Answer:
Step-by-step explanation:
From the given information:
The domain D of integration in polar coordinates can be represented by:
D = {(r,θ)| 0 ≤ r ≤ 6, 0 ≤ θ ≤ 2π) &;
The partial derivates for z = xy can be expressed as:

Thus, the area of the surface is as follows:





![= 2 \pi \times \dfrac{1}{3} \Bigg [ (37)^{3/2} - 1 \Bigg]](https://tex.z-dn.net/?f=%3D%202%20%5Cpi%20%5Ctimes%20%5Cdfrac%7B1%7D%7B3%7D%20%20%5CBigg%20%5B%20%2837%29%5E%7B3%2F2%7D%20-%201%20%5CBigg%5D)
![= \dfrac{2 \pi}{3} \Bigg [37 \sqrt{37} -1 \Bigg ]](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B2%20%5Cpi%7D%7B3%7D%20%5CBigg%20%5B37%20%5Csqrt%7B37%7D%20-1%20%5CBigg%20%5D)
Let the distance to his office be x, then
On monday, speed = x/20 miles per minutes = 3x miles per hour
On tuesday, speed = (3x + 15) miles per hour
Time = distance / speed
(20 - 6)/60 hours = x/(3x + 15) hours
7/30 = x/(3x + 15)
7(3x + 15) = 30x
21x + 105 = 30x
30x - 21x = 105
9x = 105
x = 105/9 = 11.7 miles
Therfore he travels an average of 11.7 miles to work.
Answer:
720
Step-by-step explanation:
hope it helps
Answer:
Radius = 1 in
then the volume of bubble = 4/3 π r^3
= (4/3 × 22/7 × 1) in^3 = 88/21 in^3
Hope it helps
False they don't have to be whole numbers. As long as they're greater than 0