matthew has 18 sets of baseball cards. each set has 12 cards. about how many baseball card does matthew have

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of

tresset_1 [31]

Because I've gone ahead with trying to parameterize $S$ directly and learned the hard way that the resulting integral is large and annoying to work with, I'll propose a less direct approach.

Rather than compute the surface integral over $S$ straight away, let's close off the hemisphere with the disk $D$ of radius 9 centered at the origin and coincident with the plane $y=0$ . Then by the divergence theorem, since the region $S\cup D$ is closed, we have

$\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV$

where $R$ is the interior of $S\cup D$ . $\vec F$ has divergence

$\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(xz)}{\partial x}+\dfrac{\partial(x)}{\partial y}+\dfrac{\partial(y)}{\partial z}=z$

so the flux over the closed region is

$\displaystyle\iiint_Rz\,\mathrm dV=\int_0^\pi\int_0^\pi\int_0^9\rho^3\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=0$

The total flux over the closed surface is equal to the flux over its component surfaces, so we have

$\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iint_S\vec F\cdot\mathrm d\vec S+\iint_D\vec F\cdot\mathrm d\vec S=0$

$\implies\boxed{\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=-\iint_D\vec F\cdot\mathrm d\vec S}$

Parameterize $D$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec k$

with $0\le u\le9$ and $0\le v\le2\pi$ . Take the normal vector to $D$ to be

$\vec s_u\times\vec s_v=-u\,\vec\jmath$

Then the flux of $\vec F$ across $S$ is

$\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^9\vec F(x(u,v),y(u,v),z(u,v))\cdot(\vec s_u\times\vec s_v)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^{2\pi}\int_0^9(u^2\cos v\sin v\,\vec\imath+u\cos v\,\vec\jmath)\cdot(-u\,\vec\jmath)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{2\pi}\int_0^9u^2\cos v\,\mathrm du\,\mathrm dv=0$

$\implies\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\boxed{0}$

8 0

4 years ago

He currently pays an AP$ of $1.87 per pound for fresh onions, but his yield is 50% after peeling and cooking the onions. What is

PolarNik [594]

Complete question :

Chef Charming and his mother sell cheese steak sandwiches at their food truck. They use fresh onions, and cook them slowly to caramelize them before putting them on their sandwiches.

Charming found a pre-cooked onion that was $8.3 per pound AP$, with 100% Yield. He wants to save money but isn't sure if that is a better deal than cooking the fresh onions himself.

He currently pays an AP$ of $1.87 per pound for fresh onions, but his yield is 50% after peeling and cooking the onions. What is the EP$ for the fresh onions, after caramelizing?

Answer:

$3.74

Step-by-step explanation:

Cost of fresh onions = $1.87 per pound

Percentage yield = 100% after caramelizing

Therefore EP$ for the fresh onions after caramelizing will be :

(1 + percentage yield) * cost of fresh onions

(1 + 100%) * $1.87

(1 + 1) * $1.87

2 * $1.87

= $3.74

3 0

3 years ago

The equation of s circle is x2+y2+6x+4y+10=1. What is this equation written in standard form?

Andreas93 [3]

Answer:

i think it would be x two+ y two + six x + four y+ ten= one is that one the answers if so i hope this helps if not just give me the answers and i will try to help you as much as i can thanks

Step-by-step explanation:

4 0

3 years ago

What method can be used to write the equation of a line in slope-intercept form given two points? plzzzz answer im being timed

Trava [24]

Answer:

slope intercept form is : y = mx + b

where m is the slope and b is the y-intercept.

The slope, m = (y' - y)/(x' - x)

Is found using the two pints.

The apostrophe is used to denote the other point, different from point (x,y).

once you have the slope, m for the equation y = mx + b ; use one of the points as (x,y) to solve for b.