Hmm I’ve done this before but I can’t remember sorry but I will try and think
Consider the closed region

bounded simultaneously by the paraboloid and plane, jointly denoted

. By the divergence theorem,

And since we have

the volume integral will be much easier to compute. Converting to cylindrical coordinates, we have




Then the integral over the paraboloid would be the difference of the integral over the total surface and the integral over the disk. Denoting the disk by

, we have

Parameterize

by


which would give a unit normal vector of

. However, the divergence theorem requires that the closed surface

be oriented with outward-pointing normal vectors, which means we should instead use

.
Now,



So, the flux over the paraboloid alone is
Answer:
Carmen had the largest red to green apple ratio of 5 : 3
Step-by-step explanation:
Red apples : Green apples
Carmen = 20 red apples : 12 green apples
= 20 / 12
= 5 / 3 = 1.67
= 5 : 3
Dylan = 12 red apples : 10 green apples
= 12 / 10
= 6 / 5 = 1.2
= 6 : 5
Eli = 16 red apples : 20 green apples
= 16 / 20
= 4 / 5 = 0.8
= 4 : 5
Carmen had the largest red to green apple ratio of 5 : 3
Real life scenarios of acute angles are:
- Sighting a ball from the top of a building at an angle of 55 degrees.
- The angle between two adjacent vanes of a fan that has 6 vanes
<h3>What are acute angles?</h3>
As a general rule, an acute angle, x is represented as: x < 90
This means that acute angles are less than 90 degrees.
<h3>The real life scenarios</h3>
The real life scenarios that involve acute angles are scenarios that whose measure of angle is less than 90 degrees.
Sample of the real life scenarios that satisfy the above definition are:
- Sighting a ball from the top of a building at an angle of 55 degrees.
- The angle between two adjacent vanes of a fan that has 6 vanes
Read more about acute angles at:
brainly.com/question/3217512
#SPJ1
Answer:
x = 11
y = 17
Step-by-step explanation:
We know that opposite angles (or vertical angles) are equal.
So
8x + 7 = 9x - 4
Subtract 8x from both sides of the equation
8x - 8x + 7 = 9x - 8x - 4
7 = x - 4
Add 4 to both sides of the equation
7 + 4 = x - 4 + 4
11 = x
Looking at the other 2 angles,
5y = 7y - 34
Subtract 7 y from both sides of the equation
5y - 7y = 7y - 7y - 34
-2y = -34
Divide both sides by -2
-2y/-2 = -34/-2
y = 17