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Question Number 155913 Answers: 0 Comments: 0

Question Number 155912 Answers: 0 Comments: 0

Determine the triangle with dimensions a;b;c∈N , a+b+c=even and A=P∈N. With maximum area. We denoted A=area and P=perimetr.

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{dimensions} \\ $$$$\mathrm{a};\mathrm{b};\mathrm{c}\in\mathbb{N}\:,\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{even}\:\:\mathrm{and}\:\:\mathrm{A}=\mathrm{P}\in\mathbb{N}. \\ $$$$\mathrm{With}\:\mathrm{maximum}\:\mathrm{area}.\:\mathrm{We}\:\mathrm{denoted} \\ $$$$\mathrm{A}=\mathrm{area}\:\:\mathrm{and}\:\:\:\mathrm{P}=\mathrm{perimetr}. \\ $$

Question Number 155908 Answers: 0 Comments: 0

Solve for x 3^(x+1) +100=7^(x−1) 3^x +3^x^2 =2^x +4^x^2

$$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$$\mathrm{3}^{{x}+\mathrm{1}} +\mathrm{100}=\mathrm{7}^{{x}−\mathrm{1}} \\ $$$$\mathrm{3}^{{x}} +\mathrm{3}^{{x}^{\mathrm{2}} } =\mathrm{2}^{{x}} +\mathrm{4}^{{x}^{\mathrm{2}} } \\ $$

Question Number 155910 Answers: 0 Comments: 0

Question Number 159719 Answers: 1 Comments: 0

F(x)= 3cos x + 4sin x , F^((101)) ((π/2))=?

$$\:\:\:\:\:{F}\left({x}\right)=\:\mathrm{3cos}\:{x}\:+\:\mathrm{4sin}\:{x}\:,\:{F}^{\left(\mathrm{101}\right)} \left(\frac{\pi}{\mathrm{2}}\right)=? \\ $$

Question Number 159717 Answers: 0 Comments: 0

Question Number 155897 Answers: 1 Comments: 0

∫ x(arctan x)^2 dx=?

$$\:\int\:\mathrm{x}\left(\mathrm{arctan}\:\mathrm{x}\right)^{\mathrm{2}} \:\mathrm{dx}=? \\ $$

Question Number 155893 Answers: 0 Comments: 0

Two Spheres are charged by +3μC and −3μC respectively.The charges are equally distributed in the serface of the sphere .The distance between two spheres is 100cm . Now if we Connect these two spheres with a conducting wire , a)What will be the potential difference between two ends of that wire? b)Find the amount of current flow in the wire if the resistance of that wire is 100μΩ .

$$\: \\ $$$$\:\:\mathrm{Two}\:\mathrm{Spheres}\:\mathrm{are}\:\mathrm{charged}\:\mathrm{by}\:+\mathrm{3}\mu\mathrm{C}\:\mathrm{and} \\ $$$$−\mathrm{3}\mu\mathrm{C}\:\mathrm{respectively}.\mathrm{The}\:\mathrm{charges}\:\mathrm{are}\: \\ $$$$\:\:\mathrm{equally}\:\mathrm{distributed}\:\mathrm{in}\:\mathrm{the}\:\mathrm{serface}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\:\:\mathrm{sphere}\:.\mathrm{The}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{two}\: \\ $$$$\:\:\mathrm{spheres}\:\mathrm{is}\:\mathrm{100cm}\:.\:\mathrm{Now}\:\mathrm{if}\:\mathrm{we}\:\mathrm{Connect} \\ $$$$\:\:\mathrm{these}\:\mathrm{two}\:\mathrm{spheres}\:\mathrm{with}\:\mathrm{a}\:\mathrm{conducting}\: \\ $$$$\:\:\mathrm{wire}\:, \\ $$$$\left.\:\:\mathrm{a}\right)\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{potential}\:\mathrm{difference} \\ $$$$\:\mathrm{between}\:\mathrm{two}\:\mathrm{ends}\:\mathrm{of}\:\mathrm{that}\:\mathrm{wire}? \\ $$$$\left.\:\mathrm{b}\right)\mathrm{Find}\:\mathrm{the}\:\mathrm{amount}\:\mathrm{of}\:\mathrm{current}\:\mathrm{flow}\:\mathrm{in} \\ $$$$\:\mathrm{the}\:\mathrm{wire}\:\mathrm{if}\:\mathrm{the}\:\mathrm{resistance}\:\mathrm{of}\:\mathrm{that}\:\mathrm{wire}\: \\ $$$$\:\mathrm{is}\:\mathrm{100}\mu\Omega\:. \\ $$$$\: \\ $$

