K:40) Two tanks, A and B, each contain 10 L of salt water. Initially, 31 g of salt are found in A, and 27 g of salt are found in B.At some time, a salt water solution containing 3 g per L is pumped into A at a rate of 4 L per minute, and the well stirred solution in B is pumped out at thesame rate. At exactly the same time the well stirred mixture in A is pumped into B at a rate of 6 L per minute, and the well stirred mixture in B is pumped into Aat a rate of 2 L per minute.Let u = u(t) be the amount of salt (in g) in A at time t (in minutes), and let v = v(t) be the amount of salt (in g) in B at time t (in minutes). ThendudtAA (be exact and use u, v rather than u(t), v(t))dvdtAA (be exact and use u, v rather than u(t), v(t))withu(0) = 31, and v(0) = 27.Over time, the amount of salt in A tends to Numbergrams, and the amount of salt in B tends to Numbergrams.

Name: K:40) Two tanks, A and B, each contain 10 L of salt water. Initially,
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Description: K:40) Two tanks, A and B, each contain 10 L of salt water. Initially, 31 g of salt are found in A, and 27 g of salt are found in B.At some time, a salt water solution containing 3 g per L is pumped into A at a rate of 4 L per minute, and the well sti

Given: To explain the given statement as follows, V = 10L, u(0) = 31, v(0) = 27

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Two tanks, A and B, each contain 10 L of salt water. Initially, 31 g of salt are found in A, and 27 g of salt are found in B. At some time, a salt water solution containing 3 g per L is pumped into A at a rate of 4 L per minute, and the well stirred solution in B is pur same rate. At exactly the same time the well stirred mixture in A is pumped into B at a rate of 6 L per minute, and the well stirred mixture in at a rate of 2 L per minute. Let u = u(t) be the amount of salt (in g) in A at time t (in minutes), and let v = v(t) be the amount of salt (in g) in B at time t (in minutes du dt |(be exact and use u, v rather than u(t), v(t)) dv dt | (be exact and use u, v rather than u(t), v(t)) || ||

Two tanks, A and B, each contain 10 L of salt water. Initially, 31 g of salt are found in A, and 27 g of salt are found in B. At some time, a salt water solution containing 3 g per L is pumped into A at a rate of 4 L per minute, and the well stirred solution in B is pur same rate. At exactly the same time the well stirred mixture in A is pumped into B at a rate of 6 L per minute, and the well stirred mixture in at a rate of 2 L per minute. Let u = u(t) be the amount of salt (in g) in A at time t (in minutes), and let v = v(t) be the amount of salt (in g) in B at time t (in minutes du dt |(be exact and use u, v rather than u(t), v(t)) dv dt | (be exact and use u, v rather than u(t), v(t)) || ||

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Question

K:40)

Two tanks, A and B, each contain 10 L of salt water. Initially, 31 g of salt are found in A, and 27 g of salt are found in B.
At some time, a salt water solution containing 3 g per L is pumped into A at a rate of 4 L per minute, and the well stirred solution in B is pumped out at the
same rate. At exactly the same time the well stirred mixture in A is pumped into B at a rate of 6 L per minute, and the well stirred mixture in B is pumped into A
at a rate of 2 L per minute.
Let u = u(t) be the amount of salt (in g) in A at time t (in minutes), and let v = v(t) be the amount of salt (in g) in B at time t (in minutes). Then
du
dt
AA (be exact and use u, v rather than u(t), v(t))
dv
dt
AA (be exact and use u, v rather than u(t), v(t))
with
u(0) = 31, and v(0) = 27.
Over time, the amount of salt in A tends to Number
grams, and the amount of salt in B tends to Number
grams.

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