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3 years ago

how many times can a rectangle be reflected across an axis of symmetry so that its carries onto itself

Mathematics

2 answers:

Vikki [24]3 years ago

7 0

Answer:

Step-by-step explanation:

Ostrovityanka [42]3 years ago

3 0

2 times, you can fold it without no overlapping on any line

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If DF = 170, find the value of x. Then find DE and EF.<br> DE=3x + 20<br> EF=2x + 40

Julli [10]

9514 1404 393

Answer:

DE = 86

EF = 84

Step-by-step explanation:

We assume that point E lies on segment DF, so that ...

DE + EF = DF

(3x +20) +(2x +40) = 170

5x = 110 . . . . . . . . . . . . . . . collect terms, subtract 60

x = 22 . . . . . . . . . . . . divide by 5

DE = 3×22 +20 = 66 +20 = 86

EF = 2×22 +40 = 44 +40 = 84

7 0

2 years ago

The volume of a right rectangular prism is 573.3 cm³. The length of the right rectangular prism is 7.35 cm and the height is 16.

IgorLugansk [536]

The width of the right rectangular prism is 4.8. You multiply 7.35 by 16.25 and then you divide 573.3 by that answer. So, 573.3 ÷ 119.4375 = 4.8. Hope this helped

3 0

3 years ago

Evaluate the surface integral:S

rjkz [21]

Assuming $S$ does not include the plane $z=0$ , we can parameterize the region in spherical coordinates using

$\mathbf r(u,v)=\left\langle3\cos u\sin v,3\sin u\sin v,3\cos v\right\rangle$

where $0\le u\le2\pi$ and $0\le v\le\dfrac\pi/2$ . We then have

$x^2+y^2=9\cos^2u\sin^2v+9\sin^2u\sin^2v=9\sin^2v$
$(x^2+y^2)=9\sin^2v(3\cos v)=27\sin^2v\cos v$

Then the surface integral is equivalent to

$\displaystyle\iint_S(x^2+y^2)z\,\mathrm dS=27\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^2v\cos v\left\|\frac{\partial\mathbf r(u,v)}{\partial u}\times \frac{\partial\mathbf r(u,v)}{\partial u}\right\|\,\mathrm dv\,\mathrm du$

We have

$\dfrac{\partial\mathbf r(u,v)}{\partial u}=\langle-3\sin u\sin v,3\cos u\sin v,0\rangle$
$\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle3\cos u\cos v,3\sin u\cos v,-3\sin v\rangle$
$\implies\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle-9\cos u\sin^2v,-9\sin u\sin^2v,-9\cos v\sin v\rangle$
$\implies\left\|\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}\|=9\sin v$

So the surface integral is equivalent to

$\displaystyle243\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv\,\mathrm du$
$=\displaystyle486\pi\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv$
$=\displaystyle486\pi\int_{w=0}^{w=1}w^3\,\mathrm dw$

where $w=\sin v\implies\mathrm dw=\cos v\,\mathrm dv$ .

$=\dfrac{243}2\pi w^4\bigg|_{w=0}^{w=1}$
$=\dfrac{243}2\pi$

4 0

2 years ago

A regular pentagon has a perimeter of 5x+15 what is the length of one side

dsp73

Answer:

plz give full question

its just half

6 0

2 years ago

Geometry: Help this makes no sense I don’t think there’s enough info needa find x

umka2103 [35]

The answer should be 9sqrt2 because the equation for finding the legs on a 45-45-90 triangle is hypotenuse/sqrt2.

8 0

2 years ago