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Alex17521 [72]
3 years ago
10

Need more help on this question

Mathematics
2 answers:
Bond [772]3 years ago
8 0
79
hope this helped

Alisiya [41]3 years ago
7 0

Answer: 79

Step-by-step explanation:

6 ÷ 3 + 9 x² - 4=79

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It takes Matt 3 minutes to read one page in a book. If he continues to read at the same pace, he can read 15 similar pages in mi
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a)45min

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Compute the differential of surface area for the surface S described by the given parametrization.
AysviL [449]

With S parameterized by

\vec r(u,v)=\langle e^u\cos v,e^u\sin v,uv\rangle

the surface element \mathrm dS is

\mathrm dS=\left\|\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}\right\|\,\mathrm du\,\mathrm dv

We have

\dfrac{\partial\vec r}{\partial u}=\langle e^u\cos v,e^u\sin v,v\rangle

\dfrac{\partial\vec r}{\partial v}=\langle -e^u\sin v,e^u\cos v,u\rangle

with cross product

\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}=\langle ue^u\sin v-ve^u\cos v,-ve^u\sin v-ue^u\cos v,e^{2u}\cos^2v+e^{2u}\sin^2v\rangle

\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}=\langle e^u(u\sin v-v\cos v),-e^u(v\sin v+u\cos v),e^{2u}\rangle

with magnitude

\left\|\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}\right\|=\sqrt{e^{2u}(u\sin v-v\cos v)^2+e^{2u}(v\sin v+u\cos v)^2+e^{4u}}

\left\|\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}\right\|=e^u\sqrt{u^2+v^2+e^{2u}}

So we have

\mathrm dS=\boxed{e^u\sqrt{u^2+v^2+e^{2u}}\,\mathrm du\,\mathrm dv}

8 0
3 years ago
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