Answer:
A) 
Step-by-step explanation:
To isolate
, we need to divide both sides by
. Therefore, the answer is
.
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

Subtract 10 from both sides
10 + x < 5
10 - 10 + x < 5 - 10
x < -5
So the answer is x < -5, or x is less than -5. Any number less than -5 would be the solution. Hope this helps!
V=(hπr^2)/3, we are given that h=2.5in, r=5, and π≈3.14 so:
V=(2.5*25*3.14)/3
V≈196.25/3 in^3
V≈65.42 in^3 (to nearest hundredth of a cubic inch)