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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

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

Question Number 180800 Answers: 0 Comments: 0

Question Number 180786 Answers: 1 Comments: 0

f(t)=∫_0 ^t x−⌊x⌋ dx

$${f}\left({t}\right)=\int_{\mathrm{0}} ^{{t}} {x}−\lfloor{x}\rfloor\:\:{dx} \\ $$

Question Number 180785 Answers: 2 Comments: 0

solve (1−x−x^2 ...)(2−x−x^2 ...)

$${solve}\:\left(\mathrm{1}−{x}−{x}^{\mathrm{2}} ...\right)\left(\mathrm{2}−{x}−{x}^{\mathrm{2}} ...\right) \\ $$

Question Number 180780 Answers: 0 Comments: 1

Question Number 180778 Answers: 0 Comments: 0

Question Number 180776 Answers: 2 Comments: 0

Simplify (√((4/( (√2))) + 3))

$${Simplify}\:\:\sqrt{\frac{\mathrm{4}}{\:\sqrt{\mathrm{2}}}\:+\:\mathrm{3}}\: \\ $$$$ \\ $$

Question Number 180775 Answers: 0 Comments: 7

A box contains 2 blue, 1 red balls. We randomly draw one ball then put it back and add two balls of the same color of that ball in the box. We randomly draw again one ball, if it was red then what′s the probability that the first drawn ball was blue?

$${A}\:{box}\:{contains}\:\mathrm{2}\:{blue},\:\mathrm{1}\:{red}\:{balls}.\:{We}\:{randomly} \\ $$$$\:{draw}\:{one}\:{ball}\:{then}\:{put}\:{it}\:{back}\:{and}\:{add}\:{two}\:{balls} \\ $$$$\:{of}\:{the}\:{same}\:{color}\:{of}\:{that}\:{ball}\:{in}\:{the}\:{box}.\:{We} \\ $$$$\:{randomly}\:{draw}\:{again}\:{one}\:{ball},\:{if}\:{it}\:{was}\:{red}\:{then} \\ $$$$\:{what}'{s}\:{the}\:{probability}\:{that}\:{the}\:{first}\:{drawn}\:{ball} \\ $$$$\:{was}\:{blue}? \\ $$

Question Number 180773 Answers: 1 Comments: 0

How many triangles can be formed from non−adjacent vertices of a regular polygon that it angle is 177^( °) ?

$${How}\:{many}\:{triangles}\:{can}\:{be}\:{formed}\:{from} \\ $$$$\:{non}−{adjacent}\:{vertices}\:{of}\:{a}\:{regular}\:{polygon} \\ $$$$\:{that}\:{it}\:{angle}\:{is}\:\mathrm{177}^{\:°} \:? \\ $$

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