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Question Number 174534 Answers: 0 Comments: 0

Question Number 174533 Answers: 1 Comments: 0

Question Number 174532 Answers: 0 Comments: 0

Question Number 174528 Answers: 1 Comments: 0

Question Number 174519 Answers: 1 Comments: 2

Question Number 174522 Answers: 0 Comments: 0

Let σ(n) be the sum of all positive divisors of the integer n and let p be any prime number. Show that σ(n)<2n holds true for all n of the form n=p^2 . Mastermind

$Let σ (n) be the sum of all positive divisors$ $of the integer n and let p be any prime$ $number . Show that σ (n) < 2 n holds true$ $for all n of the form n = p^{2} .$ $Mastermind$

Question Number 174514 Answers: 3 Comments: 1

a+b+c=1 a^2 +b^2 +c^2 =2 a^3 +b^3 +c^3 =3 then a^5 +b^5 +c^5 ?

$a + b + c = 1$ $a^{2} + b^{2} + c^{2} = 2$ $a^{3} + b^{3} + c^{3} = 3$ $t h e n a^{5} + b^{5} + c^{5} ?$

Question Number 174512 Answers: 1 Comments: 0

how many integer a,b∈z^+ a^5 −b^5 =10(b+1)^2 −9

$h o w m a n y i n t e g e r a, b \in z^{+}$ $a^{5} - b^{5} = 10 {(b + 1)}^{2} - 9$

Question Number 174507 Answers: 1 Comments: 0

Determine the numerical value of the following expression without the use of a calculator log[log(3)∙(log(2)∙((((√3)−2sin((π/3)))/(π^3 +1))+1))−log(2)log(3)+(−1)^(100) ] Mastermind

$Determine the numerical value of the$ $following expression without the use$ $of a calculator$ $\log [\log (3) \cdot (\log (2) \cdot (\frac{\sqrt{3} - 2 \sin (\frac{π}{3})}{π^{3} + 1} + 1)) - \log (2) \log (3) + {(- 1)}^{100}]$ $Mastermind$

Question Number 174500 Answers: 1 Comments: 0

Find the values of the following infinite sum: 1+(3/π)+(3/π^2 )+(3/π^3 )+(3/π^4 )+(3/π^5 )+... Mastermind

$Find the values of the following infinite$ $sum :$ $1 + \frac{3}{π} + \frac{3}{π^{2}} + \frac{3}{π^{3}} + \frac{3}{π^{4}} + \frac{3}{π^{5}} + . . .$ $Mastermind$

Question Number 174495 Answers: 2 Comments: 2

What are the roots of the function f(x)=(log(3^x )−2log(3))∙(x^2 −1) with x∈R? Mastermind

$What are the roots of the function$ $f (x) = (\log (3^{x}) - 2 \log (3)) \cdot (x^{2} - 1) with$ $x \in R ?$ $Mastermind$

Question Number 174492 Answers: 0 Comments: 1

lim_(x→∞) ((3x tan (2/x) − 2x sin (3/x))/(cos (1/x) − cos (2/x))) = ?

$\lim_{x \to \infty} \frac{3 x \tan \frac{2}{x} - 2 x \sin \frac{3}{x}}{\cos \frac{1}{x} - \cos \frac{2}{x}} = ?$

Question Number 174490 Answers: 0 Comments: 1

A die is rolled 57 times, what is the probability that the sum of its outcome is 100?

$A die is rolled 57 times, what is the$ $probability that the sum of its outcome$ $is 100 ?$

Question Number 174489 Answers: 0 Comments: 0

The points A, B and C have position vectors a, b and c respectively reffrred to an origin O. i. Given that the point X lie on AB produced so that AB : BX=2:1, find x, the position vector of X in terms of b and c. ii. if Y lies on BC, between B and C so that BY : YC = 1:3, find y, the position vector of Y in terms of b and c. iii. Given that Z is the mid point of AC, show that X, Y and Z are collinear.

$The points A, B and C have position vectors$ $a, b and c respectively reffrred to an origin O .$ $i . Given that the point X lie on AB produced$ $so that AB : BX = 2 : 1, find x, the position$ $vector of X in terms of b and c .$ $ii . if Y lies on BC, between B and C so that$ $BY : YC = 1 : 3, find y, the position vector$ $of Y in terms of b and c .$ $iii . Given that Z is the mid point of AC,$ $show that X, Y and Z are collinear .$