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3 years ago

Each table at a restaurant has six chairs placed around it.

Mathematics

1 answer:

Romashka-Z-Leto [24]3 years ago

3 0

Answer:

4/24

Choice B is correct

Step-by-step explanation:

From the information given, there is 1 table for every 6 chairs at the restaurant. In ratio form this can be expressed as;

1:6

The ratio that is equivalent to this given ratio is 4/24. This can easily be checked through simplification of this ratio;

4/24; If we divide both the numerator and the denominator by 4 we obtain

1/6 which is equivalent to 1:6

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Surface integrals using an explicit description. Evaluate the surface integral \iint_{S}^{}f(x,y,z)dS using an explicit represen

Jobisdone [24]

Parameterize $S$ by the vector function

$\vec r(x,y)=x\,\vec\imath+y\,\vec\jmath+f(x,y)\,\vec k$

so that the normal vector to $S$ is given by

$\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}=\left(\vec\imath+\dfrac{\partial f}{\partial x}\,\vec k\right)\times\left(\vec\jmath+\dfrac{\partial f}{\partial y}\,\vec k\right)=-\dfrac{\partial f}{\partial x}\vec\imath-\dfrac{\partial f}{\partial y}\vec\jmath+\vec k$

with magnitude

$\left\|\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}\right\|=\sqrt{\left(\dfrac{\partial f}{\partial x}\right)^2+\left(\dfrac{\partial f}{\partial y}\right)^2+1}$

In this case, the normal vector is

$\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}=-\dfrac{\partial(8-x-2y)}{\partial x}\,\vec\imath-\dfrac{\partial(8-x-2y)}{\partial y}\,\vec\jmath+\vec k=\vec\imath+2\,\vec\jmath+\vec k$

with magnitude $\sqrt{1^2+2^2+1^2}=\sqrt6$ . The integral of $f(x,y,z)=e^z$ over $S$ is then

$\displaystyle\iint_Se^z\,\mathrm d\Sigma=\sqrt6\iint_Te^{8-x-2y}\,\mathrm dy\,\mathrm dx$

where $T$ is the region in the $x,y$ plane over which $S$ is defined. In this case, it's the triangle in the plane $z=0$ which we can capture with $0\le x\le8$ and $0\le y\le\frac{8-x}2$ , so that we have

$\displaystyle\sqrt6\iint_Te^{8-x-2y}\,\mathrm dx\,\mathrm dy=\sqrt6\int_0^8\int_0^{(8-x)/2}e^{8-x-2y}\,\mathrm dy\,\mathrm dx=\boxed{\sqrt{\frac32}(e^8-9)}$

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Answer:

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2 years ago

Solve the literal equation for x: g= 4x+5xy

Andreas93 [3]

The literal equation for x is $\frac{g}{4+5y}$ given that $g= 4x+5xy$

The subject of a formula is a way of representing a variable in terms of other variables.

Given the equation

$g= 4x+5xy$

Factor out the common variable x

$g= x(4+5y)$

Divide both sides by 4+5y

$\frac{g}{4+5y} =\frac{x(4+5y)}{4+5y} \\\frac{g}{4+5y} = x\\Swap\\x = \frac{g}{4+5y}$

This shows that the literal equation for x is $\frac{g}{4+5y}$

Learn more here: brainly.com/question/21140562

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2 years ago

2xy-3x+4xy+8x simplified?

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So, Your Answer would be 6xy + 5x

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