If u multiply the first equation by -4, u get -2x - y = -20
and when u add the 2 equations..
-2x - y = -20
2x + 3/8y = 5
-----------------
0 - 5/8y = -15.....u notice that the x terms r eliminated.
Answer:
1.a. not a function
1.b. function
1.c. function
1.d. not a function
1.e. not a function
1.f. not a function
Step-by-step explanation:
1.a.
The arrows from x to y show that the ordered pairs of this function are:
(1, 4), (1, 5), (0, 7), (1, 6), (2, 5).
Since the x-coordinate 1 is used in two different ordered pairs, (1, 4) and (1, 5), this relation is not a function.
1.b.
Each x-coordinate is used only once, so this relation is a function.
1.c.
All x-coordinates are different. Function.
1.d.
Two ordered pairs have the same x-coordinate. Not a function.
1.e.
Two ordered pairs have the same x-coordinate. Not a function.
1.f.
Two ordered pairs have the same x-coordinate. It does not pass the vertical line test. Not a function.
Denote the circle of radius 
by 
. is simple and closed, so by Green's theorem the line integral reduces to a double integral over the interior of (call it 
):
is a circle of radius , so we can write the double integral in polar coordinates as
a. For 
, we have
b. Let 
denote the integral with unknown parameter ,
By the fundamental theorem of calculus,
has critical points when
If 
, then line integral is 0, so we ignore that critical point. For the other two, we would find 
.