Question Number 155883 Answers: 0 Comments: 1

∫ ((tan^2 x)/(1−tan^2 x)) dx=?

$$\int\:\frac{\mathrm{tan}\:^{\mathrm{2}} {x}}{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} {x}}\:{dx}=? \\ $$

Question Number 155878 Answers: 2 Comments: 0

the equation of : (a +sin(x))(a+cos(x))=a has solution in R hence : a ∈ ?

$$ \\ $$$$\:\:{the}\:{equation}\:{of}\:: \\ $$$$\:\:\:\:\left({a}\:+{sin}\left({x}\right)\right)\left({a}+{cos}\left({x}\right)\right)={a} \\ $$$$\:\:\:\:{has}\:\:{solution}\:{in}\:\mathbb{R}\: \\ $$$$\:\:\:\:\:\:\:{hence}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{a}\:\in\:? \\ $$$$\:\:\:\: \\ $$$$ \\ $$$$ \\ $$

Question Number 155866 Answers: 1 Comments: 0

Question Number 155863 Answers: 0 Comments: 2

monster integral ∫_0 ^( (π/4)) ln^2 (sin(2x)+ cos(3x)) dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underline{\mathrm{monster}\:\mathrm{integral}} \\ $$$$\: \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \:\mathrm{ln}^{\mathrm{2}} \left(\mathrm{sin}\left(\mathrm{2}{x}\right)+\:\mathrm{cos}\left(\mathrm{3}{x}\right)\right)\:{dx} \\ $$$$\: \\ $$$$\: \\ $$

Question Number 155857 Answers: 1 Comments: 0

1). Find (dy/dx) , if : a). y=(8x−1)(x^2 +4x+7) b). y=(3x^4 −10x+8)(2x^2 +5) 2). Find an equation of the tangen line to the graph of y=(5/(1+x^2 )) at each point a). P(0,5) b). Q(1,(5/2)) 3). Find the coordinat of all point on the graph of : y=x^3 +2x^2 −4x+5 at which the tangen line is: a). horizontal. b). paralel to the line y=2y+8x−5=0 4). Find point P on the graph of y=x^3 such that the tangen line at P has x−intercept 4 5). Find the points at which the graph f(x) and f^′ (x) is intersect , given that a). f(x)=x^3 −x^2 +x+1 b). f(x)=x^2 +2x+1

Question Number 155856 Answers: 2 Comments: 0

How many natural number from 1 to 900 which are not divisible 2,3 and 5

$$\mathrm{How}\:\mathrm{many}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{from} \\ $$$$\mathrm{1}\:\mathrm{to}\:\mathrm{900}\:\mathrm{which}\:\mathrm{are}\:\mathrm{not}\:\mathrm{divisible} \\ $$$$\mathrm{2},\mathrm{3}\:\mathrm{and}\:\mathrm{5} \\ $$

Question Number 155849 Answers: 0 Comments: 0

Ω=∫_0 ^( ∞) log(sinh(x)).log(tanh(x))dx=((7ζ(3))/8) +(π^( 2) /8)ln^ (2)

$$ \\ $$$$\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} {log}\left({sinh}\left({x}\right)\right).{log}\left({tanh}\left({x}\right)\right){dx}=\frac{\mathrm{7}\zeta\left(\mathrm{3}\right)}{\mathrm{8}}\:+\frac{\pi^{\:\mathrm{2}} }{\mathrm{8}}{ln}^{\:} \left(\mathrm{2}\right) \\ $$

