
Divergence is easier to compute:


Curl is a bit more tedious. Denote by
the differential operator, namely the derivative with respect to the variable
. Then

![\mathrm{curl}\vec F=\left(D_y\left[y\tan^{-1}\dfrac xz\right]-D_z\left[e^{xy}\sin z\right]\right)\,\vec\imath-D_x\left[y\tan^{-1}\dfrac xz\right]\,\vec\jmath+D_x\left[e^{xy}\sin z}\right]\,\vec k](https://tex.z-dn.net/?f=%5Cmathrm%7Bcurl%7D%5Cvec%20F%3D%5Cleft%28D_y%5Cleft%5By%5Ctan%5E%7B-1%7D%5Cdfrac%20xz%5Cright%5D-D_z%5Cleft%5Be%5E%7Bxy%7D%5Csin%20z%5Cright%5D%5Cright%29%5C%2C%5Cvec%5Cimath-D_x%5Cleft%5By%5Ctan%5E%7B-1%7D%5Cdfrac%20xz%5Cright%5D%5C%2C%5Cvec%5Cjmath%2BD_x%5Cleft%5Be%5E%7Bxy%7D%5Csin%20z%7D%5Cright%5D%5C%2C%5Cvec%20k)

Answer: The area of the Polygon D is 36 times larger than the area of the Polygon C.
Step-by-step explanation:
<h3>
The complete exercise is: "Polygon D is a scaled copy of Polygon C using a scale factor of 6. How many times larger is the area of Polygon D than the area Polygon C"?</h3>
In order to solve this problem it is important to analize the information provided in the exercise.
You know that the Polygon D was obtained by multiplying the lengths of the Polygon C by the scale factor of 6.
Then, you can identify that the Length scale factor used is:

Now you have to find the Area scale factor.
Knowing that the Length scale factos is 6, you can say that the Area scale factor is:

Finally, evaluating, you get that this is:

Therefore, knowing the Area scale factor, you can determine that the area of the Polygon D is 36 times larger than the area of the Polygon C.
Answer:
first you subtract 5 from both sides
your left with 3x=11
divide by 3 on both sides
x=3.666 repeating
Step-by-step explanation:
Answer:
729
Step-by-step explanation:
Volume of cube=a^3
Volume of cube=9^3=729
Step-by-step explanation:
Answer C)
Explanation:
MN + NP = MP
MP = 39
Therefore, 4(x + 5) + 2x + 1= MP
So, 4(x + 5) + 2x + 1= 39
(4x + 20) + 2x +1 = 39
So, (4x + 2x) + (20 + 1) = 39
6x + 21 = 39
Addition changes to Subtraction
So, 6x = 39 - 21
6x = 18
Multiplication changes to Division
x= 18/6
x=3
Therefore MN = 4(x + 5)
So, 4(3 + 5) = 4(8)
4(8) = 32
Therefore, MN = 32
Hope this helps!