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Question Number 180873 Answers: 1 Comments: 2

If a,b,c<0 and abc(a+b+c)=64 Then find min of P=2a+b+c

$$\mathrm{If}\:\:\:\mathrm{a},\mathrm{b},\mathrm{c}<\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{abc}\left(\mathrm{a}+\mathrm{b}+\mathrm{c}\right)=\mathrm{64} \\ $$$$\mathrm{Then}\:\mathrm{find}\:\mathrm{min}\:\mathrm{of}\:\:\:\mathrm{P}=\mathrm{2a}+\mathrm{b}+\mathrm{c} \\ $$

Question Number 180871 Answers: 0 Comments: 1

Question Number 180867 Answers: 1 Comments: 0

Question Number 180866 Answers: 1 Comments: 0

Question Number 180896 Answers: 0 Comments: 1

find the maximum of Σ_(i=1) ^(100) sin^3 x_i if Σ_(i=1) ^(100) sin x_i =0.

$${find}\:{the}\:{maximum}\:{of}\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{100}} {\sum}}\mathrm{sin}^{\mathrm{3}} \:{x}_{{i}} \\ $$$${if}\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{100}} {\sum}}\mathrm{sin}\:{x}_{{i}} =\mathrm{0}. \\ $$

Question Number 180858 Answers: 1 Comments: 0

Question Number 180856 Answers: 1 Comments: 0

find all values of m∈R such that the equation: ∫_0 ^( x) ((arctany)/y) dy = mx has two real roots: x_1 ∈(−∞;0) , x_2 ∈(0;∞)

$$\mathrm{find}\:\mathrm{all}\:\mathrm{values}\:\mathrm{of}\:\:\mathrm{m}\in\mathbb{R}\:\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\boldsymbol{\mathrm{x}}} \:\frac{\mathrm{arctan}\boldsymbol{\mathrm{y}}}{\mathrm{y}}\:\mathrm{dy}\:=\:\mathrm{mx} \\ $$$$\mathrm{has}\:\mathrm{two}\:\mathrm{real}\:\mathrm{roots}:\:\:\:\mathrm{x}_{\mathrm{1}} \in\left(−\infty;\mathrm{0}\right)\:,\:\mathrm{x}_{\mathrm{2}} \in\left(\mathrm{0};\infty\right) \\ $$

Question Number 180855 Answers: 0 Comments: 0

Find number of skew symmetric matrices of order 3×3 in which all non diagonal elements are different and belong to the set {−9,−8,−7,...,7,8,9}.

$${Find}\:{number}\:{of}\:{skew}\:{symmetric} \\ $$$${matrices}\:{of}\:{order}\:\mathrm{3}×\mathrm{3}\:{in}\:{which} \\ $$$${all}\:{non}\:{diagonal}\:{elements}\:{are}\: \\ $$$${different}\:{and}\:{belong}\:{to}\:{the}\: \\ $$$${set}\:\left\{−\mathrm{9},−\mathrm{8},−\mathrm{7},...,\mathrm{7},\mathrm{8},\mathrm{9}\right\}. \\ $$

Question Number 180894 Answers: 3 Comments: 2

x^3 +x=1 x^8 +3x^3 =?

$${x}^{\mathrm{3}} +{x}=\mathrm{1} \\ $$$${x}^{\mathrm{8}} +\mathrm{3}{x}^{\mathrm{3}} =? \\ $$

Question Number 180897 Answers: 1 Comments: 5

Question Number 180839 Answers: 1 Comments: 0

Find the derivatives f^′ (x) of the following function with respect to x: f(x)=Sin(π^(Sinx) +π^(Cosx) ). Mastermind

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{derivatives}\:\mathrm{f}^{'} \left(\mathrm{x}\right)\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{function}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to}\:\mathrm{x}: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{Sin}\left(\pi^{\mathrm{Sinx}} +\pi^{\mathrm{Cosx}} \right). \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 180838 Answers: 0 Comments: 1

Find all x∈R that are solutions to this question: 0=(1−x−x^2 −...)∙(2−x−x^2 −...) Mastermind

