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Question Number 185695 Answers: 2 Comments: 0

If u^→ and v^→ are vectors in R^3 then prove that u^→ .v^→ =(1/4)∥u^→ +v^→ ∥^2 −(1/4)∥u^→ −v^→ ∥^2

$${If}\:\overset{\rightarrow} {{u}}\:{and}\:\overset{\rightarrow} {{v}}\:{are}\:{vectors}\:{in}\:\mathbb{R}^{\mathrm{3}} \\ $$$${then}\:{prove}\:{that}\: \\ $$$$\overset{\rightarrow} {{u}}.\overset{\rightarrow} {{v}}=\frac{\mathrm{1}}{\mathrm{4}}\parallel\overset{\rightarrow} {{u}}+\overset{\rightarrow} {{v}}\parallel^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{4}}\parallel\overset{\rightarrow} {{u}}−\overset{\rightarrow} {{v}}\parallel^{\mathrm{2}} \\ $$

Question Number 185694 Answers: 0 Comments: 0

Show that the set V=R^3 with standard vector addition and multiplication defined as c(u_1 ,u_2 ,u_3 )=(0,0,cu_3 )

$${Show}\:{that}\:{the}\:{set}\:{V}=\mathbb{R}^{\mathrm{3}} \:{with} \\ $$$${standard}\:{vector}\:{addition}\:{and} \\ $$$${multiplication}\:{defined}\:{as} \\ $$$${c}\left({u}_{\mathrm{1}} ,{u}_{\mathrm{2}} ,{u}_{\mathrm{3}} \right)=\left(\mathrm{0},\mathrm{0},{cu}_{\mathrm{3}} \right) \\ $$

Question Number 185693 Answers: 1 Comments: 1

If k > 0 and f(x) = (x/(∣x∣)) Find f(- (2/7) k) + f( - 2k) = ?

$$\mathrm{If}\:\:\:\mathrm{k}\:>\:\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{x}}{\mid\mathrm{x}\mid} \\ $$$$\mathrm{Find}\:\:\:\mathrm{f}\left(-\:\frac{\mathrm{2}}{\mathrm{7}}\:\mathrm{k}\right)\:+\:\mathrm{f}\left(\:-\:\mathrm{2k}\right)\:=\:? \\ $$

Question Number 185692 Answers: 0 Comments: 0

Given u^→ =(−2,3,1) and v^→ =(7,1,−4) verify cauchy−schwartz inequarity and triangle inequarty

$${Given}\: \\ $$$$\overset{\rightarrow} {{u}}=\left(−\mathrm{2},\mathrm{3},\mathrm{1}\right)\:\:{and}\:\overset{\rightarrow} {{v}}=\left(\mathrm{7},\mathrm{1},−\mathrm{4}\right) \\ $$$${verify}\:{cauchy}−{schwartz}\: \\ $$$${inequarity}\:{and}\:{triangle}\:{inequarty} \\ $$

Question Number 185685 Answers: 1 Comments: 0

Question Number 185684 Answers: 0 Comments: 7

17 , 78, 143, 353, ? a)366 b)0 c)398 d)435

$$\mathrm{17}\:,\:\mathrm{78},\:\mathrm{143},\:\mathrm{353},\:? \\ $$$$\left.\mathrm{a}\left.\right)\left.\mathrm{3}\left.\mathrm{66}\:\:\:\:\:\mathrm{b}\right)\mathrm{0}\:\:\:\:\:\mathrm{c}\right)\mathrm{398}\:\:\:\:\:\mathrm{d}\right)\mathrm{435} \\ $$

Question Number 185678 Answers: 1 Comments: 0

Question Number 185677 Answers: 1 Comments: 0

Question Number 185674 Answers: 1 Comments: 1

Question Number 185673 Answers: 1 Comments: 0

Question Number 185672 Answers: 0 Comments: 0

Question Number 185668 Answers: 2 Comments: 0

Find: (1/(sin 10°)) − 4 sin 70° = ?

$$\mathrm{Find}:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{10}°}\:−\:\mathrm{4}\:\mathrm{sin}\:\mathrm{70}°\:=\:? \\ $$

