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Question Number 200242 Answers: 3 Comments: 0

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what is the smallest natural number which has at least 100 divisors?

$${what}\:{is}\:{the}\:{smallest}\:{natural}\:{number} \\ $$$${which}\:{has}\:{at}\:{least}\:\mathrm{100}\:{divisors}? \\ $$

Question Number 200224 Answers: 3 Comments: 0

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Question Number 200240 Answers: 0 Comments: 0

the local minimum value of the function f(x,y) = x^2 +xy+y^2 −3x−3y+11

$$\mathrm{the}\:\mathrm{local}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function} \\ $$$${f}\left({x},{y}\right)\:=\:{x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{3}{y}+\mathrm{11} \\ $$

Question Number 200200 Answers: 1 Comments: 0

Find four positive integers, each not exceeding 70000 and each having more than 100 divisors.

$${Find}\:{four}\:{positive}\:{integers}, \\ $$$$\:{each}\:{not}\:{exceeding}\:\mathrm{70000}\:{and}\: \\ $$$${each}\:{having}\:{more}\:{than}\:\mathrm{100} \\ $$$$\:{divisors}. \\ $$

Question Number 200196 Answers: 2 Comments: 3

the minimum of (x+y+z)?

$$\mathrm{the}\:\mathrm{minimum}\:\mathrm{of}\:\left(\mathrm{x}+\mathrm{y}+\mathrm{z}\right)? \\ $$

Question Number 200187 Answers: 2 Comments: 0

Question Number 200186 Answers: 2 Comments: 0

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Question Number 200175 Answers: 2 Comments: 1

find all values of x if x^2 ≡4mod(5) and 0≤x≤11 ?

$${find}\:{all}\:{values}\:{of}\:{x}\:{if}\:{x}^{\mathrm{2}} \equiv\mathrm{4}{mod}\left(\mathrm{5}\right)\:{and}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{11}\:? \\ $$

Question Number 200169 Answers: 1 Comments: 0

Rationalise the deniminator of the following fraction: (1/( (√6) − (√3) + (√2) + 1)) = ?

$$\mathrm{Rationalise}\:\mathrm{the}\:\mathrm{deniminator}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{fraction}: \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{6}}\:−\:\sqrt{\mathrm{3}}\:+\:\sqrt{\mathrm{2}}\:+\:\mathrm{1}}\:=\:? \\ $$

Question Number 200168 Answers: 1 Comments: 2

If f(x) = 2^x + 86 and g(x) = 3x^2 + x − 4 Then find: g[f^(−1) (g(14))] = ?

$$\mathrm{If}\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{86}\:\:\mathrm{and}\:\:\mathrm{g}\left(\mathrm{x}\right)\:=\:\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{x}\:−\:\mathrm{4} \\ $$$$\mathrm{Then}\:\mathrm{find}:\:\:\mathrm{g}\left[\mathrm{f}^{−\mathrm{1}} \left(\mathrm{g}\left(\mathrm{14}\right)\right)\right]\:=\:? \\ $$

Question Number 200167 Answers: 3 Comments: 0

Given f:R→R is a quadratic polynomial f(1) = 1 , f(2) = (1/2) and f(3) = (1/3) Find: f(4) = ?

$$\mathrm{Given}\:\:\:\mathrm{f}:\mathbb{R}\rightarrow\mathbb{R}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{quadratic}\:\mathrm{polynomial} \\ $$$$\mathrm{f}\left(\mathrm{1}\right)\:=\:\mathrm{1}\:,\:\mathrm{f}\left(\mathrm{2}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\:\mathrm{and}\:\:\mathrm{f}\left(\mathrm{3}\right)\:=\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\mathrm{Find}:\:\:\mathrm{f}\left(\mathrm{4}\right)\:=\:? \\ $$

Question Number 200159 Answers: 1 Comments: 2

Question Number 200155 Answers: 2 Comments: 0

Question Number 200139 Answers: 2 Comments: 0

If x : y : z = (1/7) : (1/3) : (1/(21)) 5x − 2y + z = 16 Find: y = ?

$$\mathrm{If} \\ $$$$\mathrm{x}\::\:\mathrm{y}\::\:\mathrm{z}\:=\:\frac{\mathrm{1}}{\mathrm{7}}\::\:\frac{\mathrm{1}}{\mathrm{3}}\::\:\frac{\mathrm{1}}{\mathrm{21}} \\ $$$$\mathrm{5x}\:−\:\mathrm{2y}\:+\:\mathrm{z}\:=\:\mathrm{16} \\ $$$$ \\ $$$$\mathrm{Find}:\:\:\:\mathrm{y}\:=\:? \\ $$

Question Number 200137 Answers: 1 Comments: 5

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solve by contour integrstion ∫_0 ^(2π) (dx/(1+acosx))

$$\:\:{solve}\:{by}\:{contour}\:{integrstion} \\ $$$$\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{{dx}}{\mathrm{1}+{a}\mathrm{cos}{x}}\: \\ $$

Question Number 200125 Answers: 0 Comments: 0

NO_2 (g) ⇒ 2NO (g)+O_2 (g) at 300°C The initial concentration of NO_2 is 0.01 mol/L and its concentration after 150 s is .0055 mol/L. What are the average rates of the above reaction during the first 150 s and during the second 150 s?

$$\mathrm{NO}_{\mathrm{2}} \left(\mathrm{g}\right)\:\Rightarrow\:\mathrm{2NO}\:\left(\mathrm{g}\right)+\mathrm{O}_{\mathrm{2}} \:\left(\mathrm{g}\right)\:\mathrm{at}\:\mathrm{300}°\mathrm{C} \\ $$$$\mathrm{The}\:\mathrm{initial}\:\mathrm{concentration}\:\mathrm{of}\:\mathrm{NO}_{\mathrm{2}} \:\mathrm{is}\: \\ $$$$\mathrm{0}.\mathrm{01}\:\mathrm{mol}/\mathrm{L}\:\mathrm{and}\:\mathrm{its}\:\mathrm{concentration}\: \\ $$$$\mathrm{after}\:\mathrm{150}\:\mathrm{s}\:\mathrm{is}\:.\mathrm{0055}\:\mathrm{mol}/\mathrm{L}.\:\mathrm{What}\:\mathrm{are} \\ $$$$\:\mathrm{the}\:\mathrm{average}\:\mathrm{rates}\:\mathrm{of}\:\mathrm{the}\:\mathrm{above} \\ $$$$\:\mathrm{reaction}\:\mathrm{during}\:\mathrm{the}\:\mathrm{first}\:\mathrm{150}\:\mathrm{s}\:\mathrm{and} \\ $$$$\:\mathrm{during}\:\mathrm{the}\:\mathrm{second}\:\mathrm{150}\:\mathrm{s}? \\ $$

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