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Question Number 61850 Answers: 1 Comments: 8

Find all integer solution(s): 615+x^2 =2^y

$F i n d a l l i n t e g e r s o l u t i o n (s) :$ $615 + x^{2} = 2^{y}$

Question Number 61843 Answers: 0 Comments: 3

let V be a vector space and let H and K be subspace of V. show that , H+K={x:x=h+k, where h∈H and k∈K} is a subspace of V.

$l e t V b e a v e c t o r s p a c e a n d l e t H a n d K b e$ $s u b s p a c e o f V . s h o w t h a t,$ $H + K = {x : x = h + k, w h e r e h \in H a n d k \in K} i s a s u b s p a c e o f V .$

Question Number 61842 Answers: 0 Comments: 1

consider the space Pn with H={f:f⊂Pn and ∫_0 ^1 f(x)∂x=0} . Show that H is a SUBSPACE of Pn.

$c o n s i d e r t h e s p a c e P n w i t h H = {f : f \subset P n a n d \int_{0}^{1} f (x) \partial x = 0} . S h o w t h a t H i s a S U B S P A C E o f P n .$

Question Number 61840 Answers: 1 Comments: 0

consider the triple of real numbers (x,y,z) defined by the addittion (x,y,z)+(x′,y′,z′)=(x+x′,y+y′,z+z′) and scalar multiplication by 𝛂(x,y,z)=(0,0,0). Show that all axioms for a vector space are satisfied except axiom 8.

$c o n s i d e r t h e t r i p l e o f r e a l n u m b e r s (x, y, z)$ $d e f i n e d b y t h e a d d i t t i o n (x, y, z) + (x^{'}, y^{'}, z^{'}) = (x + x^{'}, y + y^{'}, z + z^{'})$ $a n d s c a l a r m u l t i p l i c a t i o n b y α (x, y, z) = (0, 0, 0) .$ $S h o w t h a t a l l a x i o m s f o r a v e c t o r s p a c e a r e s a t i s f i e d e x c e p t a x i o m 8 .$

Question Number 61855 Answers: 1 Comments: 0

∫_(0 ) ^1 ((3x^3 −x^2 +2x−4)/(√(x^2 −3x+2))) dx

$\int_{0}^{1} \frac{3 x^{3} - x^{2} + 2 x - 4}{\sqrt{x^{2} - 3 x + 2}} d x$

Question Number 61835 Answers: 0 Comments: 1

If α = Cis(2π/7) and f(x) = A_0 + Σ_(n=1) ^(14) A_n x^n Then prove that Σ_(α=0) ^6 f(α^n x)= 7(A_0 +A_7 x^7 +A_(14) x^(14) ) where Cisθ = Cosθ + iSinθ

$If α = Cis (2 π / 7) and f (x) = A_{0} + \sum_{n = 1}^{14} A_{n} x^{n}$ $Then prove that \sum_{α = 0}^{6} f (α^{n} x) = 7 (A_{0} + A_{7} x^{7} + A_{14} x^{14})$ $where Cis θ = Cos θ + iSin θ$

Question Number 61834 Answers: 0 Comments: 3

Question Number 61825 Answers: 1 Comments: 0

Question Number 61823 Answers: 1 Comments: 0

If D,E and F are midpoints of the sides BC,CA and AB respectively of the △ABC and O be any point.Prove that OA^→ + OB^→ +OC^→ =OD^→ +OE^→ +OF^→

$I f D, E a n d F a r e m i d p o i n t s o f t h e s i d e s$ $B C, C A a n d A B r e s p e c t i v e l y o f t h e △ A B C$ $a n d O b e a n y p o i n t . P r o v e t h a t$ $O \vec{A} + O \vec{B} + O \vec{C} = O \vec{D} + O \vec{E} + O \vec{F}$

Question Number 61818 Answers: 0 Comments: 3

Find (dy/dx) y = sin^(−1) (((1−x^2 )/(1+x^2 ))), 0<x<1

$Find \frac{d y}{d x}$ $y = \sin^{- 1} (\frac{1 - x^{2}}{1 + x^{2}}), 0 < x < 1$

Question Number 61815 Answers: 0 Comments: 0

2H_2 S+SO_2 =3S+H_2 O is this a disproportionation reaction?

$2 H_{2} S + {S O}_{2} = 3 S + H_{2} O$ $i s t h i s a d i s p r o p o r t i o n a t i o n r e a c t i o n ?$

Question Number 61811 Answers: 0 Comments: 0

Question Number 61810 Answers: 0 Comments: 0

Question Number 61809 Answers: 1 Comments: 1

Question Number 61807 Answers: 0 Comments: 0

Question Number 61804 Answers: 1 Comments: 1

calculate Σ_(n=2) ^∞ Σ_(k=2) ^∞ (1/(k^n k!))

$c a l c u l a t e \sum_{n = 2}^{\infty} \sum_{k = 2}^{\infty} \frac{1}{k^{n} k!}$

Question Number 61803 Answers: 0 Comments: 3

find ∫_0 ^∞ (x^2 /(e^x^2 −1))dx

$f i n d \int_{0}^{\infty} \frac{x^{2}}{e^{x^{2}} - 1} d x$

Question Number 61801 Answers: 0 Comments: 3

∫_(2π) ^(4π) (√(1−cos(x))) dx

$\underset{2 π}{\int^{4 π}} \sqrt{1 - c o s (x)} d x$

Question Number 61799 Answers: 1 Comments: 0

If a = Cosα −iSinα and b = Cosβ −iSinβ Prove that (((a+b)(1−ab))/((a−b)(1+ab))) = ((Sinα+Sinβ)/(Sinα−Sinβ))

$If a = Cos α - iSin α and b = Cos β - iSin β$ $Prove that \frac{(a + b) (1 - ab)}{(a - b) (1 + ab)} = \frac{Sin α + Sin β}{Sin α - Sin β}$

Question Number 61796 Answers: 0 Comments: 0

Question Number 61791 Answers: 1 Comments: 1

lim_(x → ∞) (6^x /(2^x + 4^x )) = ∞ ?

$\lim_{x \to \infty} \frac{6^{x}}{2^{x} + 4^{x}} = \infty ?$

Question Number 61785 Answers: 1 Comments: 0

∫_0 ^(√(3−x^2 )) ((xy(4−x^2 −y^2 )(√(4−x^2 −y^2 ))−xy)/3) dy

$\underset{0}{\int^{\sqrt{3 - x^{2}}}} \frac{x y (4 - x^{2} - y^{2}) \sqrt{4 - x^{2} - y^{2}} - x y}{3} d y$

Question Number 61782 Answers: 0 Comments: 5

Any integer(s) which fulfill n^5 − 5n^3 + 5n + 1 ∣ n! ?

$A n y i n t e g e r (s) w h i c h f u l f i l l$ $n^{5} - 5 n^{3} + 5 n + 1 ∣ n! ?$

Question Number 61778 Answers: 1 Comments: 0

Any integer(s) which fulfill n^3 − 5n^2 + 5n + 1 ∣ n! ?

$A n y i n t e g e r (s) w h i c h f u l f i l l$ $n^{3} - 5 n^{2} + 5 n + 1 ∣ n! ?$

Question Number 61775 Answers: 0 Comments: 1

Question Number 61770 Answers: 0 Comments: 0

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