Comments: 0

((tg((x/2))−1)/(ctg((x/2))))=2sin((x/2)) x∈(180°;540°)

$$\frac{\boldsymbol{\mathrm{tg}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)−\mathrm{1}}{\boldsymbol{\mathrm{ctg}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)}=\mathrm{2}\boldsymbol{\mathrm{sin}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)\:\:\boldsymbol{\mathrm{x}}\in\left(\mathrm{180}°;\mathrm{540}°\right) \\ $$$$ \\ $$

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Find the greatest coefficient in the expansion of (6 − 4x)^(−3)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\:\:\left(\mathrm{6}\:−\:\mathrm{4x}\right)^{−\mathrm{3}} \\ $$

Question Number 62942 Answers: 1 Comments: 10

Make r the subject of the formular: S = ((a(r^n − 1))/(r − 1))

$$\mathrm{Make}\:\:\mathrm{r}\:\:\mathrm{the}\:\mathrm{subject}\:\mathrm{of}\:\mathrm{the}\:\mathrm{formular}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{S}\:\:=\:\:\frac{\mathrm{a}\left(\mathrm{r}^{\mathrm{n}} \:−\:\mathrm{1}\right)}{\mathrm{r}\:−\:\mathrm{1}} \\ $$

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∫_0 ^( x) (1/(1+x^2 )) dx

$$\int_{\mathrm{0}} ^{\:\:\mathrm{x}} \frac{\mathrm{1}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$

Question Number 62930 Answers: 0 Comments: 0

find the value ∫_0 ^1 x^(√x) dx (study first the convergence)

$${find}\:{the}\:{value}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{\sqrt{{x}}} {dx}\:\left({study}\:{first}\:{the}\:{convergence}\right) \\ $$

Question Number 62925 Answers: 1 Comments: 0

Three friends , Boakye , kwame and kojo thinking that they are decieving their parents decided to take turns to run away from their parent . Boakye run away on monday of the first week. After how many weeks will he run again on monday?

$$\mathrm{Three}\:\mathrm{friends}\:,\:\mathrm{Boakye}\:,\:\mathrm{kwame}\:\mathrm{and}\: \\ $$$$\mathrm{kojo}\:\mathrm{thinking}\:\mathrm{that}\:\mathrm{they}\:\mathrm{are}\:\mathrm{decieving}\: \\ $$$$\mathrm{their}\:\mathrm{parents}\:\mathrm{decided}\:\mathrm{to}\:\mathrm{take}\:\mathrm{turns}\:\mathrm{to}\: \\ $$$$\mathrm{run}\:\mathrm{away}\:\mathrm{from}\:\mathrm{their}\:\mathrm{parent}\:. \\ $$$$\mathrm{Boakye}\:\mathrm{run}\:\mathrm{away}\:\mathrm{on}\:\mathrm{monday}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{week}.\:\mathrm{After}\:\mathrm{how}\:\mathrm{many}\:\:\mathrm{weeks}\:\mathrm{will}\: \\ $$$$\mathrm{he}\:\mathrm{run}\:\mathrm{again}\:\mathrm{on}\:\mathrm{monday}? \\ $$

Question Number 62924 Answers: 1 Comments: 2

find min_((a,b)∈R^2 ) ∫_(−1) ^1 (ax+b)^2 dx

$${find}\:{min}_{\left({a},{b}\right)\in{R}^{\mathrm{2}} } \:\:\:\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} \left({ax}+{b}\right)^{\mathrm{2}} {dx} \\ $$

Question Number 62919 Answers: 0 Comments: 1

kelvin and price were contesting for an election in the year 2016, kelvin lost the election and prince won the election thursday of the second week of December. After how many days will prince win the election again on thursday if the eletion is postponed to the first week of january. suppose (kelvin continious to loose the eletion again in the next four years to come). please help me solve this quetion

$$\mathrm{kelvin}\:\mathrm{and}\:\mathrm{price}\:\mathrm{were}\:\mathrm{contesting}\:\mathrm{for}\:\mathrm{an} \\ $$$$\mathrm{election}\:\mathrm{in}\:\mathrm{the}\:\mathrm{year}\:\mathrm{2016},\:\mathrm{kelvin}\:\mathrm{lost}\:\mathrm{the} \\ $$$$\mathrm{election}\:\mathrm{and}\:\:\mathrm{prince}\:\mathrm{won}\:\mathrm{the}\:\mathrm{election}\:\mathrm{thursday} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{second}\:\mathrm{week}\:\mathrm{of}\:\mathrm{December}.\:\mathrm{After} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{days}\:\mathrm{will}\:\mathrm{prince}\:\mathrm{win}\:\mathrm{the}\:\mathrm{election} \\ $$$$\mathrm{again}\:\mathrm{on}\:\mathrm{thursday}\:\mathrm{if}\:\mathrm{the}\:\mathrm{eletion}\:\mathrm{is}\:\mathrm{postponed}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{first}\:\mathrm{week}\:\mathrm{of}\:\mathrm{january}.\:\mathrm{suppose}\:\left(\mathrm{kelvin}\:\mathrm{continious}\right. \\ $$$$\mathrm{to}\:\mathrm{loose}\:\mathrm{the}\:\mathrm{eletion}\:\mathrm{again}\:\mathrm{in}\:\mathrm{the}\:\mathrm{next}\:\mathrm{four} \\ $$$$\left.\mathrm{years}\:\mathrm{to}\:\mathrm{come}\right).\: \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{quetion} \\ $$

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P(x)=tan^(−1) (x)=Σ_(n=0) ^∞ (((−1)^n x^(2n+1) )/(2n+1)) P_(1000) (x)=? what is this sum in terms of x?

$${P}\left({x}\right)=\mathrm{tan}^{−\mathrm{1}} \left({x}\right)=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{2}{n}+\mathrm{1}}\: \\ $$$${P}_{\mathrm{1000}} \left({x}\right)=?\:{what}\:{is}\:{this}\:{sum}\:{in}\:{terms}\:{of}\:{x}? \\ $$

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