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:
Step-by-step explanation:
∠Y = ∠P, so AY = AP
Perimeter = AY + AP + 13 = 43
AY + AP = 30
∠Y = ∠P, so AY = AP
AP = 30/2 = 15
Well just substitute y (the first equation) into the second equation.
So
5x-4(5-3x)=-3
Then just solve the equation from there.
5x-20+12x=-3
17x=17
x=1
and if you need y, y=2
Answer:
5(9+x)
Step-by-step explanation:
5 x 9 = 45
then if do 5 times x it would look like 5x
Answer:
, see the graph attached for a visual reference.
Step-by-step explanation:
Vertical asymptotes are only present in rational functions where the parent function
has a vertical asymptote at the line
and a horizontal asymptote at the line
. Because the vertical asymptote has to be
, the denominator must be x-7 in order for the denominator to equal 0. For the horizontal asymptote to be
, then 3 must be subtracted from the rational function. Therefore, the function that has these asymptotes is
.