Mathematics, 17.08.2020 01:01 gtjermaine3249

Use the divergence theorem to find the outward flux of the vector field F(x, y,z)=2x2i+5y2j+3z2k across the boundary of the rectangular prism: 0≤x≤1,0≤y≤3,0≤z≤1.

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Answer from: mayasofia

In this exercise we have to calculate the flux by the divergent theorem:

$\int\limits\int\limits_R\, ds = 60$

By the divergence theorem, the flux of F across the boundary of a region, ∂R, is equal to the integral of div(F ) over the region itself, R. In this case, the flux would be:

$\int\limits\int\limits_R {F} \, ds= \int\limits \int\limits \int\limits_R {div(F)} \, dxdydz\\=\int\limits^1_0 \int\limits^3_0 \int\limits^1_0 {(4x+10y+6z)} \, dx dy dz= 60$

See more about vectorial calculus at : link

Answer from: markipler01

By the divergence theorem, the flux of F across the boundary of a region, ∂R, is equal to the integral of div(F ) over the region itself, R. In this case, the flux would be

$\displaystyle \iint_{\partial R}\mathbf F\cdot\,\mathrm d\mathbf S = \iiint_R\mathrm{div}(\mathbf F)\,\mathrm dx\,\mathrm dy\,\mathrm dz \\\\ = \int_0^1\int_0^3\int_0^1\frac{\partial(2x^2)}{\partial x} + \frac{\partial(5y^2)}{\partial y} + \frac{\partial(3z^2)}{\partial z} \,\mathrm dx\,\mathrm dy\,\mathrm dz \\\\ = \int_0^1\int_0^3\int_0^1 (4x+10y+6z)\,\mathrm dx\,\mathrm dy\,\mathrm dz = \boxed{60}$

Answer from: Quest

answer

the correct answer is

$x=-5,x=7$

explanation

the given function is

$\frac{ {x}^{2} - 3x - 28 }{x {}^{2} - 2x - 35}$

the excluded values are obtained by solving:

${x}^{2} - 2x - 35 = 0$

we factor to obtain:

$(x + 5)(x - 7)= 0$

the excluded values are

$x=-5,x=7$

What are the excluded values of x for.. (look at picture)

Answer from: Quest

"it's not the heat, it's the humidity". that's a partly valid phrase you may have heard in the summer, but it's actually both. the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature. this has important considerations for the human body's comfort. when the body gets too hot, it begins to perspire or sweat to cool itself off. if the perspiration is not able to evaporate, the body cannot regulate its temperature. evaporation is a cooling process. when perspiration is evaporated off the body, it effectively reduces the body's temperature. when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases. in other words, the human body feels warmer in humid conditions. the opposite is true when the relative humidity decreases because the rate of perspiration increases. the body actually feels cooler in arid conditions. there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

75% of the temperatures are below what value? how do you know? 75% of the temperatures are above w

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Use the divergence theorem to find the outward flux of the vector field F(x, y,z)=2x2i+5y2j+3z2k acr...

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