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If

**v**is half of w:**v**= w/2 and u is the mean of**v**and w: u = (**v**+ w) / 2 And you know it's a triangle...w = 80 Now that we have w we can solve for**v**and u:**v**+ w = 120**v**+ 80 = 120**v**= 40 u = (**v**+ w...3 Answers · Science & Mathematics · 25/10/2019

u = 8i + 7j → tan(u) = 7/8

**v**= 7i - j → tan(**v**) = - 1/7 tan(a - b) = sin(a - b) / cos(a - b) → recall...b)] / [1 + tan(a).tan(b)] → adapt this result to your case tan(u -**v**) = [tan(u) - tan(**v**)] / [1 + tan(u).tan(**v**)] tan(u -**v**) = [(7/8) - (- 1/7...2 Answers · Science & Mathematics · 29/04/2019

### Suppose I have vector

**v**,**v*****v**= ||**v**||^2. So can you tell me the proof on why does this make sense?**v**= ⟨a, b, c⟩ for example yields**v**•**v**= a² + b² + c² = (√(a² + b² + c²))² = ||**v**||²3 Answers · Science & Mathematics · 04/08/2019

**v**= sin(pi * t) s = (-1/pi) * cos(pi * t) + C s = 0 when t = -3 0 = (-1/pi) * cos(-3pi) + C 0 = (-1/pi) * (-1) + C 0 = 1/pi + C -1/pi = C s = (-1/pi) * cos(pi * t) - 1/pi s = (-1/pi) * (cos(pi * t) + 1)1 Answers · Science & Mathematics · 18/07/2019

Integrate from t = 0 to t = 1 u = t^2 du = 2t * dt dv = e^(-3t) * dt

**v**= (-1/3) * e^(-3t) (-1/3) * t^2 * e^(-3t) - (-2/3) * int(t * e^(-3t) * dt) => (-1/3...3 Answers · Science & Mathematics · 21/02/2019

8u - 8 = 4 - 4w 8u + 4w = 12 2u + w = 3 w = 3 - 2u w = u +

**v**3 - 2u = u +**v****v**= 3 - 3u 8u = 4 + 6v 8u = 4 + 6 * (3 - 3u) 4u = 2 + 3 * (3 - 3u) 4u = 2 + 9 - 9u 13u = 11 u = 11/13**v**= 3 - 3u**v**= 3 - 33/13**v**= 39/13 - 33/13**v**= 6/13 w = u +**v**w = 11/13 + 6/13 w = 17/132 Answers · Science & Mathematics · 16/09/2019

...the photo comment*** So the first problem is to show that if x ∈

**V**(ε, a) and y ∈**V**(ε, b) then x+y ∈**V**(2ε, a+b). Most of...1 Answers · Science & Mathematics · 18/09/2019

... are consistent with the quadratic function f(

**v**)=(**v**−2)(**v**−5). If**v**(0)>5 then initially f>0...2. The solution of this ODE is in fact**v**= ((2(v₀−5)e³ᵗ−5(v₀−2...1 Answers · Science & Mathematics · 10/02/2019

The volume of a rectangular box is

**V**= ℓ ⋅ w ⋅ h. For the box to satisfy certain requirements...3 Answers · Science & Mathematics · 12/02/2019

dot product, then cross product u•

**v**= 0, ⟨3,2,1⟩•⟨1,-1,-1⟩ = 3 - 2 - 1 = 0 so let**v**= ⟨1,-1,-1⟩ u×**v**= ⟨3...1,4,-5⟩ = w Check: u•w = ⟨3,2,1⟩•⟨-1,4,-5⟩ = -3 + 8 - 5 = 0 and**v**•w = ⟨1,-1,-1⟩•⟨-1,4,-5⟩ = -1 - 4 + 5 = 0 So all three vectors...1 Answers · Science & Mathematics · 06/09/2019