The Jacobian for this transformation is

with determinant
, hence the area element becomes

Then the integral becomes

where
is the unit circle,

so that

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

Then

<span>Simplifying
4(y + -3) = 6(y + 2)
Reorder the terms:
4(-3 + y) = 6(y + 2)
(-3 * 4 + y * 4) = 6(y + 2)
(-12 + 4y) = 6(y + 2)
Reorder the terms:
-12 + 4y = 6(2 + y)
-12 + 4y = (2 * 6 + y * 6)
-12 + 4y = (12 + 6y)
Solving
-12 + 4y = 12 + 6y
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-6y' to each side of the equation.
-12 + 4y + -6y = 12 + 6y + -6y
Combine like terms: 4y + -6y = -2y
-12 + -2y = 12 + 6y + -6y
Combine like terms: 6y + -6y = 0
-12 + -2y = 12 + 0
-12 + -2y = 12
Add '12' to each side of the equation.
-12 + 12 + -2y = 12 + 12
Combine like terms: -12 + 12 = 0
0 + -2y = 12 + 12
-2y = 12 + 12
Combine like terms: 12 + 12 = 24
-2y = 24
Divide each side by '-2'.
y = -12
Simplifying
y = -12</span>
Y=1 because no matter the x value y will be 1
Answer:
Step-by-step explanation:
What can be used as a statement in a two column proof?
A two-column proof consists of a list of statements, and the reasons why those statements are true. The statements are in the left column and the reasons are in the right column. The statements consists of steps toward solving the problem.
Answer:
58 square feet
Step-by-step explanation:
The room is already broken down into two smaller rectangles.
The smaller of the two measures 4 ft by 2 ft.
, so substitute 4 for
and 2 for
.
(smaller rectangle)
, or
.
(smaller rectangle) 
The larger measures 10 ft by 5 ft, so using the same method, multiply
times
.
(larger rectangle)
, or
.
(larger rectangle) 
Add the two rectangles' areas together to find the total area of the room.
8 + 50 = 58