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2 years ago

Please help! I do not understand!

Mathematics

1 answer:

castortr0y [4]2 years ago

5 0

Answer:

There are 31 polygons in total used to make the tessellation and the ones that make number 17 up are:

Pentagons, triangles, and hexagons.

The ones that make up number 18 are:

Pentagons, squares, and triangles.

Step-by-step explanation:

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Integrate G(x,y,z)equalsz over the parabolic cylinder yequalszsquared, 0less than or equalsxless than or equals2, 0less than

yKpoI14uk [10]

I gather you're supposed to compute the integral of $G(x,y,z)=z$ over a surface $S$ that is the part of the parabolic cylinder $y=z^2$ with $0\le x\le2$ and $0\le z\le\frac{\sqrt{15}}2$ .

We can parameterize $S$ by

$\vec s(x,z)=x\,\vec\imath+z^2\,\vec\jmath+z\,\vec k$

with the given constraints on $x$ and $z$ . Take the normal vector to $S$ to be

$\vec s_x\times\vec s_z=-\vec\jmath+2z\,\vec k$

so that the surface element is

$\mathrm dS=\|\vec s_x\times\vec s_z\|\,\mathrm dx\,\mathrm dz=\sqrt{1+4z^2}\,\mathrm dx\,\mathrm dz$

Then in the integral, we have

$\displaystyle\iint_Sz\,\mathrm dS=\int_0^2\int_0^{\sqrt{15}/2}z\sqrt{1+4z^2}\,\mathrm dz\,\mathrm dx=\boxed{\frac{21}2}$

5 0

3 years ago

I need the last two please help I need it by 11

stich3 [128]

Answer:

Rectangle - Diamond

Oval - doughnut

Step-by-step explanation:

Takes some visualisation.

7 0

2 years ago

Read 2 more answers

Name a point that is the square root of 2 away from(-1,5)

DerKrebs [107]

Answer:

Any point on the circle (x + 1)² + (y - 5)² = 2 with center (-1 , 5) and radius √2

Step-by-step explanation:

circle: (x + 1)² + (y - 5)² = 2

3 0

2 years ago

Hey loves!!! Can someone plz help me with this math question?

Otrada [13]

Answer:

Hey there!

They are congruent by AAS, where two angles and one side is congruent.

Hope this helps :)

6 0

3 years ago

What expression is equivalent to 4^7 times 4^-5

liubo4ka [24]

All you have to do is add exponents when multiplying like monomials. So it's just 4^2

6 0

3 years ago