[T] The transformation T k , 1 , 1 : R 3 → R 3 , T k , 1 , 1 ( u , v , w ) = ( x , y , z ) of the form x = ku, y = v, z = w. where k ≠ 1 is a positive real number is called a stretch if k > 1 and a compression if 0 < k < 1 in the x-direclion. Use a CAS to evaluate the integral ∭ s e − ( 4 x 2 + 9 y 2 + 25 z 2 ) d x d y d z on the solid S = { ( s , y , z ) | 4 x 2 + 9 y 2 + 25 z 2 ≤ 1 } by considering the compression T 2 , 3 , 5 ( u , v , w ) = ( x , y , z ) defined by x = u 2 , y = v 3 and z = w 5 Round your answer to four decimal places.
[T] The transformation T k , 1 , 1 : R 3 → R 3 , T k , 1 , 1 ( u , v , w ) = ( x , y , z ) of the form x = ku, y = v, z = w. where k ≠ 1 is a positive real number is called a stretch if k > 1 and a compression if 0 < k < 1 in the x-direclion. Use a CAS to evaluate the integral ∭ s e − ( 4 x 2 + 9 y 2 + 25 z 2 ) d x d y d z on the solid S = { ( s , y , z ) | 4 x 2 + 9 y 2 + 25 z 2 ≤ 1 } by considering the compression T 2 , 3 , 5 ( u , v , w ) = ( x , y , z ) defined by x = u 2 , y = v 3 and z = w 5 Round your answer to four decimal places.
[T] The transformation
T
k
,
1
,
1
:
R
3
→
R
3
,
T
k
,
1
,
1
(
u
,
v
,
w
)
=
(
x
,
y
,
z
)
of the form x = ku, y = v, z = w. where
k
≠
1
is a positive real number is called a stretch if k >1 and a compression if 0 < k < 1 in the x-direclion. Use a CAS to evaluate the integral
∭
s
e
−
(
4
x
2
+
9
y
2
+
25
z
2
)
d
x
d
y
d
z
on the solid
S
=
{
(
s
,
y
,
z
)
|
4
x
2
+
9
y
2
+
25
z
2
≤
1
}
by considering the compression
T
2
,
3
,
5
(
u
,
v
,
w
)
=
(
x
,
y
,
z
)
defined by
x
=
u
2
,
y
=
v
3
and
z
=
w
5
Round your answer to four decimal places.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Apply the transformation T (x, y) = (0.8x − 0.6y, 0.6x + 0.8y) to the scalene triangle whose vertices are (0, 0), (5, 0), and (0, 10). What kind of isometry does T seem to be? Be as specific as you can, and provide numerical evidence for your conclusion.
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Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY