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Question Number 114343 Answers: 0 Comments: 4

How many ways can we place 5 identical books and another 6 identical books on a shelf?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{we}\:\mathrm{place}\:\mathrm{5}\:\mathrm{identical} \\ $$$$\mathrm{books}\:\mathrm{and}\:\mathrm{another}\:\mathrm{6}\:\mathrm{identical}\:\mathrm{books} \\ $$$$\mathrm{on}\:\mathrm{a}\:\mathrm{shelf}? \\ $$

Question Number 114340 Answers: 1 Comments: 4

(d^2 θ/dt^2 )+(g/l)sinθ=0 Or θ^(∙∙) (t)+(g/l)θ(t)=0

$$\frac{{d}^{\mathrm{2}} \theta}{{dt}^{\mathrm{2}} }+\frac{{g}}{{l}}{sin}\theta=\mathrm{0} \\ $$$${Or}\:\:\:\:\:\overset{\centerdot\centerdot} {\theta}\left({t}\right)+\frac{{g}}{{l}}\theta\left({t}\right)=\mathrm{0} \\ $$

Question Number 114330 Answers: 2 Comments: 1

Question Number 114326 Answers: 4 Comments: 2

a)Find a four−digit number that satisfies the following condition: the sum of the squares of the extreme digits is equal to 13;the sum of the squares of the middle digits is equal to 85;if we substract 1089 from the desired number we obtain a number containing the same digits as the desired number but in reverse order. b)Prove that if the sum k+m+n of three natural numbers is divisible by 6 then k^3 +m^3 +n^3 is also divisible by6

Question Number 114320 Answers: 0 Comments: 0

Question Number 114313 Answers: 0 Comments: 1

Question Number 114302 Answers: 6 Comments: 2

.... calculus .... evaluate ::: i::∫_0 ^( 1) t^2 ln(t)ln(1−t)dt=??? ii::: ψ^′ ((1/4))=??? iii::: ∫_0 ^(π/8) ln(tan(x))dx =???

$$\:\:\:\:\:\:\:\:....\:{calculus}\:.... \\ $$$$\:\:\:\:{evaluate}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$${i}::\int_{\mathrm{0}} ^{\:\mathrm{1}} {t}^{\mathrm{2}} {ln}\left({t}\right){ln}\left(\mathrm{1}−{t}\right){dt}=??? \\ $$$${ii}:::\:\psi^{'} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)=??? \\ $$$${iii}:::\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{8}}} {ln}\left({tan}\left({x}\right)\right){dx}\:=??? \\ $$$$ \\ $$

Question Number 114299 Answers: 2 Comments: 1

solve lim_(p→∞) (((p^2 +2)/(p+2)))^((p+2)/(p^2 +2)) ?

$$\:{solve}\:\underset{{p}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{p}^{\mathrm{2}} +\mathrm{2}}{{p}+\mathrm{2}}\right)^{\frac{{p}+\mathrm{2}}{{p}^{\mathrm{2}} +\mathrm{2}}} \:? \\ $$

Question Number 114295 Answers: 1 Comments: 0

Question Number 114294 Answers: 0 Comments: 1

Question Number 114290 Answers: 1 Comments: 0

Question Number 114288 Answers: 0 Comments: 1

Question Number 114304 Answers: 0 Comments: 6

calculus..... evaluate: Ω=∫_(−1) ^( 1) xln(1^x +2^x +3^x +6^x )dx =???

$$\:\:\:\:\:\:\:{calculus}..... \\ $$$$\:{evaluate}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{−\mathrm{1}} ^{\:\mathrm{1}} {xln}\left(\mathrm{1}^{{x}} +\mathrm{2}^{{x}} +\mathrm{3}^{{x}} +\mathrm{6}^{{x}} \right){dx}\:=???\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 114263 Answers: 2 Comments: 0

3x^3 −3x−(1/2)=0 x_1 ,x_2 ,x_3 ?