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{x}\in\mathbb{R}\:\mathrm{that}\:\mathrm{are}\:\mathrm{solutions}\:\mathrm{to}\:\mathrm{this} \\ $$$$\mathrm{question}:\: \\ $$$$\mathrm{0}=\left(\mathrm{1}−\mathrm{x}−\mathrm{x}^{\mathrm{2}} −...\right)\centerdot\left(\mathrm{2}−\mathrm{x}−\mathrm{x}^{\mathrm{2}} −...\right) \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 180837 Answers: 2 Comments: 0

Without using table, find the values of: (1/((1−(√3))^2 )) − (1/((1+(√3))^2 )) Mastermind

$$\mathrm{Without}\:\mathrm{using}\:\mathrm{table},\:\mathrm{find}\:\mathrm{the}\:\mathrm{values} \\ $$$$\mathrm{of}: \\ $$$$\frac{\mathrm{1}}{\left(\mathrm{1}−\sqrt{\mathrm{3}}\right)^{\mathrm{2}} }\:−\:\frac{\mathrm{1}}{\left(\mathrm{1}+\sqrt{\mathrm{3}}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 180836 Answers: 1 Comments: 0

Determine A,B,C such that all of the following function intersect the point (2,2) ; f_1 (x)=Ax + 1, f_2 (x)=Bx^2 + 2, f_3 (x)=Cx^3 + 3 Mastermind

$$\mathrm{Determine}\:\mathrm{A},\mathrm{B},\mathrm{C}\:\mathrm{such}\:\mathrm{that}\:\mathrm{all}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{function}\:\mathrm{intersect}\:\mathrm{the}\:\mathrm{point} \\ $$$$\left(\mathrm{2},\mathrm{2}\right)\:; \\ $$$$\mathrm{f}_{\mathrm{1}} \left(\mathrm{x}\right)=\mathrm{Ax}\:+\:\mathrm{1},\:\:\mathrm{f}_{\mathrm{2}} \left(\mathrm{x}\right)=\mathrm{Bx}^{\mathrm{2}} \:+\:\mathrm{2},\:\: \\ $$$$\mathrm{f}_{\mathrm{3}} \left(\mathrm{x}\right)=\mathrm{Cx}^{\mathrm{3}} \:+\:\mathrm{3} \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 180900 Answers: 0 Comments: 0

show that ∫_1 ^( +∞) (((x−⌊x⌋)/x^2 ))dx = 1 − γ

$${show}\:{that}\:\int_{\mathrm{1}} ^{\:+\infty} \left(\frac{{x}−\lfloor{x}\rfloor}{{x}^{\mathrm{2}} }\right){dx}\:=\:\mathrm{1}\:−\:\gamma \\ $$

Question Number 180899 Answers: 1 Comments: 0

H_n = Σ_(k=1) ^n (1/k) show that H_(2n) − H_n = Σ_(k=1) ^n ((1/(2k−1))−(1/(2k)))

$${H}_{{n}} \:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}} \\ $$$${show}\:{that}\:{H}_{\mathrm{2}{n}} \:−\:{H}_{{n}} \:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{2}{k}−\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{2}{k}}\right) \\ $$

Question Number 180902 Answers: 1 Comments: 0

Calculate the root mean square speed of the molecules of a Helium gas kept in a gas cylinder at 400K. [Take R = 8.3 Jmol^(−1) K^(−1) ] The answer provided is 1.58 kms^(−1) Please I need help with the solution

$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{root}\:\mathrm{mean}\:\mathrm{square}\: \\ $$$$\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{molecules}\:\mathrm{of}\:\mathrm{a}\:{Helium} \\ $$$$\mathrm{gas}\:\mathrm{kept}\:\mathrm{in}\:\mathrm{a}\:\mathrm{gas}\:\mathrm{cylinder}\:\mathrm{at}\:\mathrm{400K}. \\ $$$$\:\:\:\:\:\:\left[{Take}\:\mathrm{R}\:=\:\mathrm{8}.\mathrm{3}\:{Jmol}^{−\mathrm{1}} {K}^{−\mathrm{1}} \right] \\ $$$${The}\:{answer}\:{provided}\:{is}\:\mathrm{1}.\mathrm{58}\:{kms}^{−\mathrm{1}} \\ $$$$\mathrm{Please}\:\mathrm{I}\:\mathrm{need}\:\mathrm{help}\:\mathrm{with}\:\mathrm{the}\:\mathrm{solution} \\ $$

