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AllQuestion and Answers: Page 74

Question Number 210457 Answers: 2 Comments: 3

Question Number 210456 Answers: 2 Comments: 5

Question Number 210441 Answers: 2 Comments: 0

Question Number 210439 Answers: 1 Comments: 1

Question Number 210432 Answers: 1 Comments: 0

How many different five-digit numbers can be written from the digits 1,2,3,4,5,6,7,8 if the digits are not repeated?

$$ \\ $$How many different five-digit numbers can be written from the digits 1,2,3,4,5,6,7,8 if the digits are not repeated?

Question Number 210416 Answers: 0 Comments: 3

Question Number 210396 Answers: 1 Comments: 2

Question Number 210392 Answers: 1 Comments: 1

Question Number 210390 Answers: 1 Comments: 0

Question Number 210421 Answers: 1 Comments: 0

Question Number 210375 Answers: 2 Comments: 4

Question Number 210374 Answers: 4 Comments: 1

Question Number 210373 Answers: 3 Comments: 2

Question Number 210372 Answers: 5 Comments: 1

Question Number 210371 Answers: 4 Comments: 0

Question Number 210355 Answers: 1 Comments: 0

Question Number 210354 Answers: 2 Comments: 0

∫_0 ^𝛂 (x/((1+x^2 )(1+𝛂x)))dx

$$\int_{\mathrm{0}} ^{\boldsymbol{\alpha}} \frac{\boldsymbol{\mathrm{x}}}{\left(\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)\left(\mathrm{1}+\boldsymbol{\alpha\mathrm{x}}\right)}\boldsymbol{\mathrm{dx}} \\ $$

Question Number 210368 Answers: 0 Comments: 0

Question Number 210362 Answers: 1 Comments: 2

If the roots of the quadratic equation (a − b + c)x^2 + (c − b − a)x + 2(b − c) = 0 are real and equal then find (a/(b − c)) .

$$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{equation} \\ $$$$\left({a}\:−\:{b}\:+\:{c}\right){x}^{\mathrm{2}} \:+\:\left({c}\:−\:{b}\:−\:{a}\right){x}\:+\:\mathrm{2}\left({b}\:−\:{c}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{are}\:\mathrm{real}\:\mathrm{and}\:\mathrm{equal}\:\mathrm{then}\:\mathrm{find}\:\frac{{a}}{{b}\:−\:{c}}\:. \\ $$

Question Number 210326 Answers: 1 Comments: 6

∫_0 ^π ((tsin(t))/(1+t^2 ))dt

$$\int_{\mathrm{0}} ^{\pi} \:\frac{{tsin}\left({t}\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$

Question Number 210324 Answers: 1 Comments: 2

rationalize the denominator: (1/(a+b^(1/3) +c^(1/3) ))

$$\mathrm{rationalize}\:\mathrm{the}\:\mathrm{denominator}: \\ $$$$\frac{\mathrm{1}}{{a}+{b}^{\mathrm{1}/\mathrm{3}} +{c}^{\mathrm{1}/\mathrm{3}} } \\ $$

Question Number 210318 Answers: 4 Comments: 1

Question Number 210314 Answers: 1 Comments: 0

2x+4=1

$$\mathrm{2}{x}+\mathrm{4}=\mathrm{1} \\ $$

Question Number 210312 Answers: 0 Comments: 0

Question Number 210311 Answers: 1 Comments: 0

Let a_1 =1 a_2 =2^1 a_3 =3^((2^1 )) a_4 =4^((3^((2^1 )) )) find the last two digits of a_(23) and so on

$${Let}\:{a}_{\mathrm{1}} =\mathrm{1}\:\:\:{a}_{\mathrm{2}} =\mathrm{2}^{\mathrm{1}} \:\:\:\:{a}_{\mathrm{3}} =\mathrm{3}^{\left(\mathrm{2}^{\mathrm{1}} \right)} \:\:{a}_{\mathrm{4}} =\mathrm{4}^{\left(\mathrm{3}^{\left(\mathrm{2}^{\mathrm{1}} \right)} \right)} \\ $$$${find}\:{the}\:{last}\:{two}\:{digits}\:{of}\:{a}_{\mathrm{23}} \:{and}\:{so}\:{on} \\ $$

Question Number 210310 Answers: 2 Comments: 4

Let a be the unique real zero of x^3 +x+1. find the simplest possible way to write ((18)/((a^2 +a+1)^2 )) as polynomial expression in a with ratio coefficients

$${Let}\:{a}\:{be}\:{the}\:{unique}\:{real}\:{zero}\:{of}\:{x}^{\mathrm{3}} +{x}+\mathrm{1}. \\ $$$${find}\:{the}\:{simplest}\:{possible}\:{way}\:{to}\:{write}\: \\ $$$$\frac{\mathrm{18}}{\left({a}^{\mathrm{2}} +{a}+\mathrm{1}\right)^{\mathrm{2}} }\:\:{as}\:{polynomial}\:{expression}\:{in}\:\:{a} \\ $$$${with}\:{ratio}\:{coefficients} \\ $$

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