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Question Number 175199 Answers: 1 Comments: 0

Question Number 175193 Answers: 2 Comments: 0

Question Number 175191 Answers: 2 Comments: 1

∫(√(1−(1/x)))dx=?

$$\int\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}{dx}=? \\ $$

Question Number 175188 Answers: 1 Comments: 0

Question Number 175180 Answers: 3 Comments: 0

a_n is an AP and S_n is sum of n terms of this AP. Given that S_(11) −S_7 =72, determine a_6 +a_(13) .

$${a}_{{n}} \:{is}\:{an}\:{AP}\:{and}\:{S}_{{n}} \:{is}\:{sum}\:{of}\:{n}\:{terms} \\ $$$${of}\:{this}\:{AP}. \\ $$$${Given}\:{that}\:{S}_{\mathrm{11}} −{S}_{\mathrm{7}} =\mathrm{72},\:{determine} \\ $$$${a}_{\mathrm{6}} +{a}_{\mathrm{13}} . \\ $$

Question Number 175176 Answers: 2 Comments: 0

Find the equation of the locus of points equidistant from the point A(4, −1) and the line x−y+2=0.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\: \\ $$$$\mathrm{points}\:\mathrm{equidistant}\:\mathrm{from}\:\mathrm{the}\:\mathrm{point} \\ $$$${A}\left(\mathrm{4},\:−\mathrm{1}\right)\:\mathrm{and}\:\mathrm{the}\:\mathrm{line}\:{x}−{y}+\mathrm{2}=\mathrm{0}. \\ $$

Question Number 175175 Answers: 1 Comments: 0

Question Number 175174 Answers: 0 Comments: 0

Question Number 175173 Answers: 0 Comments: 0

Question Number 175172 Answers: 0 Comments: 0

Question Number 175166 Answers: 1 Comments: 0

Question Number 175160 Answers: 1 Comments: 1

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Question Number 175147 Answers: 1 Comments: 0

if x is a real number in [0,1] then the value of lim_(m→∞ ) lim_(n→∞) [1+cos^(2m) (n!πx)]

$$\:\:\:\mathrm{if}\:\mathrm{x}\:\mathrm{is}\:\mathrm{a}\:\mathrm{real}\:\mathrm{number}\:\mathrm{in}\:\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\:\:\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\:\:\:\underset{{m}\rightarrow\infty\:} {\mathrm{lim}}\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left[\mathrm{1}+\mathrm{cos}^{\mathrm{2}{m}} \left({n}!\pi{x}\right)\right]\: \\ $$

Question Number 175137 Answers: 1 Comments: 0

lim_(x→2) ((((5x−9))^(1/5) ((4x−7))^(1/4) ((3x−5))^(1/3) (√(2x−3))−1)/(x−2))=?

$$\:\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{5}}]{\mathrm{5}{x}−\mathrm{9}}\:\sqrt[{\mathrm{4}}]{\mathrm{4}{x}−\mathrm{7}}\:\sqrt[{\mathrm{3}}]{\mathrm{3}{x}−\mathrm{5}}\:\sqrt{\mathrm{2}{x}−\mathrm{3}}−\mathrm{1}}{{x}−\mathrm{2}}=? \\ $$

Question Number 175132 Answers: 0 Comments: 4

≺ Question− algebra ≻ Count the number of ” zero divisor ” of ring , ( Z_( 45) , , ⊕ ) ■ m.n −−−−−−−−

$$ \\ $$$$\:\:\:\:\:\:\prec\:\:\boldsymbol{{Question}}−\:\boldsymbol{{algebra}}\:\succ \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{{Count}}\:\boldsymbol{{the}}\:\boldsymbol{{number}}\:\boldsymbol{{of}}\:\:\:''\:\boldsymbol{{zero}}\:\boldsymbol{{divisor}}\:'' \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{{of}}\:\:\boldsymbol{{ring}}\:,\:\:\:\left(\:\mathbb{Z}_{\:\mathrm{45}} \:,\: \:,\:\oplus\:\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\blacksquare\:\:\boldsymbol{{m}}.\boldsymbol{{n}}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:−−−−−−−−\:\:\:\: \\ $$

Question Number 175122 Answers: 1 Comments: 0

Question Number 175121 Answers: 2 Comments: 0

Question Number 175115 Answers: 2 Comments: 0

Question Number 175108 Answers: 1 Comments: 0

Question Number 175110 Answers: 2 Comments: 3

Prove that determinant ((1,1,1),(a,b,c),(a^2 ,b^2 ,c^2 ))= (a−b)(b−c)(c−a)

$$\mathrm{Prove}\:\mathrm{that}\begin{vmatrix}{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{{a}}&{{b}}&{{c}}\\{{a}^{\mathrm{2}} }&{{b}^{\mathrm{2}} }&{{c}^{\mathrm{2}} }\end{vmatrix}=\:\left({a}−{b}\right)\left({b}−{c}\right)\left({c}−{a}\right) \\ $$

Question Number 175104 Answers: 1 Comments: 0

log _3 (a+1)=log _4 (a+8) a=?

$$\:\:\mathrm{log}\:_{\mathrm{3}} \left({a}+\mathrm{1}\right)=\mathrm{log}\:_{\mathrm{4}} \left({a}+\mathrm{8}\right) \\ $$$$\:{a}=? \\ $$

Question Number 175103 Answers: 1 Comments: 0

If 20 (mod 9) is equivalent to y (mod 6). Find y

$$\mathrm{If}\:\:\mathrm{20}\:\left(\mathrm{mod}\:\mathrm{9}\right)\:\:\mathrm{is}\:\mathrm{equivalent}\:\mathrm{to}\:\:\:\mathrm{y}\:\left(\mathrm{mod}\:\mathrm{6}\right).\:\:\mathrm{Find}\:\:\mathrm{y} \\ $$

Question Number 175095 Answers: 1 Comments: 0

x^3 +x^2 +x+c=0 find x

$$\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{c}}=\mathrm{0} \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{x}} \\ $$

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