Answer:
4
Step-by-step explanation:
Answer:
$6
Step-by-step explanation:
Susan can easily figure the tip by the following procedure. 10% of the bill is the amount with the decimal point moved one place to the left, so is $4.00. 5% of the bill is half that, or $2.00.
15% of the bill is 10% + 5%, so is $4.00 +2.00 = $6.00. The tip will be $6.00.
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:
The measure of the angles:
24° and 66°
Step-by-step explanation:
Complementary angles sum 90°
then:
(3x + 3) + (10x-4) = 90
3x + 10x + 3 - 4 = 90
13x - 1 = 90
13x = 90+1
13x = 91
x = 91/13
x = 7°
then:
3x+3 = 3*7 + 3 = 21+3 = 24°
10x - 4 = 10*7 - 4 = 70 - 4 = 66°
Check:
66° + 24° = 90°
This is really obvious but the answer is 4 feet.