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VectorQuestion and Answers: Page 4

Question Number 158066 Answers: 0 Comments: 0

Question Number 156082 Answers: 0 Comments: 0

0< α <(π/2) (( sin(α)))^(1/( 3)) + ((cos(α))^(1/3) )= (( tan(α)))^(1/3) (( tan (α ) + cot (α ))/2) =?

$0 < α < \frac{π}{2}$ $\sqrt[3]{s i n (α)} + \sqrt[3]{c o s (α}) = \sqrt[3]{t a n (α)}$ $\frac{t a n (α) + c o t (α)}{2} = ?$

Question Number 152588 Answers: 3 Comments: 0

∫_(−1 ) ^1 ((3x+4)/(3+4x+3x^2 ))dt please,help me

$\int_{- 1}^{1} \frac{3 x + 4}{3 + 4 x + 3 x^{2}} d t$ $p l e a s e, h e l p m e$

Question Number 148151 Answers: 1 Comments: 0

Question Number 147354 Answers: 0 Comments: 0

Question Number 147195 Answers: 2 Comments: 0

Ω := ∫_0 ^( 1) Li_( 2) ( (√x) )dx = ?

$Ω := \int_{0}^{1} {Li}_{2} (\sqrt{x}) d x = ?$

Question Number 147162 Answers: 1 Comments: 0

Question Number 146472 Answers: 0 Comments: 1

Question Number 146444 Answers: 0 Comments: 0

Question Number 146420 Answers: 0 Comments: 0

Question Number 146403 Answers: 0 Comments: 1

let f(x,y)=((x^5 y^2 )/(10)) then find D_u f(−5,−3) in the direction of the vector <0,−2>?

$l e t f (x, y) = \frac{x^{5} y^{2}}{10} t h e n f i n d$ $D_{u} f (- 5, - 3) i n t h e d i r e c t i o n o f$ $t h e v e c t o r < 0, - 2 > ?$

Question Number 146315 Answers: 1 Comments: 0

Question Number 144166 Answers: 1 Comments: 0

Given p^→ =(√2) i^ +2(√3) j^ + (√3) k^ & q^→ =a i^ +j^ +2k^ . If proj_q^→ p^→ = ((2(√2))/9) q^→ then ∣q^→ ∣ =?

$Given \vec{p} = \sqrt{2} \hat{i} + 2 \sqrt{3} \hat{j} + \sqrt{3} \hat{k} &$ $\vec{q} = a \hat{i} + \hat{j} + 2 \hat{k} . If {proj}_{\vec{q}} \vec{p} = \frac{2 \sqrt{2}}{9} \vec{q}$ $then ∣ \vec{q} ∣ = ?$

Question Number 144015 Answers: 0 Comments: 0

Question Number 143127 Answers: 2 Comments: 0

Question Number 142970 Answers: 1 Comments: 0

..........CALCULUS........... prove that:: 𝛗:=Σ_(n=1) ^∞ (((−1)^(n−1) ((n−1)!)^2 )/((2n)!))=2log^2 (ϕ) ϕ=golden ratio.... .............

$. . . . . . . . . . C A L C U L U S . . . . . . . . . . .$ $p r o v e t h a t ::$ $ϕ := \underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n - 1} {((n - 1)!)}^{2}}{(2 n)!} = 2 {l o g}^{2} (φ)$ $φ = g o l d e n r a t i o . . . .$ $. . . . . . . . . . . . .$

Question Number 142927 Answers: 2 Comments: 0

Question Number 141632 Answers: 0 Comments: 0

Let f(x)=((sin(x))/x) , prove that : Σ_(n=0) ^∞ [ f(nπ+α)+f(nπ−α) ]= 1+f(α)

$Let f (x) = \frac{s i n (x)}{x}, prove that :$ $\underset{n = 0}{\sum^{\infty}} [f (n π + α) + f (n π - α)] = 1 + f (α)$

Question Number 141257 Answers: 0 Comments: 0

Question Number 141167 Answers: 0 Comments: 0

Question Number 141129 Answers: 1 Comments: 0

For what values of λ are the vectors λi^ + 2j^ + k^ , 3i^ +4j^ +λk^ , j^ + k^ coplanar

$F o r w h a t v a l u e s o f λ a r e t h e$ $v e c t o r s λ \hat{i} + 2 \hat{j} + \hat{k}, 3 \hat{i} + 4 \hat{j} + λ \hat{k}$ $, \hat{j} + \hat{k} c o p l a n a r$

Question Number 140690 Answers: 1 Comments: 0

Vector let L_1 = AC where A=(2,−1,3) and C=(1,0,−5)and let L_2 = BD where B=(1,3,0) and D=(3,−4,1). Determine the distance between L_1 and L_2 .

$Vector$ $let L_{1} = AC where A = (2, - 1, 3) and$ $C = (1, 0, - 5) and let L_{2} = BD where$ $B = (1, 3, 0) and D = (3, - 4, 1) . Determine$ $the distance between L_{1} and L_{2} .$

Question Number 140666 Answers: 1 Comments: 0

Find the coordinates of (−2,0) when the axes are rotated counterclockwise through the angle arcsin (4/5).

$F i n d t h e c o o r d i n a t e s o f (- 2, 0)$ $w h e n t h e a x e s a r e r o t a t e d c o u n t e r c l o c k w i s e$ $t h r o u g h t h e a n g l e \arcsin \frac{4}{5} .$

Question Number 140502 Answers: 0 Comments: 0

If three vector a^→ , b^→ and c^→ are such that a^→ ≠ 0 and a^→ ×b^→ = 2(a^→ ×c^→ ) ,∣a^→ ∣ = ∣c^→ ∣ = 1 , ∣b^→ ∣ = 4 and the angle between b^→ and c^→ is cos^(−1) ((1/4)), then b^→ −2c^→ = λ a^→ , where λ =?

$If three vector \vec{a}, \vec{b} and \vec{c} are$ $such that \vec{a} \neq 0 and \vec{a} \times \vec{b} = 2 (\vec{a} \times \vec{c})$ $, ∣ \vec{a} ∣ = ∣ \vec{c} ∣ = 1, ∣ \vec{b} ∣ = 4 and the$ $angle between \vec{b} and \vec{c} is \cos^{- 1} (\frac{1}{4}),$ $then \vec{b} - 2 \vec{c} = λ \vec{a}, where λ = ?$

Question Number 140176 Answers: 0 Comments: 0

Let V be a vector space of polynomials p(x)= a+bx+cx^2 with real coefficients a,b and c. Define an inner product on V by (p,q)=(1/2)∫_(−1) ^1 p(x)q(x) dx . (a) Find a orthonormal basis for V consisting of polynomials φ_o (x) , φ_1 (x) and φ_2 (x) having degree 0,1 and 2 respectively.

$Let V be a vector space of polynomials$ $p (x) = a + bx + {cx}^{2} with real coefficients$ $a, b and c . Define an inner product on V$ $by (p, q) = \frac{1}{2} \underset{- 1}{\int^{1}} p (x) q (x) dx .$ $(a) Find a orthonormal basis for V consisting$ $of polynomials ϕ_{o} (x), ϕ_{1} (x) and ϕ_{2} (x)$ $having degree 0, 1 and 2 respectively .$

Question Number 140053 Answers: 0 Comments: 3

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