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3 years ago

(c) If a pizza contains 8 slices and there are 4

Mathematics

2 answers:

Ostrovityanka [42]3 years ago

8 0

Answer:

Step-by-step explanation:

8 / 4 = 2

8 = 8 slices

4 = 4 people

slavikrds [6]3 years ago

7 0

2 slices per person

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3 years ago

Erwin earns $ 2 , 100 per month. Her deductions amount to 26 % of her paycheck. How much does Erwin take home each month?

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Answer:

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2 years ago

142 students are going on a field trip. There will be six drivers, and two different types of vehicles. A bus can hold 51 people

otez555 [7]

Answer: 2 buses and 4 vans would be needed

Step-by-step explanation:

Let x represent the number of buses that would be needed.

Let y represent the number of vans that would be needed.

There will be six drivers, and two different types of vehicles. This means that

x + y = 6

142 students are going on a field trip. A bus can hold 51 people while a van can hold 10. This means that

51x + 10y = 142 - - - - - - - - - - - 1

Substituting x = 6 - y into equation 1, it becomes

51(6 - y) + 10y = 142

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3 years ago

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