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anzhelika [568]
3 years ago
14

Charlie was having a Halloween party. She decided to make a gigantic spider to hang from the ceiling. The spider has 8 legs. Eac

h leg was 12 3/4 feet long.once she hung the spider, she decided it was too big , so she cut 2 feet of each leg. How many feet of the spiders legs were left hanging on the ceiling
Mathematics
1 answer:
lina2011 [118]3 years ago
3 0

Answer:

86 Feet

Step-by-step explanation:

Total of feet before cutting off: 102 ft

8 x 12.75 = 102 ft

8 x 2 = 16

102 - 16 = 86

OR

12.75 - 2 = 10.75

8 x 10.75 = 86

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Answer:

C

Step-by-step explanation:

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Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2 sin(z)i + y2j + xyk, S is the part of the paraboloid z = 9 − x2 −
Korolek [52]

The vector field

\vec F(x,y,z)=x^2\sin z\,\vec\imath+y^2\,\vec\jmath+xy\,\vec k

has curl

\nabla\times\vec F(x,y,z)=x\,\vec\imath+(x^2\cos z-y)\,\vec\jmath

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\vec s(u,v)=x(u,v)\,\vec\imath+y(u,v)\,\vec\jmath+z(u,v)\,\vec k

where

\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=(9-u^2)\end{cases}

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Take the normal vector to S to be

\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}=2u^2\cos v\,\vec\imath+2u^2\sin v\,\vec\jmath+u\,\vec k

Then by Stokes' theorem we have

\displaystyle\int_{\partial S}\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S

=\displaystyle\int_0^{2\pi}\int_0^3(\nabla\times\vec F)(\vec s(u,v))\cdot\left(\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right)\,\mathrm du\,\mathrm dv

=\displaystyle\int_0^{2\pi}\int_0^3u^3(2u\cos^3v\sin(u^2-9)+\cos^3v\sin v+2u\sin^3v+\cos v\sin^3v)\,\mathrm du\,\mathrm dv

which has a value of 0, since each component integral is 0:

\displaystyle\int_0^{2\pi}\cos^3v\,\mathrm dv=0

\displaystyle\int_0^{2\pi}\sin v\cos^3v\,\mathrm dv=0

\displaystyle\int_0^{2\pi}\sin^3v\,\mathrm dv=0

\displaystyle\int_0^{2\pi}\cos v\sin^3v\,\mathrm dv=0

4 0
3 years ago
to design the interior surface of a huge stainless-steel tank, you revolve the curve y=x^2 on the interval 0x4 about the y-axis.
Oksana_A [137]

Answer:

W = 21.44*10⁶J

Step-by-step explanation:

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7 0
3 years ago
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Marina CMI [18]

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6 0
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Pls put the answers in order ty!! I really appreciate giving me the answers!! :)))
Valentin [98]

Answer:

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6 0
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