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3 years ago

A convex polyhedron has faces that consist of 1 pentagon, 5 congruent equilateral triangles, and 5 congruent

Mathematics

2 answers:

-Dominant- [34]3 years ago

6 0

Answer:

Step-by-step explanation:

Ivanshal [37]3 years ago

5 0

Answer:

Step-by-step explanation:

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Suppose that 2,4166666 is just 2,416. So the fraction will be 2 in front of a fraction 416 (in nominator) and 1000 ( in denominator) I hooope you understood

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3 years ago

Simplify the algebraic expression (8x + 16y)/2 + 4(x - y)

Karo-lina-s [1.5K]

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3 years ago

Evaluate the surface integral ModifyingBelow Integral from nothing to nothing Integral from nothing to nothing With Upper S f (x

kykrilka [37]

Parameterize $S$ by

$\vec s(u,v)=6\cos u\sin v\,\vec\imath+6\sin u\sin v\,\vec\jmath+6\cos v\,\vec k$

with $0\le u\le2\pi$ and $0\le v\le\frac\pi2$ . Take a normal vector to $S$ ,

$\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec s}{\partial u}=36\cos u\sin^2v\,\vec\imath+36\sin u\sin^2v\,\vec\jmath+36\cos v\sin v\,\vec k$

which has norm

$\left\|\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec s}{\partial u}\right\|=36\sin v$

Then the integral of $f(x,y,z)=x^2+y^2$ over $S$ is

$\displaystyle\iint_Sx^2+y^2\,\mathrm dS=\iint_S\left((6\cos u\sin v)^2+(6\sin u\sin v)^2\right)\left\|\frac{\partial\vec s}{\partial v}\times\frac{\partial\vec s}{\partial u}\right\|\,\mathrm du\,\mathrm dv$

$=\displaystyle36^2\int_0^{\pi/2}\int_0^{2\pi}\sin^3v\,\mathrm du\,\mathrm dv=\boxed{1728\pi}$

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4 years ago