I assume each path
is oriented positively/counterclockwise.
(a) Parameterize
by

with
. Then the line element is

and the integral reduces to

The integrand is symmetric about
, so

Substitute
and
. Then we get

(b) Parameterize
by

with
. Then

and

Integrate by parts with



(c) Parameterize
by

with
. Then

and

There are 180 degrees in total inside a triangle.
If something is equilateral that means that all the angles are equal.
180/3 equals 60 degrees.
That means that all angles of an equilateral triangle are always equal to each other and if you must know, are 60 degrees
It can help because 9×4 =36, and 9×8=72. if you divide 72 by 2 you get 36 which is the answer to 9 ×4. basically because nine is the same in both problems you are multiplying by 4 (and you know 4 is half of 8) you can assume that multiplying the sum of 4 and 9 that you will get the sum of 8 and 9.
Answer: −
3
X
−
x
−
4
Step-by-step explanation:
Answer:
see below the first three problems
Step-by-step explanation:
f(g(-2))
First, find g(-2) using function g(x). Then use that value as input for function f(x).
g(x) = -2x + 1
g(-2) = -2(-2) + 1
g(-2) = 5
f(x) = 5x
f(5) = 5(5)
f(5) = 25
f(g(-2)) = 25
g(h(3))
First, find h(3) using function h(x). Then use that value as input for function g(x).
h(x) = x^2 + 6x + 8
h(3) = 3^2 + 6(3) + 8 = 9 + 18 + 8
h(3) = 35
g(x) = -2x + 1
g(35) = -2(35) + 1 = -70 + 1
g(35) = -69
g(h(3)) = -69
f(g(3a))
First, find g(3a) using function g(x). Then use that value as input for function f(x).
g(x) = -2x + 1
g(3a) = -2(3a) + 1
g(3a) = -6a + 1
f(x) = 5x
f(-6a + 1) = 5(-6a + 1)
f(-6a + 1) = -30a + 5
f(g(3a)) = -30a + 5