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... x is in V and T is onto then we can find

**u**in**U**such that T(**u**)=x. Applying S on both sides...2 Answers · Science & Mathematics · 31/10/2012

**u**= y + xy v = y - xy Add**u**+ v:**u**+ v = 2y y = (**u**+ v) / 2 Subtract**u**- v:**u**- v = y + xy - (y - xy)**u**- v = xy + xy**u**- v = 2xy x = (**u**- v) / 2y x = (**u**- v) / (**u**+ v) Answer: x = (**u**- v) / (**u**+ v) y = (**u**+ v) / 23 Answers · Science & Mathematics · 24/11/2015

**u**and v are parallel**u**.v = |**u**||v|**u**x v = 0 (Cross product) Note they do not necessarily lie on the same plane or line, all we can say is that they have the same direction.4 Answers · Science & Mathematics · 29/06/2010

...of sine and cosine. [More explicitly, the rational function is R(

**u**, v) = v/(**u**+ uv). So, R(sin x, cos x) = cos x/(sin x + sin x cos x...1 Answers · Science & Mathematics · 01/04/2012

Hello, ∫ [x /(2x + 1)] dx = let: 2x + 1 =

**u**2x =**u**- 1 x = (1/2)(**u**- 1) dx = (1/2) du then, substituting...**u**) du = (1/4)**u**- (1/4) ln |**u**| + C let's substitute back 2x + 1 for**u**: (1/4)(2x + 1) - (1/4) ln |2x + 1| + C = (1/2)x + (1/2) - (1/4) ln |2x...1 Answers · Science & Mathematics · 01/03/2013

...attempt submitted whilst non compos mentis (a) If

**u**=(u1,u2,u3,u4) ∈**U**┴ then**u**is perp to both spanning... to u2=1/11, u4=8/11 ∴ p−w belongs to**U**┴1 Answers · Science & Mathematics · 11/04/2012

...3u|^2 + |v|^2 - 2|3u||v|cosθ, where θ is the angle between 3u (and, thus,

**u**) and v. Since |3u| = 3|**u**|, we have: |3u + v|^2 = (3|**u**|)^2 + |v|^2 - 2(3...2 Answers · Science & Mathematics · 12/09/2012

Let X = {a_n: n ≥ 1}

**U**{a}. Suppose x ∈ R^k \ X. Then x ≠ a and x...2 Answers · Science & Mathematics · 28/11/2013

Consider the linear transformation F :

**U**→ (**U**+ W)/W given by F...v in**U**: v is in W} .........=**U**∩ W. The result now follows from...2 Answers · Science & Mathematics · 17/03/2012

ln

**u**= ln (2vx²) ln**u**= ln (2v) + ln (x²) ln**u**= ln (2v) + 2 ⋅ ln (x) If you allow for a little substitution: y = 2⋅x + ln...3 Answers · Science & Mathematics · 19/10/2007