Question Number 185665 Answers: 1 Comments: 0

f(((2x−1)/(3x+2)))=((x−1)/(x−2)) faind f^(−1) (2)=?

$${f}\left(\frac{\mathrm{2}{x}−\mathrm{1}}{\mathrm{3}{x}+\mathrm{2}}\right)=\frac{{x}−\mathrm{1}}{{x}−\mathrm{2}}\:\:\:\:\:\:{faind}\:\:\:{f}^{−\mathrm{1}} \left(\mathrm{2}\right)=? \\ $$

Question Number 185664 Answers: 0 Comments: 0

Question Number 185663 Answers: 0 Comments: 0

Question Number 185659 Answers: 1 Comments: 1

prove for r, n ∈ N Σ_(k=r) ^n ((k),(r) ) = (((n+1)),((r+1)) ) (Hockey−stick identity)

$${prove}\:{for}\:{r},\:{n}\:\in\:\mathbb{N} \\ $$$$\underset{{k}={r}} {\overset{{n}} {\sum}}\begin{pmatrix}{{k}}\\{{r}}\end{pmatrix}\:=\begin{pmatrix}{{n}+\mathrm{1}}\\{{r}+\mathrm{1}}\end{pmatrix} \\ $$$$\left({Hockey}−{stick}\:{identity}\right) \\ $$

Question Number 185647 Answers: 1 Comments: 0

Question Number 185637 Answers: 1 Comments: 0

Question Number 185642 Answers: 1 Comments: 1

Question Number 185640 Answers: 2 Comments: 0

Question Number 185619 Answers: 1 Comments: 1

Question Number 185719 Answers: 1 Comments: 2

Find the next number: a_0 =a_1 =1, a_2 =2 a_3 =?

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{next}\:\mathrm{number}: \\ $$$${a}_{\mathrm{0}} ={a}_{\mathrm{1}} =\mathrm{1},\:{a}_{\mathrm{2}} =\mathrm{2} \\ $$$${a}_{\mathrm{3}} =? \\ $$

Question Number 185602 Answers: 2 Comments: 0

Question Number 185601 Answers: 0 Comments: 0

Hello please I experienced a little difficulty with this question. A charge Qa =−20mC is located at (−6 4 7) and a charge Qb=50mC at (5 8 −2). If distances are given in meters find (a)R^− ab (b)Rab (c) The vector force exerted on Qa by Qb if ε_0 =10^(−9) /36⊼ F╱m

$${Hello}\:{please}\:{I}\:{experienced}\:{a}\:{little} \\ $$$$\:{difficulty}\:{with}\:{this}\:{question}.\: \\ $$$$ \\ $$$${A}\:{charge}\:{Qa}\:=−\mathrm{20}{mC}\:\:{is}\:{located}\:{at}\:\left(−\mathrm{6}\:\mathrm{4}\:\mathrm{7}\right)\:{and}\: \\ $$$${a}\:{charge}\:{Qb}=\mathrm{50}{mC}\:{at}\:\left(\mathrm{5}\:\mathrm{8}\:−\mathrm{2}\right).\: \\ $$$$\mathrm{I}{f}\:{distances}\:{are}\:{given}\:{in}\:{meters}\: \\ $$$${find}\:\left({a}\right)\overset{−} {{R}ab}\:\left({b}\right){Rab} \\ $$$$\:\left({c}\right)\:{The}\:{vector}\:{force}\:{exerted}\:{on}\: \\ $$$${Qa}\:{by}\:{Qb}\:\:{if}\:\:\varepsilon_{\mathrm{0}} =\mathrm{10}^{−\mathrm{9}} /\mathrm{36}\barwedge\:{F}\diagup{m} \\ $$

Question Number 185599 Answers: 4 Comments: 3

x!=x^3 −x faind x=?

$${x}!={x}^{\mathrm{3}} −{x}\:\:\:\:\:\:\:\:\:\:{faind}\:{x}=? \\ $$

Question Number 185598 Answers: 0 Comments: 0

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