We want to find a scalar function

such that

.
So we need to have

Integrating both sides with respect to

gives

Differentiating with respect to

gives



So we find that

By the fundamental theorem of calculus, we then know the line integral depends only on the values of

at the endpoints of the path. Therefore
Answer:
$33 336
Step-by-step explanation:
Increase = 30 000 × 0.112
Increase = $3336
New salary = 30 000 + 3336
New salary = $33 336
Answer:
25π ≈ 78.5 cm squared
Step-by-step explanation:
Area of circle= πr²
Substitute: π(5)²
Solution: 25π or about 78.5 cm²
#25.
Convert the fractional numbers into decimals for easier comparison.
3 2/3 is approximately 3.66
-4 2/5 is approximately -4.4
We now have: 3, 3.66, -4.2, -4.4
In order: -4 2/5, -4.2, 3, 3 2/3
#26.
All positive numbers are greater than negative numbers.
When comparing two negative numbers, the one with the larger absolute value, will be less.
So (G) is correct
#27.
25 = m + 6.3
25 - 6.3 = m + 6.3 - 6.3
m = 18.7
#28.
h = 3.2-1.6 = 1.6
#29.
x = 15.6 - 9.8 = 5.8
#30
p = 17 - 4.5 = 12.5