The inside of a container is an ellipsoid (as shown) 2 2 (²) ³² + ( )² + (²) ²³ = 1 ree holes are made (one at the south pole, and one at the equator, for leaking, one Z at the north pole for air intake) to enable the same draining constant k for the leaking holes. The draining process follows the IVP A(h)dh = -k√h dt
The inside of a container is an ellipsoid (as shown) 2 2 (²) ³² + ( )² + (²) ²³ = 1 ree holes are made (one at the south pole, and one at the equator, for leaking, one Z at the north pole for air intake) to enable the same draining constant k for the leaking holes. The draining process follows the IVP A(h)dh = -k√h dt
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.2: Ellipses
Problem 32E
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![X
Three holes are made (one at the south pole, and one at the equator, for leaking, one
at the north pole for air intake) to enable the same
draining constant k for the leaking holes. The
draining process follows the IVP
A(h)dh
-k√h
Z
The inside of a container is an ellipsoid (as shown)
2
2
(²) ² + (²)² + (²³)² =
b
1
h
=
dt
h(t = 0) = ho
y
introduced by Torricelli in 1643. In the DE, A (h) is
the cross-section area at the height (from the
leaking point) h.
Derive the formula for the time needed to empty a
fully filled tank.
Note: Both leaking holes are at work while draining the upper half tank and, naturally, only one hole
leaks while draining the lower half.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F093e7116-3e01-49ad-9157-7a22a5caeb16%2Ffd25eeb4-8d28-4697-9f83-f50cf83045d0%2Fplzrv6d_processed.png&w=3840&q=75)
Transcribed Image Text:X
Three holes are made (one at the south pole, and one at the equator, for leaking, one
at the north pole for air intake) to enable the same
draining constant k for the leaking holes. The
draining process follows the IVP
A(h)dh
-k√h
Z
The inside of a container is an ellipsoid (as shown)
2
2
(²) ² + (²)² + (²³)² =
b
1
h
=
dt
h(t = 0) = ho
y
introduced by Torricelli in 1643. In the DE, A (h) is
the cross-section area at the height (from the
leaking point) h.
Derive the formula for the time needed to empty a
fully filled tank.
Note: Both leaking holes are at work while draining the upper half tank and, naturally, only one hole
leaks while draining the lower half.
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