Direct computation:
Parameterize the top part of the circle
by

with
, and the line segment by

with
. Then



Using the fundamental theorem of calculus:
The integral can be written as

If there happens to be a scalar function
such that
, then
is conservative and the integral is path-independent, so we only need to worry about the value of
at the path's endpoints.
This requires


So we have

which means
is indeed conservative. By the fundamental theorem, we have

Answer:
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Answer:
The gallons of gas the tank contain now is <u>35 1/12</u>.
Step-by-step explanation:
Given:
Fuel tank contains 1 3/4 gallons of gasoline.
Casey adds 33 1/3 gallons of gasoline to the tank.
Now, to find the total gallons of gas the tank contain.
Converting the mixed fractions into improper.
Gallons of gasoline in fuel tank
.
Gallons of gasoline Casey adds
.
<u>According to question:</u>
By adding we get the total gallons of gasoline now tank contain:





Therefore, the gallons of gas the tank contain now is 35 1/12.
9 games
You can get this by multiplying each percentage by the total number of games to see what they have to expect.
.55*180 = 99 games (red team)
.60*180 = 108 games (blue team)
Now subtract the blue team expectation from the red team.
108 - 99 = 9 games.
Answer:
1:44
Step-by-step explanation:
You can subtract 32 minutes from 2:32 to get 2:00.
Since you only subtracted 32, subtract 16 (16+32=48) from 60, since 60 minutes is one hour, to get 1:44