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4 years ago

A mountain path climbs 220 vertically before every 2500 feet horizontal what is the grade of the path

Mathematics

1 answer:

kramer4 years ago

5 0

$\bf slope=m=\cfrac{rise}{run}\implies \cfrac{220}{2500}\implies \cfrac{11}{125}$

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at joe's cafe 1 cup of coffee and 3 donuts is $4.10 and 2 cups of coffee and 2 donuts is $4.60, how much is 1 count? 1 cup of co

bazaltina [42]

The answer is 1.20 sooooooooooooooooooooooooooooooo

3 0

3 years ago

Read 2 more answers

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

4 years ago

A different class has 285 students, and 51.2% of them are men. how many men are in the class?

Zanzabum

Answer:

146

Step-by-step explanation:

Get a percent calculator, Then, you put 51.2% of 285 and you actually get 145.96 but the rounded of what you need is 146

6 0

3 years ago

C=3h-ah solve for h

Rainbow [258]

Answer:

a= -c-3h/h

Step-by-step explanation:

8 0

3 years ago

How do I solve this question ?

Phoenix [80]

Answer:

x=37 CD=20

Step-by-step explanation:

We know this becuase the two triangles are congruent.

3 0

3 years ago