Question Number 180901 Answers: 1 Comments: 0

∫_1 ^( n) ((⌊x⌋)/x^2 )dx =

$$\int_{\mathrm{1}} ^{\:{n}} \frac{\lfloor{x}\rfloor}{{x}^{\mathrm{2}} }{dx}\:=\: \\ $$

Question Number 180828 Answers: 1 Comments: 1

H_n =1+(1/2)+(1/3)+...+(1/n) H_(2n) =? compute H_(2n) −H_n and H_(n+1) −H_n

$${H}_{{n}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+...+\frac{\mathrm{1}}{{n}} \\ $$$${H}_{\mathrm{2}{n}} =?\:{compute}\:{H}_{\mathrm{2}{n}} −{H}_{{n}} \:{and}\:{H}_{{n}+\mathrm{1}} −{H}_{{n}} \\ $$

Question Number 180827 Answers: 0 Comments: 1

which is not range of f(x)=((2x+1)/(x−2))? 1) 2 2) 3 3)10 4) (2/3)

$${which}\:{is}\:{not}\:{range}\:{of}\:{f}\left({x}\right)=\frac{\mathrm{2}{x}+\mathrm{1}}{{x}−\mathrm{2}}? \\ $$$$\left.\mathrm{1}\left.\right)\left.\:\left.\mathrm{2}\:\:\:\:\:\:\:\:\mathrm{2}\right)\:\mathrm{3}\:\:\:\:\:\:\:\:\:\mathrm{3}\right)\mathrm{10}\:\:\:\:\:\:\:\mathrm{4}\right)\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$

Question Number 180826 Answers: 1 Comments: 0

If , 2sin(θ )−3cos(θ) =3 ⇒ 2sin((θ/2)) − 3cos((θ/2)) = ?

$$ \\ $$$$\:\:\:\:\mathrm{I}{f}\:\:,\:\:\:\mathrm{2}{sin}\left(\theta\:\right)−\mathrm{3}{cos}\left(\theta\right)\:=\mathrm{3} \\ $$$$\:\Rightarrow\:\:\:\mathrm{2}{sin}\left(\frac{\theta}{\mathrm{2}}\right)\:−\:\mathrm{3}{cos}\left(\frac{\theta}{\mathrm{2}}\right)\:=\:? \\ $$$$ \\ $$

Question Number 180821 Answers: 0 Comments: 0

We want to randomly fill six digits with one of −1 or +1, what′s the probability that the sum value of those digits is zero provided that the same values of digits aren′t adjacents?

$${We}\:{want}\:{to}\:{randomly}\:{fill}\:{six}\:{digits}\:{with}\:{one}\:{of} \\ $$$$\:−\mathrm{1}\:{or}\:+\mathrm{1},\:{what}'{s}\:{the}\:{probability}\:{that}\:{the}\:{sum} \\ $$$$\:{value}\:{of}\:{those}\:{digits}\:{is}\:{zero}\:{provided}\:{that}\:{the}\:{same} \\ $$$$\:{values}\:{of}\:{digits}\:{aren}'{t}\:{adjacents}? \\ $$

Question Number 180819 Answers: 0 Comments: 0

Question Number 180815 Answers: 0 Comments: 0

Question Number 180813 Answers: 1 Comments: 5

Question Number 180801 Answers: 1 Comments: 0

Solve the Differential equation : (3xy+6y^2 )dx+(2x^2 +9xy)dy=0 Mastermind

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{Differential}\:\mathrm{equation}\:: \\ $$$$\left(\mathrm{3xy}+\mathrm{6y}^{\mathrm{2}} \right)\mathrm{dx}+\left(\mathrm{2x}^{\mathrm{2}} +\mathrm{9xy}\right)\mathrm{dy}=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

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