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AllQuestion and Answers: Page 1048

Question Number 107905 Answers: 1 Comments: 3

Which of the following set of horizontal forces would lead an object in equilibrium? (a) 5N 10N 20N (b) 6N 12N 18N (c) 8N 8N 8N (b) 2N 4N 8N 16N

$$\mathrm{W}{hich}\:{of}\:{the}\:{following}\:{set}\:{of}\:{horizontal} \\ $$$${forces}\:{would}\:{lead}\:{an}\:{object}\:{in}\:{equilibrium}? \\ $$$$\left({a}\right)\:\mathrm{5}{N}\:\:\:\mathrm{10}{N}\:\:\mathrm{20}{N} \\ $$$$\left({b}\right)\:\mathrm{6}{N}\:\:\:\mathrm{12}{N}\:\:\:\:\mathrm{18}{N} \\ $$$$\left({c}\right)\:\mathrm{8}{N}\:\:\:\mathrm{8}{N}\:\:\:\mathrm{8}{N} \\ $$$$\left({b}\right)\:\mathrm{2}{N}\:\:\:\:\mathrm{4}{N}\:\:\:\mathrm{8}{N}\:\:\:\mathrm{16}{N} \\ $$

Question Number 107900 Answers: 2 Comments: 0

((Σ BeMath Σ)/□) Given tan x−sec x = ϑ then sin x = ?

$$\:\:\:\:\:\:\:\frac{\Sigma\:\mathcal{B}{e}\mathcal{M}{ath}\:\Sigma}{\Box} \\ $$$$\:\:{Given}\:\mathrm{tan}\:{x}−\mathrm{sec}\:{x}\:=\:\vartheta\: \\ $$$$\:{then}\:\mathrm{sin}\:{x}\:=\:? \\ $$

Question Number 107883 Answers: 1 Comments: 0

Expand e^(1/x) (√(x(x+2)))

$$\mathrm{Expand}\:\mathrm{e}^{\mathrm{1}/\mathrm{x}} \sqrt{\mathrm{x}\left(\mathrm{x}+\mathrm{2}\right)} \\ $$

Question Number 107882 Answers: 1 Comments: 5

lim_(x→∞) (((a^(1/x) +b^(1/x) )/2))^x

$$\underset{\mathrm{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{a}^{\mathrm{1}/\mathrm{x}} +\mathrm{b}^{\mathrm{1}/\mathrm{x}} }{\mathrm{2}}\right)^{\mathrm{x}} \\ $$

Question Number 107877 Answers: 0 Comments: 0

Question Number 107867 Answers: 0 Comments: 0

Question Number 107859 Answers: 0 Comments: 0

find A_n =∫_0 ^1 x^n (√(1+x+x^2 ))dx (n natural)

$$\mathrm{find}\:\mathrm{A}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{x}^{\mathrm{n}} \sqrt{\mathrm{1}+\mathrm{x}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}\:\:\left(\mathrm{n}\:\mathrm{natural}\right) \\ $$

Question Number 107858 Answers: 0 Comments: 1

calculate ∫_0 ^1 ((ln(1+x^2 ))/(1+x^4 ))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }\mathrm{dx} \\ $$

Question Number 107855 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((lnx)/((1+x)^4 ))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{lnx}}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{4}} }\mathrm{dx}\: \\ $$

Question Number 107852 Answers: 2 Comments: 0

Question Number 107847 Answers: 0 Comments: 0

Question Number 107844 Answers: 0 Comments: 0

A general case: we have totally n letters, among them n_1 times A, n_2 times B, n_3 times C, n_4 times D etc. (n_1 ,n_2 ,n_3 ,n_(4,) ...≥2, n>n_1 +n_2 +n_3 +n_4 +....) how many different words can be formed using these n letters such that same letters are not next to each other. see also Q107451.

$${A}\:{general}\:{case}: \\ $$$${we}\:{have}\:{totally}\:{n}\:{letters},\:{among}\:{them} \\ $$$${n}_{\mathrm{1}} \:{times}\:{A},\:{n}_{\mathrm{2}} \:{times}\:{B},\:{n}_{\mathrm{3}} \:{times}\:{C}, \\ $$$${n}_{\mathrm{4}} \:{times}\:{D}\:{etc}. \\ $$$$\left({n}_{\mathrm{1}} ,{n}_{\mathrm{2}} ,{n}_{\mathrm{3}} ,{n}_{\mathrm{4},} ...\geqslant\mathrm{2},\:{n}>{n}_{\mathrm{1}} +{n}_{\mathrm{2}} +{n}_{\mathrm{3}} +{n}_{\mathrm{4}} +....\right) \\ $$$${how}\:{many}\:{different}\:{words}\:{can}\:{be} \\ $$$${formed}\:{using}\:{these}\:{n}\:{letters}\:{such}\:{that} \\ $$$${same}\:{letters}\:{are}\:{not}\:{next}\:{to}\:{each} \\ $$$${other}. \\ $$$$ \\ $$$${see}\:{also}\:{Q}\mathrm{107451}. \\ $$

Question Number 107839 Answers: 1 Comments: 2

App update for teachers 2.136 A new option is added to generate long division method for square root under matrix menu. Enter a number and app will generate table like below.

$$\mathrm{App}\:\mathrm{update}\:\mathrm{for}\:\mathrm{teachers}\:\mathrm{2}.\mathrm{136} \\ $$$$\mathrm{A}\:\mathrm{new}\:\mathrm{option}\:\mathrm{is}\:\mathrm{added}\:\mathrm{to}\:\mathrm{generate} \\ $$$$\mathrm{long}\:\mathrm{division}\:\mathrm{method}\:\mathrm{for}\:\mathrm{square} \\ $$$$\mathrm{root}\:\mathrm{under}\:\mathrm{matrix}\:\mathrm{menu}. \\ $$$$\mathrm{Enter}\:\mathrm{a}\:\mathrm{number}\:\mathrm{and}\:\mathrm{app}\:\mathrm{will} \\ $$$$\mathrm{generate}\:\mathrm{table}\:\mathrm{like}\:\mathrm{below}. \\ $$

Question Number 107835 Answers: 2 Comments: 0

compute In=∫_0 ^1 x^n (√(1−x)) dx

$${compute}\:{In}=\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} \sqrt{\mathrm{1}−{x}}\:{dx} \\ $$

Question Number 107831 Answers: 2 Comments: 0