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AllQuestion and Answers: Page 389

Question Number 180917 Answers: 1 Comments: 0

Question Number 180890 Answers: 0 Comments: 2

We have 7 sets with 2 subsets each (yes and no are the 2 subsets of each of the 7 sets) how many possible combinations are there if one of the subset is picked for each of the 7 sets.

Question Number 180889 Answers: 0 Comments: 1

the average of 10 numbers is 5. the sum of their squares is 5000. how large can the largest number among them at most be and how small can the smallest number among them at most be?

$${the}\:{average}\:{of}\:\mathrm{10}\:{numbers}\:{is}\:\mathrm{5}.\:{the} \\ $$$${sum}\:{of}\:{their}\:{squares}\:{is}\:\mathrm{5000}.\:{how}\: \\ $$$${large}\:{can}\:{the}\:{largest}\:{number}\:{among} \\ $$$${them}\:{at}\:{most}\:{be}\:{and}\:{how}\:{small}\:{can}\: \\ $$$${the}\:{smallest}\:{number}\:{among}\:{them} \\ $$$${at}\:{most}\:{be}? \\ $$

Question Number 180886 Answers: 1 Comments: 0

Question Number 180882 Answers: 1 Comments: 1

Question Number 180877 Answers: 1 Comments: 1

Q. find the largest value of such that the positive integers a, b > 1 satisfy. a^b .b^a + a^b + b^a = 5329

Question Number 180874 Answers: 1 Comments: 2

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

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

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