Answer:
Something like this
Step-by-step explanation:
distance √(-1 - 5)² + (-6 - -4)² = √36 + 4 = √40 = 6.32
slope = 2/-6 = -1/3
distance (-1,-4) to (0, -4.63)
√(-1 - 0)² + (-4 - -4.63...)² = √1.4 = 1.18
6.32 - 1.18 = 5.14
1.18 : 5.14
Answer: x = 39 because 39 + 102 = 141 and 180 - 141 = 39
Rewrite the equations of the given boundary lines:
<em>y</em> = -<em>x</em> + 1 ==> <em>x</em> + <em>y</em> = 1
<em>y</em> = -<em>x</em> + 4 ==> <em>x</em> + <em>y</em> = 4
<em>y</em> = 2<em>x</em> + 2 ==> -2<em>x</em> + <em>y</em> = 2
<em>y</em> = 2<em>x</em> + 5 ==> -2<em>x</em> + <em>y</em> = 5
This tells us the parallelogram in the <em>x</em>-<em>y</em> plane corresponds to the rectangle in the <em>u</em>-<em>v</em> plane with 1 ≤ <em>u</em> ≤ 4 and 2 ≤ <em>v</em> ≤ 5.
Compute the Jacobian determinant for this change of coordinates:

Rewrite the integrand:

The integral is then

Answer: 36
Step-by-step: 6 2/3 + 5 1/3 = 12
12 x 3 = 36