Question Number 155898 Answers: 2 Comments: 0

Show that tan^(− 1) ((1/3)) + sin^(− 1) ((1/3)) = (π/4)

$$\mathrm{Show}\:\mathrm{that}\:\:\:\:\:\mathrm{tan}^{−\:\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{3}}\right)\:\:\:+\:\:\:\mathrm{sin}^{−\:\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{3}}\right)\:\:\:=\:\:\:\frac{\pi}{\mathrm{4}} \\ $$

Question Number 155899 Answers: 1 Comments: 0

Find the nth root of 1. Find these values when n = 6.

$$\mathrm{Find}\:\mathrm{the}\:\:\:\mathrm{nth}\:\:\:\mathrm{root}\:\mathrm{of}\:\:\:\mathrm{1}.\:\:\mathrm{Find}\:\mathrm{these}\:\mathrm{values}\:\mathrm{when}\:\:\:\mathrm{n}\:\:=\:\:\mathrm{6}. \\ $$

Question Number 155842 Answers: 1 Comments: 1

Prof that: Σ_(n=1) ^(10) n.n!=11!−1

$$\mathrm{Prof}\:\mathrm{that}: \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\:\mathrm{n}.\mathrm{n}!=\mathrm{11}!−\mathrm{1} \\ $$

Question Number 155979 Answers: 0 Comments: 0

prove that: ∫_0 ^( 1) ∫_0 ^( 1) (((√x) +(√y))/((1−xy)((xy))^(1/4) )) dxdy=4 (4 −π)

$$ \\ $$$${prove}\:{that}: \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\sqrt{{x}}\:+\sqrt{{y}}}{\left(\mathrm{1}−{xy}\right)\sqrt[{\mathrm{4}}]{{xy}}}\:{dxdy}=\mathrm{4}\:\left(\mathrm{4}\:−\pi\right) \\ $$$$ \\ $$

Question Number 155978 Answers: 0 Comments: 2

Question Number 155829 Answers: 1 Comments: 2

Find this excercise about limits trigonometri 1). lim_(θ→0) ((2cos θ−2)/(3θ)) 2). lim_(x→0) ((1−cos x)/x^(2/3) ) 3). lim_(t→0) ((4t^2 +3t sin t)/t^2 ) 4). lim_(x→0) ((x^2 +1)/(x+cos x)) 5). lim_(x→0) ((sin^2 ((x/2)))/(sin x))

$$\mathrm{Find}\:\mathrm{this}\:\mathrm{excercise}\:\mathrm{about}\:\mathrm{limits} \\ $$$$\mathrm{trigonometri} \\ $$$$\left.\mathrm{1}\right).\:\underset{\theta\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2cos}\:\theta−\mathrm{2}}{\mathrm{3}\theta} \\ $$$$\left.\mathrm{2}\right).\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{x}}{\mathrm{x}^{\frac{\mathrm{2}}{\mathrm{3}}} } \\ $$$$\left.\mathrm{3}\right).\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{4t}^{\mathrm{2}} +\mathrm{3t}\:\mathrm{sin}\:\mathrm{t}}{\mathrm{t}^{\mathrm{2}} } \\ $$$$\left.\mathrm{4}\right).\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{x}+\mathrm{cos}\:\mathrm{x}} \\ $$$$\left.\mathrm{5}\right).\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\:\frac{\mathrm{sin}\:^{\mathrm{2}} \:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)}{\mathrm{sin}\:\:\mathrm{x}} \\ $$$$ \\ $$

Question Number 156776 Answers: 1 Comments: 1

Σ_(n=1) ^∞ (n ln(((2n+1)/(2n−1))) −1)=?

$$ \\ $$$$\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left({n}\:{ln}\left(\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{2}{n}−\mathrm{1}}\right)\:−\mathrm{1}\right)=? \\ $$$$ \\ $$

Question Number 156775 Answers: 1 Comments: 1

f is a function that assigns to each natural number multiplication of its digits for exampl : f( 200)=0 f ( 128 )=1×2×8 =16 find the value of : f (100) + f(101 )+ f (102 )+...f(999)=?

