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

2 years ago

Which ordered pairs are solutions to the system? Check all of the boxes that apply.

77julia77 [94]

Answer:

the answer is the 3rd & 5th one for anyone doing this question ; )

Step-by-step explanation:

I just did this question

It's right i just checked

7 0

2 years ago

Read 2 more answers

QUICK, BRAINLIEST FOR 1ST ANSWER. <br><br>14.5 is incorrect!

ra1l [238]

To get the *percent increase* from week 1 to week 2, we calculate the change in distance from week 1 to week 2 (13.5 - 12.5 = 1 mile) over the week 1 distance (12.5 miles). Doing that, we find that Matthew increased his distance by

1/12.5 = 0.08, or 8%

We’re given that he’ll increase his distance by the same percentage from week 2 to 3, so to find his week 3 distance, we can find 8% of the week 2 distance and add that on. 8% of 13.5 miles is 0.08 x 13.5 = 1.08 miles, so by week 3, he’ll be running 13.5 + 1.08 = 14.58 miles.

4 0

2 years ago