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faust18 [17]
3 years ago
7

How many seconds are there in a year?

Mathematics
1 answer:
alina1380 [7]3 years ago
5 0

Answer:

31,536,000 seconds

Step-by-step explanation:

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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
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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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How can you prove:<br><br> secθ = cscθtanθ
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\sec \theta=\csc \theta\tan \theta\\\\ \dfrac{1}{\cos \theta}=\dfrac{1}{\sin \theta}\cdot\dfrac{\sin \theta}{\cos \theta}\\\\ \dfrac{1}{\cos \theta}=\dfrac{1}{\cos \theta}

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Housing Price.The file calledsaratoga.JMPcontains data on 1728 houses in Saratoga, NewYork in the year 2006. The dataset include
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Answer:

iii. priceof a house in Saratoga, N.Y.

Step-by-step explanation:

In this question, we take a sample from house prices of 1728 houses in Saratoga, New York.

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In this question:

Sample to find house prices in Saratoga, which is the variable of interest. The correct answer is given by option iii.

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We don’t have any of the “images” to answer this question.
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