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AllQuestion and Answers: Page 182

Question Number 200265 Answers: 1 Comments: 0

Question Number 200262 Answers: 2 Comments: 0

Question Number 200257 Answers: 1 Comments: 0

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Question Number 200254 Answers: 1 Comments: 0

calculate ... Ω = ∫_(∫_0 ^( (π/2)) ln(tan(x))dx) ^( ∫_0 ^( ∞) ((sin^2 (x))/x^2 ) dx) ln(sin(x))dx=?

$$ \\ $$$$\:\:\:\:\:\:{calculate}\:... \\ $$$$\:\:\Omega\:=\:\int_{\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\mathrm{ln}\left(\mathrm{tan}\left({x}\right)\right){dx}} ^{\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{sin}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} }\:{dx}} \mathrm{ln}\left(\mathrm{sin}\left({x}\right)\right){dx}=? \\ $$

Question Number 200253 Answers: 2 Comments: 0

Question Number 200251 Answers: 1 Comments: 0

Question Number 200250 Answers: 2 Comments: 0

Question Number 200249 Answers: 1 Comments: 1

Solve: find the distance of the point P(3,4) from the line y=−2x+3

$$\boldsymbol{{Solve}}:\:\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{distance}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{point}}\:\boldsymbol{{P}}\left(\mathrm{3},\mathrm{4}\right)\:\boldsymbol{{from}}\:\boldsymbol{{the}}\:\boldsymbol{{line}}\:\boldsymbol{{y}}=−\mathrm{2}\boldsymbol{{x}}+\mathrm{3} \\ $$

Question Number 200242 Answers: 3 Comments: 0

Question Number 200236 Answers: 1 Comments: 0

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 200204 Answers: 1 Comments: 7

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

Question Number 200183 Answers: 0 Comments: 0

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

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