Answer:
1. C. cylindrical coordinates
2 A. spherical coordinates
3. A. spherical coordinates
4. D. Cartesian coordinates
5 B. polar coordinates
Step-by-step explanation:
USE THE BOUNDARY INTERVALS TO IDENTIFY
1. ∭E dV where E is:
x^2 + y^2 + z^2<= 4, x>= 0, y>= 0, z>= 0 -- This is A CYLINDRICAL COORDINATES SINCE x>= 0, y>= 0, z>= 0
2. ∭E z^2 dV where E is:
-2 <= z <= 2,1 <= x^ 2 + y^2 <= 2 This is A SPHERICAL COORDINATES
3. ∭E z dV where E is:
1 <= x <= 2, 3<= y <= 4,5 <= z <= 6 -- This is A SPHERICAL COORDINATES
4. ∫10∫y^20 1/x dx ---- This is A CARTESIAN COORDINATES
5. ∬D 1/x^2 + y^2 dA where D is: x^2 + y^2 <=4 This is A POLAR COORDINATES
I thnk 83 if the year has 365 days
Answer:
Yes
Step-by-step explanation:
8²+6²=100
√100
=10
Well, in the real would many people spend more than $30.
The main rule we use in this exercise is

and the more general case:
![( \sqrt[n]{a} ) ^{m} =( a^{ \frac{1}{n}} )^{m} = a^{ \frac{1}{n}*m}=a^{ \frac{m}{n}}](https://tex.z-dn.net/?f=%28%20%20%5Csqrt%5Bn%5D%7Ba%7D%20%20%29%20%5E%7Bm%7D%20%3D%28%20a%5E%7B%20%5Cfrac%7B1%7D%7Bn%7D%7D%20%29%5E%7Bm%7D%20%3D%20a%5E%7B%20%5Cfrac%7B1%7D%7Bn%7D%2Am%7D%3Da%5E%7B%20%5Cfrac%7Bm%7D%7Bn%7D%7D)
Using these rules, we make all the indices, or exponents, look like

, and compare them to each other.
A.

B.

C.
![( \sqrt[3]{125} ) ^{7} =( 125^{ \frac{1}{3}} )^{7} = 125^{ \frac{1}{3}*7}= 125^{ \frac{7}{3}}](https://tex.z-dn.net/?f=%28%20%20%5Csqrt%5B3%5D%7B125%7D%20%29%20%5E%7B7%7D%20%3D%28%20125%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%7D%20%29%5E%7B7%7D%20%3D%20125%5E%7B%20%20%5Cfrac%7B1%7D%7B3%7D%2A7%7D%3D%20125%5E%7B%20%5Cfrac%7B7%7D%7B3%7D%7D%20%20%20)
D.