Explanation Procedure used: Solve the differential equation d h d t = − c A h A w 2 g h by the variable separable method. Find the value of constant c 1 using the given conditions. Find the values of A h , A w . Then finally the time that hole will take can be found. Calculation: Integrate the differential equation d h d t = − c A h A w 2 g h . ∫ d h h = ∫ − c A h A w 2 g d t 2 h = − c A h A w 2 g t + c 1 h = 1 2 ( − c A h A w 2 g t + c 1 ) h = 1 4 ( − c A h A w 2 g t + c 1 ) 2 ...... ( 1 ) Substitute 0 for h and 0 for t in the above equation. 0 = 1 4 ( − c A h A w 2 g × 0 + c 1 ) 2 c 1 = 0 Substitute the value of c 1 in the equation (1)

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 2.8, Problem 14E

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The time that the hole will take to empty the tank if the model for the problem is given by, dhdt=−cAhAw2gh where c=0.6, h=10 ft, the radius of the tank is 2 ft and the radius of the hole is 0.5 inch.

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Chapter 2.8, Problem 13E

Chapter 2.8, Problem 15E

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ם Hwk 25 Hwk 25 - (MA 244-03) (SP25) || X Answered: [) Hwk 25 Hwk 28 - (X + https://www.webassign.net/web/Student/Assignment-Responses/last?dep=36606604 3. [1.14/4 Points] DETAILS MY NOTES LARLINALG8 6.4.013. Let B = {(1, 3), (-2, -2)} and B' = {(−12, 0), (-4, 4)} be bases for R², and let 42 - [13] A = 30 be the matrix for T: R² R² relative to B. (a) Find the transition matrix P from B' to B. 6 4 P = 9 4 (b) Use the matrices P and A to find [v] B and [T(V)] B, where [v]B[31]. 26 [V] B = -> 65 234 [T(V)]B= -> 274 (c) Find P-1 and A' (the matrix for T relative to B'). -1/3 1/3 - p-1 = -> 3/4 -1/2 ↓ ↑ -1 -1.3 A' = 12 8 ↓ ↑ (d) Find [T(v)] B' two ways. 4.33 [T(v)]BP-1[T(v)]B = 52 4.33 [T(v)]B' A'[V]B' = 52 目 67% PREVIOUS ANSWERS ill ASK YOUR TEACHER PRACTICE ANOTHER

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The time that the hole will take to empty the tank if the model for the problem is given by, d h d t = − c A h A w 2 g h where c = 0.6 , h = 10 ft , the radius of the tank is 2 ft and the radius of the hole is 0.5 inch .

Solution Summary: The author calculates the time that the hole will take to empty the tank by the variable separable method.

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The time that the hole will take to empty the tank if the model for the problem is given by, dhdt=−cAhAw2gh where c=0.6, h=10 ft, the radius of the tank is 2 ft and the radius of the hole is 0.5 inch.

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Chapter 2 Solutions