Mathematics, 17.07.2021 06:40, zack66828
Find the arclength of the curve r(t) = ⟨ 10sqrt(2)t , e^(10t) , e^(−10t)⟩, 0≤t≤1
Answers: 3
![\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)](/tpl/images/1395/5319/4bc1d.png)
![\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](/tpl/images/1395/5319/fb0e0.png)
![\displaystyle AL = \int\limits^b_a {\sqrt{[i'(t)]^2 + [j'(t)]^2 + [k'(t)]^2}} \, dt](/tpl/images/1395/5319/9efe3.png)
Substitute in variables [Arc Length Formula - Vector]: ![\displaystyle AL = \int\limits^1_0 {\sqrt{\bigg[\frac{d}{dt}[10\sqrt{2}t \textbf i]\bigg]^2 + \bigg[\frac{d}{dt}[e^{10t} \textbf j]\bigg]^2 + \bigg[\frac{d}{dt}[e^{-10t} \textbf k ]\bigg]^2}} \, dt](/tpl/images/1395/5319/667ea.png)
[Integrand] Differentiate [Respective Differentiation Rules]: ![\displaystyle AL = \int\limits^1_0 {\sqrt{[10\sqrt{2} \textbf i]^2 + [10e^{10t} \textbf j]^2 + [-10e^{-10t} \textbf k]^2}} \, dt](/tpl/images/1395/5319/4b705.png)
[Integrand] Simplify: 
[Integral] Evaluate: 
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Mathematics, 21.06.2019 15:30, DJEMPGYT
Will give are given that xy is parallel to zw. if xz is a transversal that intercepts xy and zw, angle angle alternate interior angles. since xy is parallel to zw, we know that these angles are we also know that angle xvy and angle zvw are , and thus congruent. we can conclude that △xyv ~ △zwv using the similarity theorem.
Answers: 2
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Find the arclength of the curve r(t) = ⟨ 10sqrt(2)t , e^(10t) , e^(−10t)⟩, 0≤t≤1...
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