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Oksanka [162]
3 years ago
15

Find the area and perimeter the Gym, Cafeteria, and Locker

Mathematics
1 answer:
Serjik [45]3 years ago
3 0

Answer:

Gym: A=100 P=41

Cafeteria: A=144 P=48

Locker room: A=75 P= 37

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G verify that the divergence theorem is true for the vector field f on the region
Alenkasestr [34]
\mathbf f(x,y,z)=\langle z,y,x\rangle\implies\nabla\cdot\mathbf f=\dfrac{\partial z}{\partial x}+\dfrac{\partial y}{\partial y}+\dfrac{\partial x}{\partial z}=0+1+0=1

Converting to spherical coordinates, we have

\displaystyle\iiint_E\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=6}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=288\pi

On the other hand, we can parameterize the boundary of E by

\mathbf s(u,v)=\langle6\cos u\sin v,6\sin u\sin v,6\cos v\rangle

with 0\le u\le2\pi and 0\le v\le\pi. Now, consider the surface element

\mathrm d\mathbf S=\mathbf n\,\mathrm dS=\dfrac{\mathbf s_v\times\mathbf s_u}{\|\mathbf s_v\times\mathbf s_u\|}\|\mathbf s_v\times\mathbf s_u\|\,\mathrm du\,\mathrm dv
\mathrm d\mathbf S=\mathbf s_v\times\mathbf s_u\,\mathrm du\,\mathrm dv
\mathrm d\mathbf S=36\langle\cos u\sin^2v,\sin u\sin^2v,\sin v\cos v\rangle\,\mathrm du\,\mathrm dv

So we have the surface integral - which the divergence theorem says the above triple integral is equal to -

\displaystyle\iint_{\partial E}\mathbf f\cdot\mathrm d\mathbf S=36\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(\mathbf s_v\times\mathbf s_u)\,\mathrm du\,\mathrm dv
=\displaystyle36\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}(12\cos u\cos v\sin^2v+6\sin^2u\sin^3v)\,\mathrm du\,\mathrm dv=288\pi

as required.
3 0
3 years ago
What is the answer the the problem -15-(-9)?
harina [27]

-15-(-9)

-15+9 = -6

so, your answer is -6

7 0
4 years ago
Use the diagram to answer the questions
IRISSAK [1]

Answer:

1.  B. BD

2. C. 15

3. A. 2

Step-by-step explanation:

1.  From the figure,

∠DAB = ∠DAC

Therefore, BD is the bisector of ∠ABC.


2.  From the figure, IG = GH

3x = 5x - 10

10 = 5x - 3x

2x = 10

x = 5

So, GH = 5x - 10

= 5(5) - 10

= 25 - 10

= 15

Therefore, GH = 15.


3.  From the figure,

∠DAB = ∠DAC

10y = 8y + 4

10y - 8y = 4

2y = 4

y = 2

8 0
3 years ago
Jim Climbed 80 mountains in 10 months. Find his climbing rate in mountains per month
OverLord2011 [107]

Answer:

If he climbed 80 mountains in the span of 10 months then you should divide the 80 by 10 which makes it 8.. so I believe the correct answer is 8 mountains per month

8 0
3 years ago
Read 2 more answers
The sum of a number and 2 times its reciprocal is -3
Marysya12 [62]

Answer:

(-2,-1)

Step-by-step explanation:

let the number=x

its reciprocal=1/x

x+2(1/x)=-3

x+2/x=-3

x²+2=-3x

x²+3x+2=0

(x+2)(x+1)=0

x=-2,-1

6 0
3 years ago
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