9514 1404 393
Answer:
(x, y, z) = (-1, 0, -3)
Step-by-step explanation:
We notice that the coefficients of z are such that elimination of the z term from the equations is made easy.
Adding equations 1 and 2:
(2x -3y -2z) +(x +3y +2z) = (4) +(-7)
3x = -3
x = -1
Adding equations 2 and 3:
(x +3y +2z) +(-4x -4y -2z) = (-7) +(10)
-3x -y = 3
Substituting for x, we get ...
(-3)(-1) -y = 3
0 = y . . . . . . . . . . . add y-3 to both sides
Then z can be found from any equation. Substituting for x and y in the second equation gives ...
-1 +2z = -7
2z = -6 . . . . . add 1
z = -3 . . . . . .divide by 2
The solution is (x, y, z) = (-1, 0, -3).
Answer:
-
Step-by-step explanation:
You should multiply 20 time 8 to get your answer
Using the shell method, the volume is given exactly by the definite integral,

Splitting up the interval [0, 1] into 5 subintervals gives the partition,
[0, 1/5], [1/5, 2/5], [2/5, 3/5], [3/5, 4/5], [4/5, 5]
with left and right endpoints, respectively, for the
-th subinterval


where
. The midpoint of each subinterval is

Then the Riemann sum approximating the integral above is



(compare to the actual value of the integral of about 14.45)