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GuDViN [60]
3 years ago
7

A deep-sea diver must descend and ascend in short steps to equalize pressure on his body. If the diver rises toward the surface

too fast, he mat suffer from a physical condition called "the bends". Suppose the diver started at 82 feet below the surface and rose in 5 steps of 15 feet each. Use an integer to describe his new position in relation to the water surface
Mathematics
2 answers:
lilavasa [31]3 years ago
3 0
<span>82 - 5(15) = 82 - 75 = 7</span>
fgiga [73]3 years ago
3 0
The answer is 7.:D Hope I helped!
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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

Parameterize S by

\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}

with 0\le u\le3 and 0\le v\le2\pi.

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
If 4 : 9 is equivalent to (5x+13) : 63, then what is the value of x?
Aleksandr [31]

\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}

The value of x is 3

Step-by-step explanation:

\textsf{\underline{\large{To find :-}}}

The value of x

\textsf{\underline{\large{Given :-}}}

4 : 9 = (5x + 13) : 63

\textsf{\underline{\underline{\large{Solution :-}}}}

we can write this as

\sf \frac{4}{9}  =  \frac{(5x + 13)}{63}

Now we will cross multiply the values

\sf 4 \times 63 = 9(5x + 13) \\  \\  \sf  252 = 45x + 117 \\  \\  \sf 252 - 117 = 45x \\  \\  \sf 135 = 45x \\  \\  \sf  \frac{135}{45}  = x \\  \\  \sf  \orange {3 = x}

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Step-by-step explanation:

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