Answer:
Increases 64 times
Step-by-step explanation:
The volume of the box can be calculated using formula
where
V = volume,
l = length,
w = width,
h = height
If the length was 0.3 inches, then the volume was
When the length became 1.2 inches, then all dimensions became times greater, then the volume was
The volume increases
times
Answer:
Step-by-step explanation:
The line integral with respect to arc length of the function f(x, y, z) = xy2 along the parametrized curve that is the line segment from (1, 1, 1) to (2, 2, 2) followed by the line segment from (2, 2, 2) to (−9, 6, 5) equals the sum of the line integral of f along each path separately.
Let
be the two paths.
Recall that if we parametrize a path C as with the parameter t varying on some interval [a,b], then the line integral with respect to arc length of a function f is
Given any two points P, Q we can parametrize the line segment from P to Q as
r(t) = tQ + (1-t)P with 0≤ t≤ 1
The parametrization of the line segment from (1,1,1) to (2,2,2) is
r(t) = t(2,2,2) + (1-t)(1,1,1) = (1+t, 1+t, 1+t)
r'(t) = (1,1,1)
and
The parametrization of the line segment from (2,2,2) to
(-9,6,5) is
r(t) = t(-9,6,5) + (1-t)(2,2,2) = (2-11t, 2+4t, 2+3t)
r'(t) = (-11,4,3)
and
Hence