Hello from MrBillDoesMath
Answer:
[email protected] = - sqrt(7)/ 4
which is choice B
Discussion:
This problem can be solved by drawing triangles and looking at ratios of sides or by using the trig identity:
([email protected])^2 + (sin2)^2 = 1
If [email protected] = 3/4
, the
([email protected])^2 + (3/4)^2 = 1 => (subtract (3/4)^2 from both sides)
([email protected])^2 = 1 - (3/4)^2 = 1 - 9/16 = 7/16
So...... taking the square root of both sides gives
[email protected] = +\- sqrt(7)/ sqrt(16) = +\- sqrt(7)/4
But is [email protected] positive or negative? We are told that @ is in the second quadrant and cos(@) is negative in this quadrant, so our answer must be negative
[email protected] = - sqrt(7)/ 4
which is choice B
Thank you,
Mr. B
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

For miles... 0.333333 Miles per Mile
I believe 8.23 is greater because 8.2 can be 8.20 so that’s why my answer is 8.23
3x - 2 when X = 2
= 3(2) - 2
= 6 - 2
= 4
So, in conclusion, the answer to this question is 4.