I gather you're supposed to compute the integral of $G(x,y,z)=z$ over a surface $S$ that is the part of the parabolic cylinder $y=z^2$ with $0\le x\le2$ and $0\le z\le\frac{\sqrt{15}}2$ .

We can parameterize $S$ by

$\vec s(x,z)=x\,\vec\imath+z^2\,\vec\jmath+z\,\vec k$

with the given constraints on $x$ and $z$ . Take the normal vector to $S$ to be

$\vec s_x\times\vec s_z=-\vec\jmath+2z\,\vec k$

so that the surface element is

$\mathrm dS=\|\vec s_x\times\vec s_z\|\,\mathrm dx\,\mathrm dz=\sqrt{1+4z^2}\,\mathrm dx\,\mathrm dz$

Then in the integral, we have

$\displaystyle\iint_Sz\,\mathrm dS=\int_0^2\int_0^{\sqrt{15}/2}z\sqrt{1+4z^2}\,\mathrm dz\,\mathrm dx=\boxed{\frac{21}2}$

5 0

3 years ago

Two angles in a triangle measure (2.3x+25)° and (5.8x+11)°. what is the value of x if the two angles are congruent to one anothe

Anton [14]

Answer:

The answer is D. x= 4

Step-by-step explanation:

The angles are congruent so

2.3x +25 = 5.8x + 11

2.3x - 5.8x = 11 - 25

-3.5x = -14

x = 14/3.5

x = 4.

5 0

3 years ago

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Hey I need help with this maths question

irinina [24]

Answer:

X=4

Step-by-step explanation:

2X - 10 = -2

2X = 8

X = 8/2

X = 4

Best regards

8 0

3 years ago

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