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USPshnik [31]
3 years ago
10

I HAVE 4 MATH QUESTIONS AND I REALLY NEED HELP FAST. PLEASE ONLY COMMENT IF YOU ARE GOING TO HELP. I GAVE AS MANY POINTS AS POSS

IBLE. ALSO PLEASE PUT RIGHT ANSWERS AND BE SERIOUS.

Mathematics
1 answer:
Andru [333]3 years ago
3 0
# 3 is 4 and # 4 is 1
You might be interested in
484,343 rounded to the nearest thousand
Semmy [17]

Answer:

484,000

Step-by-step explanation:

The hundreds place is less than 5 so you round down.

3 0
3 years ago
Read 2 more answers
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
I need help on this one please
Advocard [28]
1 lemon costs 20p and 1 orange costs 45p so an orange costs 25p more
7 0
3 years ago
Offering 15 points for a good and explained answer.
Romashka [77]
The answer is False
3 0
2 years ago
HELP APPRECIATED PLEASEEE<br> WILL GIVE BRAINLIEST !!!
kakasveta [241]

Answer:

the first line

Step-by-step explanation:

because 1.75 is almost to the number 2

hope this helps

8 0
3 years ago
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