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sineoko [7]
3 years ago
8

List all pairs of matching angles

Mathematics
1 answer:
anyanavicka [17]3 years ago
3 0

Answer:

Listed

Please mark me as the brainliest and thanks

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{(1,3) (2,4) (3,5) (4,3)}
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What is the measure of the central angle of a circle with radius 15 ft that intercepts a 10 ft arc?
olga2289 [7]
  • L=10ft
  • R=15ft
  • We have to find theta

\Large{\underline{\sf Solution:-}}

\\ \sf\dashrightarrow L=\dfrac{\Theta}{180}\times \pi r

\\ \sf\dashrightarrow 10=\dfrac{\Theta}{180}\times 3.14\times 15

\\ \sf\dashrightarrow 10=\dfrac{\Theta}{180}\times 47.1

\\ \sf\dashrightarrow \Theta=\dfrac{10(180)}{47.1}

\\ \sf\dashrightarrow \Theta=\dfrac{1800}{47.1}

\\ \sf\dashrightarrow \Theta=38.2°

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How to compare 2 quantites so that the second quantity has a value of 1 without using a diagram
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3 years ago
Find the area of the helicoid (or spiral ramp) with vector equation r(u, v) = ucos(v) i + usin(v) j + v k, 0 ≤ u ≤ 1, 0 ≤ v ≤ 9π
Natasha2012 [34]
Let H denote the helicoid parameterized by

\mathbb r(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+v\,\mathbf k

for 0\le u\le1 and 0\le v\le9\pi. The surface area is given by the surface integral,

\displaystyle\iint_H\mathrm dS=\iint_H\|\mathbf r_u\times\mathbf r_v\|\,\mathrm du\,\mathrm dv

We have

\mathbf r_u=\dfrac{\partial\mathbf r(u,v)}{\partial u}=\cos v\,\mathbf i+\sin v\,\mathbf j
\mathbf r_v=\dfrac{\partial\mathbf r(u,v)}{\partial v}=-u\sin v\,\mathbf i+u\cos v\,\mathbf j+\mathbf k
\implies\mathbf r_u\times\mathbf r_v=\sin v\,\mathbf i-\cos v\,\mathbf j+u\,\mathbf k
\implies\|\mathbf r_u\times\mathbf r_v\|=\sqrt{1+u^2}

So the area of H is

\displaystyle\iint_H\mathrm dS=\int_{v=0}^{v=9\pi}\int_{u=0}^{u=1}\sqrt{1+u^2}\,\mathrm du\,\mathrm dv
=\dfrac{9(\sqrt2+\sinh^{-1}(1))\pi}2
5 0
3 years ago
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