<span>Let r(x,y) = (x, y, 9 - x^2 - y^2)
So, dr/dx x dr/dy = (2x, 2y, 1)
So, integral(S) F * dS
= integral(x in [0,1], y in [0,1]) (xy, y(9 - x^2 - y^2), x(9 - x^2 - y^2)) * (2x, 2y, 1) dy dx
= integral(x in [0,1], y in [0,1]) (2x^2y + 18y^2 - 2x^2y^2 - 2y^4 + 9x - x^3 - xy^2) dy dx
= integral(x in [0,1]) (x^2 + 6 - 2x^2/3 - 2/5 + 9x - x^3 - x/3) dx
= integral(x in [0,1]) (28/5 + x^2/3 + 26x/3 - x^3) dx
= 28/5 + 40/9 - 1/4
= 1763/180 </span>
Answer: mountains
Explanation: The snow melts into the rivers
Equation 1) 3x + 2y - 5z = 3
Equation 2) 4x - 2y - 3z = -10
Equation 3) 5x - 2y - 2z = -11
Add equation 1 with equation 2.
Equation 4) 7x - 8z = 7
Then subtract equation 3 from equation 2.
Equation 5) -x -z = 1
Multiply all of equation 5 with 7.
5) -7x - 7z = 7
4) 7x - 8z = 7
Add equations together.
z = 14
Plug in 14 for z in equation 4.
7x - 8z = 7
7x - 8(14) = 7
7x - 112 = 7
7x = 119
x = 17
Plug in 17 for x in equation 1, and 14 for z.
1) 3x + 2y - 5z = 3
3(17) + 2y - 5(14) = 3
51 + 2y - 70 = 3
2y - 19 = 3
2y = 22
y = 11
So, x = 17, y = 11, and z = 14
~Hope I helped!~
6xy -3x -8y +4
3x (2y - 1 ) - 4 (2y -1)
(2y-1) (3x-4)
In order to answer the question, we simply substitute the value of p and q to the given expression and solve. We do as follows:
<span>P^2q^2+pq–q^3–p^3
</span>0.5^2(-0.5)^2+0.5(-0.5)–(-0.5)^3–(0.5)^3
-3/16 or -0.1875
Hope this answers the question. Have a nice day.