$$\mathrm{3x}^{\mathrm{3}} −\mathrm{3x}−\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{0} \\ $$$$\mathrm{x}_{\mathrm{1}} ,\mathrm{x}_{\mathrm{2}} ,\mathrm{x}_{\mathrm{3}} \:? \\ $$

Question Number 114259 Answers: 3 Comments: 0

lim_(x→0) ((x arc sin (x^2 ))/(x cos x−sin x)) ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\:\mathrm{arc}\:\mathrm{sin}\:\left({x}^{\mathrm{2}} \right)}{{x}\:\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}\:? \\ $$

Question Number 114239 Answers: 2 Comments: 1

lim_(x→∞) ((((cos ((4/x))))^(1/(3 )) −1)/(cos ((2/x))−cos ((4/x)))) ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}\:}]{\mathrm{cos}\:\left(\frac{\mathrm{4}}{{x}}\right)}−\mathrm{1}}{\mathrm{cos}\:\left(\frac{\mathrm{2}}{{x}}\right)−\mathrm{cos}\:\left(\frac{\mathrm{4}}{{x}}\right)}\:? \\ $$

Question Number 114272 Answers: 3 Comments: 3

find solution set of equation cos 3x = −cos x , x∈(0,3π)

$${find}\:{solution}\:{set}\:{of}\:{equation}\: \\ $$$$\mathrm{cos}\:\mathrm{3}{x}\:=\:−\mathrm{cos}\:{x}\:,\:{x}\in\left(\mathrm{0},\mathrm{3}\pi\right) \\ $$

Question Number 114236 Answers: 2 Comments: 0

70% of the employees in a multinational corporation have VCD players, 75% have microwave ovens, 80% have ACs and 85% have washing machines. At least what percentage of employees has all four gadgets?

$$\mathrm{70\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{employees}\:\mathrm{in}\:\mathrm{a} \\ $$$$\mathrm{multinational}\:\mathrm{corporation}\:\mathrm{have}\:\mathrm{VCD} \\ $$$$\mathrm{players},\:\mathrm{75\%}\:\mathrm{have}\:\mathrm{microwave}\:\mathrm{ovens}, \\ $$$$\mathrm{80\%}\:\mathrm{have}\:\mathrm{ACs}\:\mathrm{and}\:\mathrm{85\%}\:\mathrm{have}\:\mathrm{washing} \\ $$$$\mathrm{machines}.\:\mathrm{At}\:\mathrm{least}\:\mathrm{what}\:\mathrm{percentage}\:\mathrm{of} \\ $$$$\mathrm{employees}\:\mathrm{has}\:\mathrm{all}\:\mathrm{four}\:\mathrm{gadgets}? \\ $$

Question Number 114235 Answers: 2 Comments: 0

Let A={(n,2n):n∈N} and B={(2n,3n):n∈N}. Then A∩B is equal to

$$\mathrm{Let}\:\mathrm{A}=\left\{\left(\mathrm{n},\mathrm{2n}\right):\mathrm{n}\in\mathrm{N}\right\}\:\mathrm{and} \\ $$$$\mathrm{B}=\left\{\left(\mathrm{2n},\mathrm{3n}\right):\mathrm{n}\in\mathrm{N}\right\}.\:\mathrm{Then}\:\mathrm{A}\cap\mathrm{B}\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 114233 Answers: 1 Comments: 0

If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets A×B and B×A is

$$\mathrm{If}\:\mathrm{two}\:\mathrm{sets}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{having}\:\mathrm{99} \\ $$$$\mathrm{elements}\:\mathrm{in}\:\mathrm{common},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{elements}\:\mathrm{common}\:\mathrm{to}\:\mathrm{each} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{sets}\:\mathrm{A}×\mathrm{B}\:\mathrm{and}\:\mathrm{B}×\mathrm{A}\:\mathrm{is} \\ $$

Question Number 114223 Answers: 1 Comments: 0