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Question Number 157099 Answers: 0 Comments: 2

Question Number 157098 Answers: 1 Comments: 0

n ∈ N^∗ ; n is not a square of any integer. Show that (√n) ∉ Q .

$n \in N^{*}; n i s n o t a s q u a r e o f a n y$ $i n t e g e r . S h o w t h a t \sqrt{n} \notin Q .$

Question Number 157096 Answers: 1 Comments: 0

∫_0 ^(π/2) xsin(x)ln(sin(x))dx=?

$\int_{0}^{\frac{π}{2}} xsin (x) \ln (\sin (x)) dx = ?$

Question Number 157087 Answers: 0 Comments: 0

Let ABCD be a tetrahedron, G, G' and G" the centers of gravity of faces ABC, ACD and ADB, I and J the midpoints of edges [BC] and [CD]. 1) Show that lines (IJ) and (GG' ) are parallel. 2) Prove that the points G, G' and G" are not aligned. 3) Show that the planes (GG 'G ") and (BCD) are parallel.

Question Number 157083 Answers: 0 Comments: 0

Question Number 157080 Answers: 3 Comments: 2

Question Number 157074 Answers: 2 Comments: 0

(√(4+(√(4^2 +(√(4^3 +(√(4^4 +…))))))))=?

$\sqrt{4 + \sqrt{4^{2} + \sqrt{4^{3} + \sqrt{4^{4} + \dots}}}} = ?$

Question Number 157071 Answers: 0 Comments: 0

if 0<x≤(π/2) then: (1/(sinx)) + (2/(πx)) ≤ (1 - (2/π))^2 + (1/x) + (2/π)

$if 0 < x ⩽ \frac{π}{2} then :$ $\frac{1}{\sin x} + \frac{2}{π x} ⩽ {(1 - \frac{2}{π})}^{2} + \frac{1}{x} + \frac{2}{π}$

Question Number 157065 Answers: 0 Comments: 1

prove that cos 36°=((1+(√5))/4)

$prove that \cos 36 ° = \frac{1 + \sqrt{5}}{4}$

Question Number 157061 Answers: 2 Comments: 0

Show that ∀ n ∈ N, ⌊((√n)+(√(n+1)))^2 ⌋=4n+1

$S h o w t h a t \forall n \in N,$ $⌊ {(\sqrt{n} + \sqrt{n + 1})}^{2} ⌋ = 4 n + 1$

Question Number 157055 Answers: 1 Comments: 1

Question Number 157053 Answers: 0 Comments: 2

If you want to easily write any quadratic function in vertex form, just use these formulas: f(x)=ax^2 +bx+c if a>0, then: f(x)=(x+(b/2))^2 −((b/2))^2 +c if a<0, then: f(x)=−(x−((b/2)))^2 +((b/2))^2 +c Let′s take some examples: f(x)=x^2 −6x+7 f(x)=(x−(6/2))^2 −((6/2))^2 +7 f(x)=(x−3)^2 −9+7 f(x)=(x−3)^2 −2 Now let′s take the same example, but when a<0: f(x)=−x^2 −6x+7 f(x)=−(x−(−(6/2)))^2 +((6/2))^2 +7 f(x)=−(x+3)^2 +9+7 f(x)=−(x+3)^2 +16 Another example: f(x)=x^2 +4x−5 f(x)=(x+(4/2))^2 −((4/2))^2 −5 f(x)=(x+2)^2 −4−5 f(x)=(x+2)^2 −9 Now let′s also see what happens when a<0: f(x)=−x^2 +4x−5 f(x)=−(x−((4/2)))^2 +((4/2))^2 −5 f(x)=−(x−2)^2 +4−5 f(x)=−(x−2)^2 −1

$If you want to easily write any quadratic function in vertex form, just use these formulas :$ $f (x) = {a x}^{2} + b x + c$ $if a > 0, then :$ $f (x) = {(x + \frac{b}{2})}^{2} - {(\frac{b}{2})}^{2} + c$ $if a < 0, then :$ $f (x) = - {(x - (\frac{b}{2}))}^{2} + {(\frac{b}{2})}^{2} + c$ ${Let}^{'} s take some examples :$ $f (x) = x^{2} - 6 x + 7$ $f (x) = {(x - \frac{6}{2})}^{2} - {(\frac{6}{2})}^{2} + 7$ $f (x) = {(x - 3)}^{2} - 9 + 7$ $f (x) = {(x - 3)}^{2} - 2$ $Now {let}^{'} s take the same example, but when a < 0 :$ $f (x) = - x^{2} - 6 x + 7$ $f (x) = - {(x - (- \frac{6}{2}))}^{2} + {(\frac{6}{2})}^{2} + 7$ $f (x) = - {(x + 3)}^{2} + 9 + 7$ $f (x) = - {(x + 3)}^{2} + 16$ $Another example :$ $f (x) = x^{2} + 4 x - 5$ $f (x) = {(x + \frac{4}{2})}^{2} - {(\frac{4}{2})}^{2} - 5$ $f (x) = {(x + 2)}^{2} - 4 - 5$ $f (x) = {(x + 2)}^{2} - 9$ $Now {let}^{'} s also see what happens when a < 0 :$ $f (x) = - x^{2} + 4 x - 5$ $f (x) = - {(x - (\frac{4}{2}))}^{2} + {(\frac{4}{2})}^{2} - 5$ $f (x) = - {(x - 2)}^{2} + 4 - 5$ $f (x) = - {(x - 2)}^{2} - 1$

Question Number 157046 Answers: 0 Comments: 1

q={a+((a/9)−(1/(108))−a^3 )^(1/3) }^(1/3) +{b+((b/9)−(1/(108))−b^3 )^(1/3) }^(1/3) a=((9+(√(37)))/(72)) , b=((9−(√(37)))/(72)) find q correct to 5 decimal places.

$q = {a + {(\frac{a}{9} - \frac{1}{108} - a^{3})}^{1 / 3}}^{1 / 3}$ $+ {b + {(\frac{b}{9} - \frac{1}{108} - b^{3})}^{1 / 3}}^{1 / 3}$ $a = \frac{9 + \sqrt{37}}{72}, b = \frac{9 - \sqrt{37}}{72}$ $f i n d q c o r r e c t t o 5 d e c i m a l$ $p l a c e s .$