$$ \\ $$$$\:\:\:{f}\:\:{is}\:\:{a}\:{function}\:{that}\:{assigns} \\ $$$$\:\:\:{to}\:{each}\:{natural}\:{number}\: \\ $$$$\:\:\:\:\:{multiplication}\:{of}\:{its}\:{digits}\: \\ $$$$\:\:\:\:{for}\:{exampl}\::\:\:{f}\left(\:\mathrm{200}\right)=\mathrm{0} \\ $$$$\:\:\:\:{f}\:\left(\:\mathrm{128}\:\right)=\mathrm{1}×\mathrm{2}×\mathrm{8}\:=\mathrm{16} \\ $$$$\:\:\:\:\:{find}\:{the}\:{value}\:{of}\:: \\ $$$$\:\:\:\:\:{f}\:\left(\mathrm{100}\right)\:+\:{f}\left(\mathrm{101}\:\right)+\:{f}\:\left(\mathrm{102}\:\right)+...{f}\left(\mathrm{999}\right)=? \\ $$$$ \\ $$

Question Number 155816 Answers: 1 Comments: 0

How many of the number formed by using all the digits 1,2,3,4,5,6 only once divisible by 25.

$$\:\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number}\:\mathrm{formed} \\ $$$$\:\mathrm{by}\:\mathrm{using}\:\mathrm{all}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6} \\ $$$$\:\mathrm{only}\:\mathrm{once}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{25}. \\ $$

Question Number 155812 Answers: 2 Comments: 0

Use algebraic simplifications to help find the limits, if they exist. 1). lim_(x→2) ((x^2 −4)/(x−2)) 2). lim_(x→1) ((x^2 −x)/(2x^2 +5x−7)) 3). lim_(x→1) ((3x^2 −13x−10)/(2x^2 −7x−15)) 4). lim_(x→1) ((3x^2 −13x−10)/(2x^2 −7x−15)) 5). lim_(x→2) ((x^3 −8)/(x^2 −4))

$$\mathrm{Use}\:\mathrm{algebraic}\:\mathrm{simplifications}\:\mathrm{to}\:\mathrm{help} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{limits},\:\mathrm{if}\:\mathrm{they}\:\mathrm{exist}. \\ $$$$\left.\mathrm{1}\right).\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{4}}{\mathrm{x}−\mathrm{2}} \\ $$$$\left.\mathrm{2}\right).\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\:\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{x}}{\mathrm{2x}^{\mathrm{2}} +\mathrm{5x}−\mathrm{7}} \\ $$$$\left.\mathrm{3}\right).\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\:\:\frac{\mathrm{3x}^{\mathrm{2}} −\mathrm{13x}−\mathrm{10}}{\mathrm{2x}^{\mathrm{2}} −\mathrm{7x}−\mathrm{15}} \\ $$$$\left.\mathrm{4}\right).\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\:\:\frac{\mathrm{3x}^{\mathrm{2}} −\mathrm{13x}−\mathrm{10}}{\mathrm{2x}^{\mathrm{2}} −\mathrm{7x}−\mathrm{15}} \\ $$$$\left.\mathrm{5}\right).\:\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\:\frac{\mathrm{x}^{\mathrm{3}} −\mathrm{8}}{\mathrm{x}^{\mathrm{2}} −\mathrm{4}}\: \\ $$

Question Number 156188 Answers: 0 Comments: 2

Given a rational function f(x) = ((ax^2 +bx+c)/(x+q)) has minimum point at (−2,9) and maximum point at (2,1) . Find value of a, b, c, and q .

$${Given}\:\:{a}\:\:{rational}\:\:{function} \\ $$$$\:\:\:\:\:{f}\left({x}\right)\:=\:\:\frac{{ax}^{\mathrm{2}} +{bx}+{c}}{{x}+{q}} \\ $$$${has}\:\:{minimum}\:\:{point}\:\:{at}\:\left(−\mathrm{2},\mathrm{9}\right)\:\:{and}\:\:{maximum}\:\:{point}\:\:{at}\:\:\left(\mathrm{2},\mathrm{1}\right)\:. \\ $$$${Find}\:\:{value}\:\:{of}\:\:{a},\:{b},\:{c},\:\:{and}\:\:{q}\:. \\ $$

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