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Question Number 215754    Answers: 1   Comments: 0

Question Number 215755    Answers: 1   Comments: 0

Tow men complet a work in 3hr, three women complet it in 5hr, and five children complet it in 10hr. if we consider among these one man, one woman and one child in how much time they will complet it together?

$${Tow}\:{men}\:{complet}\:{a}\:{work}\:{in}\:\mathrm{3}{hr},\:{three} \\ $$$${women}\:{complet}\:{it}\:{in}\:\mathrm{5}{hr},\:{and}\:{five}\: \\ $$$${children}\:{complet}\:{it}\:{in}\:\mathrm{10}{hr}.\:{if}\:{we}\:{consider} \\ $$$${among}\:{these}\:{one}\:{man},\:{one}\:{woman}\:{and}\:{one} \\ $$$${child}\:{in}\:{how}\:{much}\:{time}\:{they}\:{will} \\ $$$${complet}\:{it}\:{together}? \\ $$

Question Number 215739    Answers: 1   Comments: 0

Question Number 215737    Answers: 2   Comments: 1

Question Number 215730    Answers: 1   Comments: 0

Determine a, b, c [Lazy problem] J181-2. x^3 −6x^2 +15x−7=(x+a)^3 +bx+c J182-(1) x^3 +ax+2=(x+1)(x^2 +bx+c)

$$\boldsymbol{\mathrm{Determine}}\:\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}}\:\left[\mathrm{Lazy}\:\mathrm{problem}\right] \\ $$$$\mathrm{J181}-\mathrm{2}.\:{x}^{\mathrm{3}} −\mathrm{6}{x}^{\mathrm{2}} +\mathrm{15}{x}−\mathrm{7}=\left({x}+{a}\right)^{\mathrm{3}} +{bx}+{c} \\ $$$$\mathrm{J182}-\left(\mathrm{1}\right)\:{x}^{\mathrm{3}} +{ax}+\mathrm{2}=\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +{bx}+{c}\right) \\ $$

Question Number 215723    Answers: 2   Comments: 0

Question Number 215718    Answers: 1   Comments: 0

lim_(x→∞) (ln(9/2))^((1/2)x) =?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left({ln}\frac{\mathrm{9}}{\mathrm{2}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}{x}} =? \\ $$$$ \\ $$

Question Number 215715    Answers: 1   Comments: 1

Question Number 215708    Answers: 1   Comments: 0

Question Number 215704    Answers: 1   Comments: 1

Question Number 215710    Answers: 1   Comments: 0

3 different integer numbers are chosen from 0 to 10. what is the probability that they form 1 Cluster 3 Clusters 2 Clusters A cluster is a set of numbers that has maximum range of 2. for example 0,1,2 forms only one cluster. 0,1,4 forms 2 {0,1} and {4}. 0,1,3 also forms 2 {0,1} and {1,2}

$$ \\ $$3 different integer numbers are chosen from 0 to 10. what is the probability that they form 1 Cluster 3 Clusters 2 Clusters A cluster is a set of numbers that has maximum range of 2. for example 0,1,2 forms only one cluster. 0,1,4 forms 2 {0,1} and {4}. 0,1,3 also forms 2 {0,1} and {1,2}

Question Number 215696    Answers: 2   Comments: 0

Question Number 215687    Answers: 2   Comments: 0

Question Number 215679    Answers: 2   Comments: 0

Question Number 215764    Answers: 2   Comments: 0

∫_0 ^1 x^(99) cos^4 (x)dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{x}^{\mathrm{99}} \mathrm{cos}^{\mathrm{4}} \left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 215667    Answers: 2   Comments: 0

lim_(x→1) sec((π/2)x)(arctanx−(π/4))=?

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{sec}\left(\frac{\pi}{\mathrm{2}}{x}\right)\left({arctanx}−\frac{\pi}{\mathrm{4}}\right)=? \\ $$

Question Number 215757    Answers: 0   Comments: 0

Question Number 215659    Answers: 2   Comments: 0

Question Number 215656    Answers: 1   Comments: 0

3x^3 −2x^2 −12x+8=0

$$\mathrm{3}{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} −\mathrm{12}{x}+\mathrm{8}=\mathrm{0} \\ $$

Question Number 215650    Answers: 2   Comments: 2

Question Number 215641    Answers: 1   Comments: 0

Question Number 215640    Answers: 2   Comments: 0

If 2025^(sin^2 x) − 2025^(cos^2 x) = (√(2025)) then 2025^(cos2x) + (1/(2025^(cos2x) )) = ?

$${If}\:\:\mathrm{2025}^{{sin}^{\mathrm{2}} {x}} \:−\:\mathrm{2025}^{{cos}^{\mathrm{2}} {x}} \:=\:\sqrt{\mathrm{2025}} \\ $$$${then}\:\mathrm{2025}^{{cos}\mathrm{2}{x}} \:+\:\frac{\mathrm{1}}{\mathrm{2025}^{{cos}\mathrm{2}{x}} }\:=\:? \\ $$

Question Number 215639    Answers: 2   Comments: 0

(1+(1/z))^((1+z)) =2

$$\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{z}}\right)^{\left(\mathrm{1}+\mathrm{z}\right)} =\mathrm{2} \\ $$

Question Number 215625    Answers: 1   Comments: 5

x^4 +x^3 −8x^2 +2x+4=0 x=1 ∨ x=2 ∨ x=2±(√2) Is this right? I have not enough time to edit my solution

$${x}^{\mathrm{4}} +{x}^{\mathrm{3}} −\mathrm{8}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}=\mathrm{0} \\ $$$${x}=\mathrm{1}\:\vee\:{x}=\mathrm{2}\:\vee\:{x}=\mathrm{2}\pm\sqrt{\mathrm{2}} \\ $$$$\mathrm{Is}\:\mathrm{this}\:\mathrm{right}?\:\mathrm{I}\:\mathrm{have}\:\mathrm{not}\:\mathrm{enough}\:\mathrm{time}\:\mathrm{to}\:\mathrm{edit}\:\mathrm{my}\:\mathrm{solution} \\ $$

Question Number 215608    Answers: 1   Comments: 3

Question Number 215604    Answers: 1   Comments: 0

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