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Svetllana [295]
3 years ago
10

100 POINTS WILL GIVE BRAINLIEST TO RIGHT ANSWER

Mathematics
2 answers:
OLEGan [10]3 years ago
6 0

Answer: I think R2. is reflexive property (?)

Step-by-step explanation:

Mandarinka [93]3 years ago
3 0

<u>Missing reason/statements:</u>

  • R2. Vertical angles are congruent
  • R4. Definition of congruence
  • S5. 14x + 20 = 13x + 23
  • R6. Subtraction property of Equality.
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Answer:

4

Step-by-step explanation:

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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
3 years ago
Which point lies on the y-axis?<br> 2,1 2,0 1,2 0,2
exis [7]
(0,2) because following the formula x,y, the 2 is the y, while the 0 is the x.
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irina1246 [14]

Answer: 15 (3/5) cupcakes did not have pink icing

Step-by-step explanation:25 divided by 5 is 5. Then 5 multiplied by 2 equals 10. There are 10 cupcakes with icing which means there are 15 cupcakes without pink icing

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